International Journal of Structural Stability and Dynamics

The aircraft and space industry strives for significantly reduced development and operating costs. Reduction of structural weight at safe design is one possibility to reach this objective which is aimed by the following two running research projects: the EC project “COCOMAT” and the ESA study “Probabilistic Aspects of Buckling Knock Down Factors”. These projects develop improved concepts and tools for a fast and reliable simulation of the buckling and the postbuckling behavior of thin-walled structures up to collapse, respectively, which allow the exploitation of considerable reserves in primary fibre composite structures in aerospace applications. For the validation of the concepts and tools, a sound database of experiments is needed which is also performed within these projects. This paper focuses on the experimental activities within these projects performed at the buckling test facility of the Institute of Composite Structures and Adaptive Systems (DLR). It presents an overview about the DLR buckling, postbuckling and collapse tests which are already finished and gives an outlook to the results which are expected until the end of the running projects. This paper explains the working of the buckling test facility, the advanced measurement systems, which are running in parallel to the tests, and gives exemplarily two test results. The structures considered are unstiffened cylinders (ESA study) as well as panels, which are understood as sections of cylinders, stiffened by stringers (COCOMAT project). The unstiffened cylinders are more related to space applications (e.g. Ariane busters or parts of the international space station ISS) and the stiffened panels focus more on aircraft structures (e.g. fuselage). The load case considered for all investigations presented in this paper is axial compression under static loading although the test facility is also ready to apply torsion and internal pressure, as well as dynamic axial impact.

This paper presents the results of dynamic responses and fire resistance of concretefilled steel tubular (CFST) frame structures in fire conditions by using non-linear finite element method. Both strength and stability criteria are considered in the collapse analysis. The frame structures are constructed with circular CFST columns and steel beams of I-sections. In order to validate the finite element solutions, the numerical results are compared with those from a fire resistance test on CFST columns. The finite element model is then adopted to simulate the behaviour of frame structures in fire. The structural responses of the frames, including critical temperature and fire-resisting limit time, are obtained for the ISO-834 standard fire. Parametric studies are carried out to show their influence on the load capacity of the frame structures in fire. Suggestions and recommendations are presented for possible adoption in future construction and design of these structures.

This paper clarifies the terminologies used to describe the size effect on fatigue behavior of welded joints. It summarizes the existing research on size effect in the perspective of newly defined terminologies. It identifies knowledge gaps in designing tubular joints using the hot spot stress method, i. e. thin-walled tubular joints with wall thickness less than 4 mm and thick-walled tubular joints with wall thickness larger than 50 mm, or diameter to thickness ratio less than 24. It is the thin-walled tubular joints that are addressed in this paper. It is found that thin-walled tube-plate T-joints do not follow the conventional trend: the thinner the section is, the higher the fatigue life. It is also found that simple extrapolation of existing fatigue design curves may result in unsafe design of thin-walled tube-tube T-joints. The effect of chord stiffness on fatigue behavior of thin-walled tubular T-joints is also discussed.

The semi-periodic vortex-shedding phenomenon caused by flow separation at the windward corners of a rectangular cylinder would result in significant vortex-induced vibrations (VIVs). Based on the aeroelastic experiment of a rectangular cylinder with side ratio of 1.5:1, 2-dimensional (2D) and 2.5-dimensional (2.5D) numerical simulations of the VIV of a rectangular cylinder were comprehensively validated. The mechanism of VIV of the rectangular cylinder was in detail discussed in terms of vortex-induced forces, aeroelastic response, work analysis, aerodynamic damping ratio and flow visualization. The outcomes showed that the numerical results of aeroelastic displacement in the cross-wind direction and the vortex-shedding procedure around the rectangular cylinder were in general consistence with the experimental results by 2.5D numerical simulation. In both simulations, the phase difference between the lift and displacement response increased with the reduced wind speed and the vortex-induced resonance (VIR) disappeared at the phase difference of approximately 180 ∘ . The work done by lift force shows a close relationship with vibration amplitudes at different reduced wind speeds. In 2.5D simulations, the lift force of the rectangular cylinder under different wind speeds would be affected by the presence of small-scale vortices in the turbulence flow field. Similarly, the phase difference between lift force and displacement response was not a constant with the same upstream wind speed. Aerodynamic damping identified from the VIV was mainly dependent on the reduced wind speed and negative damping ratios were revealed at the lock-in regime, which also greatly influenced the probability density function (PDF) of wind-induced displacement.

Excessive vibrations seriously affected the comfort of residents living on the upper floors of a high-rise shear walled building in Beijing. The ambient vibration tests were conducted to measure the floor acceleration responses, which were found to contain almost periodic signals likely to be excited by vibration sources with frequency of about 1.5(Formula presented.)Hz. The transverse vibration levels of the building above the 8th floor are not acceptable as revealed by the one-third octave spectra and weighted acceleration levels according to the ‘Standard for Allowable Vibration of Building Engineering’ of China. The modal properties of the building are identified by a Bayesian FFT method, indicating that the resonance between the building and the vibration sources caused the excessive vibrations. For comparison, the vibration test of an adjacent building with the same structural design was also conducted, together with modal analysis by the finite element method. It is found that as the story level increases, different trends of amplification in floor root mean square (RMS) acceleration and mode shape component of the two buildings cause different vibration levels. After tests outside the residence community, the main vibration sources were identified to be the working machines in two stone processing factories a few hundred meters away from the building. The vibration tests with measurements in the building and near the vibration sources with different number of machines in the two factories were also conducted. The results show that the vibration levels of the building can be controlled below the acceptance value by reducing the number of machines.

This paper supports quick and accurate prediction of the flutter onset speed of an F-16 Block 40/50 configured with external stores in the transonic flight regime. Current flutter prediction methods are reviewed and hypothesized mechanisms for limit cycle oscillation (LCO) are summarized. New efforts to correlate transonic small disturbance (TSD) theory methods with flight tests are outlined. Vibration analysis and structural optimization of an F-16 finite element model were used to match ground vibration testing results. Frequency tuning was found to be critical for accurate flutter speed predictions. Sensitivity to nonlinear aerodynamic effects and store modeling was examined.

Steel tapered-I-columns are popular in modern buildings due to its material efficiency and the convenience in construction. For evaluating the flexural buckling strength of these columns, the current design methods with empirical and idealized assumptions are sometimes unreliable, especially for slender columns with significant tapering ratios. To accurately calculate the flexural buckling resistance, this paper proposes a numerical framework for tapered-I-sections. The direct analysis method (DM) with the non-prismatic high-order beam-column elements considering the factors, including the second-order effects, the geometric imperfections, and the residual stresses is developed. A new shape-function representing the most critical initial out-of-straightness curve of a tapered member is adopted. An advanced non-prismatic beam-column element incorporating this imperfection shape-function named the curved tapered-three-hinges (TTH) element is derived. With the availability of the internal degree-of-freedoms, the one-element-per-member (OEPM) modeling method is permitted. Sequentially, a series of parametric studies using the proposed numerical method are conducted for generating the buckling curves for the non-prismatic columns with various tapered-stiffness ratios. The sophisticated finite-element method is adopted to verify the proposed numerical framework. Based on the proposed numerical approach, the design method in ANSI/AISC-360-16 is modified for tapered-I-section columns.

The paper presents a study of the capacities of steel rack frames based on linear analysis (LA), geometric nonlinear analysis (GNA), and geometric and material nonlinear analysis (GMNIA). In the case of linear and geometric nonlinear analyses, the design is carried out to the Australian cold-formed steel structures AS/NZS4600. The study includes braced, unbraced, and semi-braced frames, and compact and noncompact cross sections. The paper shows axial force and bending moment paths for geometric and geometric and material nonlinear analyses, and explains the differences observed in the design capacities obtained using the different types of analysis based on these paths. The paper provides evidence to support the use of advanced GMNIA for the direct design of steel rack frames without the need for checking section or member capacities to a structural design standard.

Introduced herein is a new structural damping identification approach based on a two-dimensional (2D) amplitude and phase estimation (APES) method. The original APES method is suitable for application to an undamped and complex harmonic vibration signal. Hence, it has to be modified for application to real damped vibration signals such as the vibration test signals in engineering structures. This modified approach will be named as dr_APES. It can transform one-dimensional (1D) signals in time domain into their corresponding signals in the 2D domain of frequency and damping factor. By applying this dr_APES approach, the three-dimensional (3D) amplitude spectrum, with peaks corresponding to the vibration modes, can be obtained for any given vibration signals. By accurately locating the coordinates of the peaks, modal frequencies and damping factors can be identified. Owing to the high-resolution of the location of 2D ordinates of the spectral line and the value of spectrum, the accurate location of peaks can be estimated, and therefore, the modal frequencies and damping factor can be accurately determined. This is demonstrated by a numerical case study. Moreover, by applying the proposed approach to a real onsite dynamic test on two cables in a cable-stayed bridge, the inherent damping of the two cables was identified accurately, thereby verifying the ability of proposed damping identification approach in meeting the requirement of weak damping characteristics identification in flexible structures such as naked cables.

Calculations of nonlinear displacements and vibrations of inhomogeneous loaded shells with developable principal surface by means of different analytical methods are represented. It is shown that solutions to these methods are the expansions of exact solution in the Taylor series for an independent variable, and in the particular case — for the powers of a natural parameter. A method that provides a polynomial asymptotic approximation of the exact solution of the general form and its meromorphic continuation based on 1D and 2D Padé approximations is proposed. Calculations of nonlinear deformation and stability of elastic flexible circular cylindrical shell under uniform external pressures and of free oscillations of simply supported stringer shell demonstrate the efficiency and accuracy of the proposed method.

The present work uses a semi-analytic mathematical model to study the dynamic response of the partially liquid-filled rectangular tank equipped with a vertical rigid baffle at the bottom subjected to pitching excitation. The velocity potential consists of the rigid container velocity potential and the disturbance potential, which contains a Stokes–Joukowski potential. The liquid domain is divided into four simple sub-domains. The formal solution of the Stokes–Joukowski potential in each sub-domain is solved using the superposition principle and the separation of variables method. The dynamic response equation is established by using the free liquid surface equation. The ADINA solution is compared with the present method solution, which verifies the correctness of the proposed method. Finally, the effect of baffle parameters on liquid sloshing for a baffled tank subjected to harmonic and seismic pitching excitations is discussed in detail.

A vast number of papers are devoted to studying the complete integrability of equations of four-dimensional rigid-body motion. Although in studying low-dimensional equations of motion of quite concrete (two- and three-dimensional) rigid bodies in a nonconservative force field, the author arrived at the idea of generalizing the equations to the case of a four-dimensional rigid body in an analogous nonconservative force field. As a result of such a generalization, the author obtained the variety of cases of integrability in the problem of body motion in a resisting medium that fills the four-dimensional space in the presence of a certain tracing force that allows one to reduce the order of the general system of dynamical equations of motion in a methodical way.

In this paper, a new finite element for 2D non-prismatic (curved and tapered) elastic beams with narrow rectangular cross-section is proposed. The element is geometrically exact, hence capable of handling large displacements and finite rotations, and allows for cross-section arbitrary warping through the inclusion of additional degrees of freedom (DOFs). These additional DOFs make it possible to capture the non-standard shear stress distributions that are developed in tapered members. All expressions required to implement the proposed finite element are derived and written in a simple vector/matrix form. To assess the accuracy and demonstrate the capabilities of the proposed element, several numerical examples are presented. For comparison purposes, results obtained with refined meshes of standard 2D finite elements are also shown. It is concluded that the proposed element leads to very accurate results with a small computational cost.

In this study, a promising pattern recognition based approach is introduced for structural damage identification using the measured dynamic data. The frequency response function (FRF) is preferably employed as the input of the proposed algorithm since it contains the most information of structural dynamic characteristics. The 2D principal component analysis (2D-PCA) is used to reduce the large size of FRFs data. The output data generated by the 2D-PCA are used to extract the damage indexes for each of the damage scenarios. A dataset of all probable damage indexes is provided; of which 30% are selected to form the train dataset and to be compared with the unknown damage index for an unidentified state of the structure. The sum of absolute errors (SAE) are calculated between the unknown damage index and the selected indexes from the dataset; of which the minimum refers to the most similar damage condition to the unknown one. The artificial neural networks (ANNs) are used to form a smooth function of the SAEs and the imperialist competitive algorithm (ICA) is utilized to minimize this function in order to find the location and severity of the damages of the unknown state of the structure. To validate the proposed method, the damage identification of a truss bridge structure and a two-story frame structure is conducted by considering all the single damage cases as well as multi damage scenarios. In addition, the robustness of the proposed method to measurement noise up to 20% is thoroughly investigated.

A pattern recognition-based damage detection method using a brand-new damage index (DI) obtained from the frequency response function (FRF) data is proposed in this paper. One major issue of using the FRF data is the large size of input variables. The proposed method reduces the dimension of the initial FRF data and transforms it into new damage indices by applying a data reduction technique called the two-dimensional principal component analysis (2D-PCA). The proposed damage indices can be used as the unique patterns. After introducing the damage indices, a dataset of damage scenarios and related patterns is composed. Pattern recognition techniques such as the artificial neural networks and look-up-table (LUT) method are employed to find the most similar known DI to the unknown DI obtained for the damaged structure. As the result of this procedure, the actual damage location and severity can be determined. In this paper, the 2D-PCA and LUT method for damage detection is introduced for the first time. The damage identification of a truss bridge and a two-story frame structure is performed for verification of the proposed method, considering all single damage cases as well as many multiple damage scenarios. In addition, the robustness of the proposed algorithm to measurement noise was investigated by polluting the FRF data with 5%, 10%, 15% and 20% noises.

High and slender towers may experience excessive vibrations caused by both wind and seismic loads. To avoid excessive vibrations in towers, tuned mass dampers (TMDs) are often used as passive control devices due to their low cost. The TMDs can absorb part of the energy of vibration transmitted from the main structure. These devices need to be finely tuned in order to work as efficient dampers; otherwise, they can adversely amplify structural vibrations. This article presents the optimal parameters of a pendulum TMD (PTMD) to control the vibrations of slender towers subjected to an external random force. The tower is modelled as a single degree of freedom (SDOF) mass-spring system via an assumed-mode procedure with a pendulum attached. A genetic algorithm (GA) toolbox developed by the authors is used to find the optimal parameters of the PTMD, such as the support flexural stiffness/damping, the mass ratio and the pendulum length. The chosen fitness function searches for a minimization of the maximum frequency peaks. The results are compared with a sensibility map that contains the information of the maximum amplitude as a function of the pendulum length and the mass ratio between the pendulum and the tower. The optimal parameters can be expressed as a power law function of the supporting flexural stiffness. In addition, a parametric analysis and a time-history verification are performed for several combinations of mass ratio and pendulum length.

The deflection, bending moment, shear force and acceleration-time histories of a two-span beam subjected to moving sprung vehicles are presented. The vehicle model is a 2DOF system with a constant velocity. The two-span beam with a rough surface is used as structure model. The beam is defined in modal domain by natural frequencies, mode shapes and modal damping values. The rough surface is modeled by filtered white noise. The equations of motion for the coupled vehicle-structure system are formulated, for non-dimensionalized variables in the system equation. The first-order linear stochastic differential equations are solved, and the effects of the span passage rate and other important parameters are studied.

The aim of this paper is to present a flutter analysis of a 3D Box-Wing Aircraft (BWA) configuration. The box wing structure is considered as consisting of two wings (front and rear wings) connected with a winglet. Plunge and pitch motions are considered for each wing and the winglet is modeled by a longitudinal spring. In order to exert the effect of the wing-joint interactions (bending and torsion coupling), two ends of the spring are located on the gravity centers of the wings tip sections. Wagner unsteady model is used to simulate the aerodynamic force and moment on the wing. The governing equations are extracted via Hamilton’s variational principle. To transform the resulting partial integro-differential governing equations into a set of ordinary differential equations, the assumed modes method is utilized. In order to confirm the aerodynamic model, the flutter results of a clean wing are compared and validated with the previously published results. Also, for the validation, the 3D box wing aircraft configuration flutter results are compared with MSC NASTRAN software and good agreement is observed. The effects of design parameters such as the winglet tension stiffness, the wing sweep and dihedral angles, and the aircraft altitude on the flutter velocity and frequency are investigated. The results reveal that physical and geometrical properties of the front and rear wings and also the winglet design have a significant influence on BWA aeroelastic stability boundary.

The present study deals with structural sensitivity of dynamic response having uncertainties in design parameters subjected to random earthquake loading. Earthquake is modeled as stationary random process defined by Kanai–Tajimi power spectral density. The uncertain design parameters are modeled as homogeneous Gaussian process and discretized through 3D local averaging. Subsequently the Cholesky decomposition of respective co-variance matrix is used to simulate random values of design parameters. The Neumann expansion blended with Monte Carlo simulation (NE-MCS) is explored for computing response sensitivity in frequency domain. Application examples related to a building frame and a gravity dam are presented serving to validate the NE-MCS technique in terms of its accuracy and effectiveness compared to direct Monte Carlo simulation and perturbation method.

Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.

Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.

Thermoelastic damping (TED) can lead to energy loss in microscale resonators, which is an intrinsic mechanism. To minimize the energy loss, it is required to determine the TED of resonators. Laminated plate resonators are commonly used in practice. However, existing researches on TED of the laminated resonators use mainly the one-dimensional (1D) heat conduction model, as the 3D governing equation is complicated, which cannot show the influences of boundary conditions along the supporting edges. In this paper, the governing equation of thermoelastic problems with 3D heat conduction was established for the out-of-plane vibration of the laminated rectangular plate. The analytical expression of the TED was derived using its physical meaning, namely, the ratio of the energy dissipated to the total elastic strain energy stored per cycle of vibration. It was found that the size and shape of the plate affect crucially the TED. The values of TED for higher-order vibration modes were also evaluated. Most importantly, the influences of supporting conditions and heat conduction conditions along the four edges were studied, which is the first report for laminated plates. The present approach can provide guidance for the design of high-quality bilayered resonators.

Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

This paper presents three-dimensional (3D) infinite elements for the multi-layered elastodynamics problems. There are three types of elements, namely horizontal, vertical and corner elements. They have been developed using wave functions in function spaces that can simulate real wave problems properly. The elements are extended forms of the axisymmetric infinite elements developed previously. Since these elements can simulate multiple layers and multiple wave numbers, the response of a 3D general structural system considering soil-structure interaction effect can be determined effectively. Numerical analyses are carried out for a rigid massless disk and square footings on the surface of various layer conditions for verification purposes. The calculated results are compared with existing analytical and numerical data and they were found to be in good agreement.

The purpose of this paper is to develop a detailed 3D maglev vehicle and guideway model and investigate the dynamic response characteristics of the coupled system. For this, the maglev vehicle is modeled as one cabin and four bogies having eight electromagnetics, four sensors, and four secondary suspensions based on the Urban Transit Maglev (UTM) system in Korea. The 3D dynamic equilibrium equations of the cabin and bogies are derived by considering the actively controlled electromagnetic forces. Also, the equations of motion for the guideway are derived using the modal superposition method for vertical, lateral, and torsional modes. The resulting coupled equations of motion are then solved using a predictor–corrector iterative algorithm. Finally, through the numerical simulation of the developed system, the responses using the 3D maglev vehicle model are compared with those obtained by the corresponding 2D model. The effects of surface irregularity on the dynamic interaction behaviors are then evaluated for increasing vehicle speeds. Particularly, the 3D resonance conditions of the guideway girder and the maglev vehicle are presented considering the resonance conditions due to equidistant moving loads. In addition, some resonance phenomena are rigorously explored, including the lateral resonance by a series of vehicles running on a girder.

Spalling is a typical tensile fracture phenomenon due to insufficient tensile strength of concrete. Concrete structure might experience severe spall damage at the rear surface of the structure owing to reflected tensile stress wave induced by impulsive load. In recent years, metaconcrete consisting of engineered aggregates has attracted attentions as metaconcrete exhibits extraordinary wave-filtering characteristics. Metaconcrete can be used to attenuate stress wave generated by impulsive load and hence possibly mitigate the spall damage. In this study, engineered aggregate is designed via the software COMSOL to have the frequency bandgap coincide with the dominant frequency band of stress wave propagating in the normal concrete (NC) specimen to reduce the stress wave propagation and hence spall damage. The wave propagation behaviors in metaconcrete specimen with periodically distributed engineered aggregates have been investigated in a previous study. This study establishes 3D meso-scale model of metaconcrete including mortar, randomly distributed natural aggregates and engineered aggregates to simulate spall behaviors of metaconcrete via the software LS-DYNA. The responses of metaconcrete composed of engineered aggregates with single bandgap and multiple bandgaps are studied. The results show that stress wave can be more effectively attenuated by using engineered aggregates with multiple bandgaps. It is found that although engineered aggregates mitigate stress wave propagation, the soft coating of the engineered aggregates reduces the concrete material strength, therefore spall damage of metaconcrete specimen is not necessarily less severe than the normal concrete, but has different damage mode. In addition, the influences of loading intensity and duration on stress wave, as well as the spall behaviors of metaconcrete specimen are also studied.

A new simple approach is proposed to search for the optimal placement of dampers in nonsymmetrical three-dimensional (3D) structures. Dampers are placed uniformly and initially at each storey of two selected bays of the bare structures and the time-history seismic analysis is performed. The maximal inter-storey drift ratio is chosen as the performance index. Then the inter-storey drift ratio is checked for the locations where dampers were added. The damper in the location with the minimal inter-storey drift ratio is moved to the location having the maximal inter-storey drift ratio. This process is repeated until the prescribed stop criterion is met. Both linear and nonlinear viscous dampers are used in this study. The damping coefficient of added dampers for the initial damper placement is determined by setting the maximal inter-storey drift ratio of the whole structure equal to a certain value when a ground motion is applied. In the proposed relocation process, the maximal inter-storey drift ratio will be reduced significantly. Three examples, including two 10-storey and one 20-storey 3D nonsymmetrical structures, are used to demonstrate the efficiency and accuracy of the proposed approach. The results are compared with those obtained using the simplified sequential search algorithm (SSSA). It is found that the proposed approach requires fewer number of time-history analysis than that using the SSSA while their accuracy is comparable.

This paper studies the vibration of a nonlinear 3D-string fixed at both ends and supported by a nonlinear elastic foundation. Newton’s second law is adopted to derive the equations of motion for the string resting on an elastic foundation. Then, the method of multiple scales (MOMS) is employed for the analysis of the nonlinear system. It was found that 1:3 internal resonance exists in the first and fourth modes of the string when the wave speed in the transverse direction is (Formula presented.) and the elasticity coefficient of the foundation is (Formula presented.). Fixed point plots are used to obtain the frequency responses of the various modes and to identify internal resonance through observation of the amplitudes and mode shapes. To prevent internal resonance and reduce vibration, a tuned mass damper (TMD) is applied to the string. The effects of various TMD masses, locations, damper coefficients ((Formula presented.)), and spring constants ((Formula presented.)) on overall damping were analyzed. The 3D plots of the maximum amplitude (3D POMAs) and 3D maximum amplitude contour plots (3D MACPs) are generated for the various modes to illustrate the amplitudes of the string, while identifying the optimal TMD parameters for vibration reduction. The results were verified numerically. It was concluded that better damping effects can be achieved using a TMD mass ratio (Formula presented.) located near the middle of the string. Furthermore, for damper coefficient (Formula presented.), the use of spring constant (Formula presented.) can improve the overall damping.

This article presents the differential equation in the global coordinates governing the structural behavior of 3D curved beams existing in building structures and civil works. This differential equation presented is of the lower-triangular form, which allows us to obtain the transfer matrix, also of lower-triangular form and with unit diagonal, through simple integrals. The stiffness matrix is determined from the transfer matrix expression, only by reordering operations, without employing additional structural methods, energy theorems or other. This rearrangement can be more easily done under the global system, compared with the natural reference system, since the order of the matrices involved has been reduced. The examples presented show the process to apply this general procedure to derivation of the stiffness matrix of a member from its transfer expression, through reordering operations.

In this study, the effects of micro-structural parameters such as particle volume fraction, size and random distribution of Al 6061/SiC particulate metal-matrix composite (MMC) beams on free vibration response and the active vibration control are investigated. For this purpose, numerical particle-reinforced MMC (PRMMC) beam specimens were modeled with 3D finite elements, and the cubic-shaped reinforcing SiC particles were randomly distributed in Al 6061 metal matrix similar to an actual micro-structure. The particle size and especially volume fraction play an important role on the natural frequencies of the smart PRMMCs although they have no effect on the mode shapes. The random particle distribution has minor effect on the natural frequencies of the smart PRMMCs. With the increase of the feedback control gain, both the vibration amplitude and the suppression time are reduced reasonably. Increasing the particle volume fraction induces an important reduction in the damping time and the vibration amplitude for both the controlled and uncontrolled damped vibrations. Finally, increasing the particle size decreases the vibration suppression capacity and increases the vibration amplitude and time slightly. Random particle distribution had no obvious effect on the uncontrolled and controlled vibrations.

This paper studies the dynamic interaction between two or more adjacent foundations resting on the surface of a stratified soil. The precise integration scheme adopted ensures that the numerical results obtained are highly accurate. Only the interfaces between the foundations and the soil need to be discretized and there is no limit on the thickness or on the number of soil layers to be considered. Numerical examples are provided to verify the accuracy and computational stability of the proposed approach. A series of parametric studies have been carried out to clarify the effects of layer depth, soil damping, spacing between adjacent foundations, masses and moment inertias of supporting structures and the wave propagation velocity on the dynamic behavior of three-dimensional (3D) foundation–soil–foundation interaction (FSFI).

Using the ideas of variational differential quadrature (VDQ) technique and position transformation, an efficient numerical approach is developed herein in order to address the free vibration problem of compressible and nearly-incompressible solid bodies with arbitrary deformed shape within the framework of 3D hyperelasticity. The 3D hyperelasticity is first formulated by vector-matrix relations with the purpose of applying in coding process. An energy principle together with the Neo-Hookean strain energy function is also employed in the derivation of governing equations. The proposed numerical method is capable of addressing problems with irregular domains. Simple application, being free from the locking problem, and fast convergence rate are the key features of the approach. Hyperelastic rectangular/sector plates and cylindrical panel subjected to bending load are selected as test problems whose free vibrations are analyzed. The developed numerical method is found to be capable of yielding accurate solutions to the considered problems. Moreover, the effects of mode transition and geometrical properties are investigated in the numerical examples.

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of a hermetic capsule comprising a cylinder closed with hemi-ellipsoidal caps at both ends. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur, uθ, and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in θ and in time, and the Legendre polynomials in the r and z directions instead of ordinary ones. Potential (strain) and kinetic energies of the hermetic capsule are formulated, and the Ritz method is used to solve the eigenvalue problem, thereby yielding upper bound values of the frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Typical convergence studies are carried out for the first five frequencies. The frequencies from the present 3D method are in good agreement with those obtained from other 3D approach and 2D shell theories proposed by previous researchers.

Problems related to the three-dimensional (3D) dynamics of the deploying flexible arms subjected to base angular motions are studied with simulated tip payloads and actual deployment trajectories. To facilitate the solution, an equivalent dynamical system is developed by introducing the inertial reaction forces on the arm, while the equations of motion are derived in the non-Newtonian reference frame attached to the arm. The dynamic behavior of the arm is investigated both by the finite element and assumed Modes methods for the purpose of verification. This study reveals that base angular motions lead to considerable couplings between the two lateral displacements and axial motions. Meanwhile, the induced loadings on the flexible arm due to the base angular motions are obtained, which are useful for the design of more efficient arms. Furthermore, one may use the resulting arm–tip position envelop to predict the antenna positioning accuracy, which paves the way for possible control systems to limit undesirable motions.

This paper proposes a finite-element (FE) and perfectly matched layer (PML)modeling of three-dimensional (3D) scattering of transient elastic waves in a cracked infinite plate with rectangular cross-section. The FE predictions are validated against 3D semi-analytical literature results. The effects of PML parameters on a root-mean-square error estimate are measured against the reference FE predictions computed using extended meshes. The proposed model is shown, through the numerical examples, to offer huge saving in real run-time at a slight degradation in accuracy. Practical applications indicate its potential in modeling elastic-wave-based nondestructive evaluation of engineering structures.

This paper concentrates on axisymmetric free vibration of functionally graded (FG) sandwich annular plates obtained using a quasi-3D plate theory. Motion equations and corresponding boundary conditions are established via the mentioned plate theory which takes into consideration the non-uniform shear strains across the thickness and also stretching trough the thickness. Generalized differential quadrature method (GDQM) is applied to discrete the annular sandwich plate governing equations. The results of this study are applicable for optional thick plates since the adopted theory considers the shear and normal strains across the thickness direction. Outcoming results are verified on the basis of information accessible in the open literature. To investigate the influences of power law index of functionally graded materials (FGMs) and dimensions of the sandwich annular plate layers, parametric studies are presented. It was well demonstrated that the applied theory precisely predicts the natural frequencies of FG annular sandwich plates with arbitrary thickness.

Quasi-three-dimensional (3D) stability and free vibration analyses of bi-axially loaded, simply-supported, sandwich piezoelectric plates with an embedded either a functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) core or a multilayered fiber-reinforced composite (FRC) one are presented. Three different distributions of carbon nanotubes (CNTs) through the thickness of the CNTRC core, i.e. uniformly distributed and FG V-, rhombus- and X-type variations, are considered, and the effective material properties of the CNTRC core are estimated using the rule of mixtures. The Pagano method, which is conventionally used for the analysis of multilayered FRC plates, is modified to be feasible for the study of sandwich hybrid CNTRC and piezoelectric ones, in which Reissner mixed variational theorem, the successive approximation and transfer matrix methods, and the transformed real-valued solutions of the system equations are used. The modified Pagano solutions for the stability and free vibration of multilayered hybrid FRC and piezoelectric plates are in excellent agreement with the exact 3D ones available in the literature, and those for sandwich hybrid CNTRC and piezoelectric plates may be used as the benchmark solutions to assess the ones obtained by using various 2D theories and numerical models.

Steel moment frames supported on two different ground levels have been widely constructed in the mountainous high-seismicity regions of China. To investigate the seismic collapse behavior of such frames, 3D numerical analysis models were established in Perform-3D and verified to simulate the collapse process. Different structural configurations were considered, including the number of stories below upper ground and the number of spans supported on two different ground levels. Two limit states were defined according to the different structural parts that reach their limitations. Incremental dynamic analyses were performed in both the lateral and longitudinal directions. Seismic collapse fragility curves, collapse margin ratios, and collapse patterns corresponding to eight cases were exhibited. Seismic fragility curves corresponding to four performance levels were used to assess structural vulnerability. Analytical results indicated that two different collapse patterns would exist in the lateral and longitudinal directions. Therefore, two limit states should be considered in the analyses of such steel moment frames.

The experimental and analytical behavior of 400 kV S/C portal-type guyed towers under different loading conditions is presented. The portal-type tower essentially consists of two masts extending outward in the transverse direction from the beam level to the ground. In addition, two sets of guys connected at the ground level project outward along the longitudinal axes and converge in the transverse axes. The experimental behavior of the guyed tower is compared with the results of finite element analysis. The 400 kV portal-type guyed towers with III and IVI type insulator strings are analyzed using finite element software. Full scale tower test results are verified through comparison with the results of the finite element analysis. The initial prestress in the guys is allowed to vary from 5% to 15% in the finite element modeling. The effect of prestress variation of the guys on the tower behavior is also studied.

The current study is focused on the static and vibration analysis of a sigmoid smart functionally graded (SFG) plate resting on the two parameters elastic foundation exposed to electromechanical loading at different boundary conditions. The sigmoid law (S-Law) is used to evaluate the distribution of SFG properties along the thickness direction. The governing equation of the motion of the SFG plate is obtained using first-order shear deformation theory (FSDT) and Hamilton's principle. The derived governing equation is then solved employing the higher-order finite element method (HFEM) using 9-noded Lagrange quadrilateral elements with 54 degrees of freedom (DOFs) per element. Convergence and comparative tests were carried out for the effectiveness and accuracy of the present approach. Non-dimensional frequency increases negative electric loading (V) and reduces positive electric loading at a constant side to thickness ratio. The effect of the shear layer parameter on the stress and deflection of the SFG plate is more compared to the Winkler foundation. The obtained results are helpful for the accurate design of the SFG based structures under electromechanical loading.