Anh Tay Nguyen

Northwestern University | NU · Department of Mechanical Engineering

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the disp...

This paper developes the multi-parameter equivalent linearization (mpEL) investigating the replacement of the original nonlinear part A(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...

Long-term deep sequestration of CO2-rich brine in deep formations of ultramafic rock (e.g. Oman serpentinized harzburgite) will be feasible only if a network of hydraulic cracks could be produced and made to grow for years and decades. Fraccing of gas- or oil-bearing shales has a similar objective. The following points are planned to be made in the...

Storage of anthropogenic CO2 as permanent carbonate minerals has emerged as a promising method for control of carbon dioxide. One approach consists of injecting low-pH, CO2-rich water in ultramafic rock that serves as a buffering medium. Accordingly, the rock dissolution will increase the solution pH such that carbonate minerals can precipitate. Th...

Within the framework of linear elasticity, the M-integral is connected to energy changes due to a self-similar expansion of a configuration. In this contribution, we will calculate the M-integral by evaluating a path-independent contour integral and by calculating the virial of material tractions active at boundaries and interfaces for the simple c...

A preceding 2023 study argued that the resistance of a heterogeneous material to the displacement field curvature is the physically most realistic localization limiter for softening damage. The curvature was characterized by the second gradient of the displacement vector field, which includes the material rotation gradient, and was named the ‘sprai...

Classical ways of determination of influence lines for structural responses are often inefficient due to high computational cost, especially if properties of the structure are uncertain. The combination of Muller-Breslau principle and the finite element analysis can resolve this problem. In this study, formulations for new finite elements tailored...

Generation of a large network of hydraulic cracks is of key importance not only for the success of fracking of shale but also for the recent scheme of sequestration of CO2 in deep formations of basalt and peridotite, which are mafic and ultramafic rocks that combine chemically with CO2. In numerical simulation of the creation of a fracture network...

One way to mitigate global warming is to withdraw CO2 from the atmosphere and inject it into deep formations of porous basalt to form carbonate minerals that can bind large quantities of CO2. Such formations are found in many places in the world. The process is to some extent similar to frac. It requires hydraulic fracturing of the basalt to create...

Dynamic vibration absorber (DVA) integrated with a piezoelectric stack energy harvesting subjected to base excitation is introduced in this paper. The system of dynamic vibration absorber and piezoelectric stack energy harvesting system (DVA-PSEH) has two functions, the first is to reduce vibrations for the primary system, and the second is to conv...

The paper develops the dual equivalent linearization with one weighting coefficient to nonlinear deterministic dynamic systems. The problem of equivalent replacement of a nonlinear function by a linear function is briefly revised using the dual approach that involves two forward and backward replacements. Further selecting a weighting coefficient c...

This paper presents a dual approach to the conventional averaging (CA) in order to construct a weighted averaging. A one-parameter weighting function for the novel weighted local averaging (WLA) is presented and analyzed in detail. The advantage of the proposed WLA is demonstrated by its application to the Galerkin method, which leads to a so-calle...

In the paper, the procedure of the high order averaging method is applied to Van der pol system subject to white noise excitation, and the third order stationary joint probability density function of amplitude and phase is given. The accuracy of the approximate solution is confirmed by the Monte-Carlo method. The effects of the system parameters on...

In the paper, the potential of harvesting vibratory energy via a mono-stable Duffing energy harvester with base excitation in super-harmonic resonance is investigated. The averaging method is exploited to provide an approximate analytical solution for the system. The displacement and voltage responses are determined depending explicitly on the disp...

The effects of lattice-mismatched strain on the optical properties of type-I core/shell quantum dot nanostructures are investigated theoretically using the simple continuum elasticity and the effective mass quantum mechanics models. The misfit strains are calculated based on the spherically anisotropic linear elasticity solution for a misfitted inc...

The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler – Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin met...

This paper presents the dynamics analysis and control of the upper limb exoskeleton for supporting user movement using the force feedforward model. The device can sense the force feedback of the user’s hand, and can produce necessary forces through joints at wrist, elbow and shoulder. When the user exerts force at the handle, a 3-axis force sensor...

The paper presents a new approach to the conventional averaging in which the role of boundary values is considered in a more detailed way. It results in a new weighted local averaging operator (WLAO) taking into account the particular role of boundary values. A remarkable feature of WLAO is that this operator contains a parameter of boundary regula...

The smart structures with the harmonic nonlinear vibration are used widely to broaden the frequency range of vibrations energy harvesting. In the paper, the potential of harvesting vibratory energy via a mono-stable Duffing energy harvester subjected to sub-harmonic excitation is investigated. The averaging method is used to derive the approximate...

This paper reviews key ideas of the researches on the dual approach to the vibration analysis. Three types of dual techniques, namely, forward - return dual technique, global-local dual technique, weighted averaging dual technique for the problem of equivalent replacement are summarized. Different implements and realizations of dual techniques to n...

This paper introduces and discusses a weighted form of the dual mean-square error criterion by considering weighted contributions of forward and return replacements adjusted by a specific non-dimensional weight coefficient. The simplicity and accuracy of the proposed weighted dual equivalent linearization technique are checked on several random vib...

This paper aims to investigate the stationary probability density functions of the Duffing oscillator with time delay subjected to combined harmonic and white noise excitation by the method of stochastic averaging and equivalent linearization. By the transformation based on the fundamental matrix of the degenerate Duffing system, the paper shows th...

The purpose of this study is to extend the dual equivalent linearization to the problem of thermal analysis of small satellites in Low Earth Orbit (LEO) using two-node model. The satellite is modeled as a body with two iso-thermal nodes, namely, outer and inner ones. The outer node represents for the shell of the satellite whereas the inner node st...

In this paper, the Equivalent Linearization Method (ELM) with a weighted averaging, which is proposed by Anh (Anh, 2015), is applied to analyze some vibrating systems with nonlinearities. The strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the other strongly nonlinear oscillators and the cubic Duffing w...

Among approximate methods, the method of equivalent linearization proposed by N. Krylov and N. Bogoliubov and extended by Caughey has remained an effective tool for both deterministic and stochastic problems. The idea of the method is based on the replacement of a nonlinear oscillator by a linear one under the same excitation. The standard way of i...

In this paper, the nonlinear random vibration of a uniform beam clamped at both of its ends is investigated by the regulated stochastic linearization technique. A closed system of nonlinear algebraic equations for linearization coefficients is obtained using the frequency–response function matrix. Root mean-square response of maximum deflection of...

In this paper responses of beams subjected to random loading are analyzed by the dual approach of the equivalent linearization method. The external random loading is assumed to be a space-wise and time-wise white noise in which the exact solutions of the modal equations can be found. A system of nonlinear algebraic equations for linearization coeff...

An analytical approach is presented to investigate the optimal problem of non-traditional type of Dynamic vibration absorber (DVA) for damped primary structures subjected to ground motion. Different from the standard configuration, the non-traditional DVA contains a linear viscous damper connecting the absorber mass directly to the ground instead o...

A schema of slack-moored wave-energy converter using linear permanence magnet is developed. For suitable use in this device, a structure of coreless linear permanence magnet generator is designed. The advantage of this model is the absence of steel core in coils that mean no cogging force is induced. A numerical simulation for analyzing structure c...

In this paper, the method of equivalent linearization is extended to the thermal analysis of satellite using both conventional and dual criteria of linearization. These criteria are applied to a differential nonlinear equation of single-node model of the heat transfer of a small satellite in the Low Earth Orbit. A system of nonlinear algebraic equa...

Averaged values play major roles in the study of dynamic processes. The use of those values allows transforming varying processes to some constant characteristics that are much easier to be investigated. In order to extend the use of averaged values one may apply the dual approach which suggests a consideration of two different aspects of a problem...

The dynamic vibration absorber (DVA) has attracted attention since its invention. This paper deals with the optimization problems of the standard DVA and two other models of DVA called three-element DVA and non-traditional DVA for damped primary structures. Unlike the standard configuration, the three-element DVA contains two spring elements in whi...

A weighted dual mean square criterion for stochastic equivalent linearization method is considered in which the forward and backward replacements are weighted. The normalized weighting coefficient is suggested as a piecewise linear function of the squared correlation coefficient and is defined by the least square method based on the data of Lutes-S...

A new technique is proposed to investigate the response of Van der Pol-Duffing (V-D for short) oscillator to a combination of harmonic and random excitations in the primary resonant frequency region. The analytical approach is based on the stochastic averaging method and equivalent linearization method. The stochastic averaging is applied to the or...

The response of the Van der Pol oscillator subjected to combined harmonic and random excitations is investigated by a technique combining two excellent methods, namely the stochastic averaging method and the equivalent linearization method. The original equation is averaged by the stochastic averaging method at first. Then the resulting nonlinear a...

The problem of equivalent replacement plays a basic role in many fields of science and technology. In the classical approach the original object A is to be replaced by an equivalent object kB by using the mean square minimum criterion. When the difference between A and B is significant, the replacement leads to unaccepted errors. To reduce the erro...

The Voigt-type of dynamic vibration absorber is a classical model and has attracted considerable attention in many years because of its simple design, high reliability and useful applications in the fields of civil and mechanical engineering. Recently, a non-traditional type of dynamic vibration absorber was proposed. Unlike the traditional damped...

Design of tuned mass damper (TMD) for damped linear structures has attracted considerable attention in recent years. Some approximate expressions of optimal tuning ratio of a TMD attached to a damped linear structure have been proposed. In the paper, another closed-form expression for the optimum tuning ratio is presented for two models, excitation...

The standard type of dynamic vibration absorber (DVA) called the Voigt DVA is a classical model and has long been investigated. In the paper, we will consider an optimization problem of another model of DVA that is called three-element type DVA for damped primary structures. Unlike the standard absorber configuration, the three-element DVA contains...

The problem of equivalent replacement plays a basic role in many fields ofscience and technology. In the classical approach the original object A is to be replaced byan equivalent object kB using the mean square minimum criterion. When the differencebetween A and kB is significant the replacement leads to unaccepted errors. In orderto reduce the er...

Based on the dual conception, the paper suggests a consideration at global level to the local mean square error criterion of the stochastic equivalent linearization method. It results in new values of linearization coefficients that are obtained as global averaged values of all local linearization coefficients. The numerical analysis of some typica...

In this study, a version of the regulated stochastic linearization technique is proposed for the nonlinear random vibrations of Bernoulli–Euler nonlinear beams. For analysis, in order to balance the error of linearization, we utilize the regulated technique; namely, the appearing nonlinear terms are first replaced by higher-order nonlinear expressi...

In this paper, a dual criterion of stochastic linearization method is developed for multi-degree-of-freedom systems subjected to random excitation. A closed system is obtained for determining coefficient matrices of the linearized system. Two examples of two-degree-of-freedom systems subjected to random excitation are presented. The mean-square res...

The vibration absorber has been used in many applications since invented. In the case of vibration control by the tuned mass damper (TMD), the selection of optimum absorber parameters is extremely important. This paper presents a closed-form expression for the optimum tuning ratio of a TMD attached to a damped primary system. The result is obtained...

The Duffing oscillator under combined periodic and random excitations is investigated by a simple technique. The system response is separated into the deterministic and random parts governed by two coupled differential equations. The couple relation is expressed through varying on time coefficients which are approximately replaced by their averagin...

Averaged values play major roles in the study of dynamic processes. The use of those values allows transforming varying processes to some constant characteristics that are much easier to be investigated. In order to extend the use of averaged values one may apply the dual approach which suggests the consideration of two different aspects of a probl...

Random turbulent loading on engineering structures which immersed in the atmospheric turbulent flow is often represented as the multi-dimensional and/or multi-variate Gaussian random loading processes. Gust response prediction, however, usually burdens a lot of computational difficulties due to turbulent loading projection on the generalized struct...

Recent models of wind turbulence and turbulence-force relation as well still contain uncertainties. Further studies on them are needed to gain the better knowledge to refine the existing problems from analytical computations to wind tunnel's physical simulations in the wind engineering. The continuous and discrete wavelet transforms have been appli...

In a previous paper [1], the identification algorithm is presented for feedback active controlled systems. However, this method can only be applied to complete measured systems. The aim of this paper is to present a combination of the identification algorithm and the modal superposition method to control the incomplete measured systems. The system...

Linear quadratic regulator (LQR) is an effective method of feedback active control theory. However, the LQR control is not truly optimal because it is only a feedback algorithm, i.e. the external excitation term is ignored in the optimal equation. In a previous paper [1] , the identification algorithm is presented for feedback active controlled sys...

The paper presents an extended averaged equation approach to the investigation of nonlinear vibration problems. The proposed method is applied to some free/self excitedoscillators, nonlinear free and forced oscillations of a suspension system with two-degree-of-freedom. The results in analyzing the vibration systems with different nonlinearity show...

The averaging method is an useful tool for investigating both deterministic and stochastic quasilinear system. In the stochastic problems, however, the method has often been developed only for mechanical systems subjected to white noise excitations.In the paper this method is applied to high order stochastic differential equations. The nonlinear os...

The design of active TMD for multi-degree-of-freedom systems subjected to second order coloured noise excitation is considered using the linear quadratic optimal theory. A detailed numerical study is carried out for a 2-DOF system. It is shown that the effectiveness of active TMD is better than the one of passive TMD.

In this short communication the main ideas of the method of equivalent linearization and dual conception are further extended to suggest a new technique for solving nonlinear differential equations. This technique allows improving the accuracy when the nonlinearity is strong and getting nonlinear features of responses. For illustration the Duffing...

In the study an extension of the Bubnov-Galerkin method in terms of the equivalent linearization method is presented. It is combined with sequential linearization and nonlinear procedure to yield a new method for solving nonlinear equations which can improve the accuracy when the nonlinearity is strong. For illustration the Duffing oscillator is co...

A dual criterion of equivalent linearization method is suggested. The mean-square responses of Duffing, Van der Pol and Lutes-Sarkani oscillators subjected to random excitation are considered. The obtained results are compared with the numerical calculations of original systems and approximate solutions obtained by three different methods including...

The article proposes a new method of mathematical modeling evolutional systems interacting with medium. A cutting process or tribo-space formed in the contact area of two conjugate mechanical subsystems is considered as medium. The features of the medium depend not only on state coordinates of systems but also on trajectories. It is obtained that t...

There are two types of dynamic vibration absorbers (DVAs) for vibration reduction of a pendulum structure. The first one moving in the tangential direction of the pendulum's orbit can reduce all kinds of vibrations but the effectiveness is quite poor when the DVA locates near the centre of oscillation. Conversely, the second one moving in the norma...

In this paper, the vibration reduction of a pendulum structure with dynamic vibration absorber (DVA) using Coriolis force is investigated. When the pendulum structure is subjected to a single harmonic excitation, the effective damping of Coriolis force is used with the second-order approximations to obtain the closed forms of optimal parameters of...

The paper provides a new view on the averaging procedure and equivalent linearization in the study of nonlinear mechanics. It is shown that the duality of those techniques can be used to obtain better approximate solutions or to separate the original nonlinear systems subjected to periodic and random excitations into deterministic and stochastic on...

In this paper, the vibration reduction for a stable inverted pendulum with passive mass–spring-pendulum-type dynamic vibration absorber (DVA) is investigated. Results obtained contain the conventional pendulum systems as a special case. Equivalent mass ratio established shows that the DVA on an inverted pendulum is more effective than the DVA on a...

The paper presents an extended averaged equation approach to the investigation of nonlinear vibration problems. The proposed method is applied to a nonlinear suspension system with two degrees of freedom. The results in analyzing the oscillations with arbitrary values of nonlinearity show the efficiency of the method.

In a previous paper [1], the identification algorithm is presented for feedback active controlled systems. However, this method can only be applied to complete measured systems. The aim of this paper is to present a combination of the identification algorithm and the modal superposition method to control the incomplete measured systems. The system...

The paper presents an extended averaged equation approach to the investigation of nonlinear vibration problems. The proposed method is applied to some free and self-excited oscillators, the Duffing's forced oscillators including main resonance, subharmonic resonance and super harmonic resonance. The results in analyzing the vibration systems with a...

Among the fundamental concepts for structure control, passive control systems have a significant role since they do not require additional energies produced by actuator. The basic of passive control is to incorporate a secondary system into the primary structure in order to transfer a part of the vibration energy of the primary system into the seco...

Active control is one of the promising aspects in recent years that use the control counterforces produced by actuators to balance or reduce the energy of the environmental loading. There are some basic problems in the active control such as control law, magnitude, and location of the control counterforces. This chapter presents a local feedback-fe...

The paper present the so-called "an extended averaged equation approach" to the investigation of nonlinear vibration problems. The numerical results in analysing the vibration systems with weak, middle and strong non-linearity show the advantages of the method.

In this paper, the problem of controlling a bar supporting, at one end a pointer and hinged, at the other end, to a structural system vibrating under any extern excitation is investigated. The problem is to maintain the pointer toward the target with a prescribed tolerance. Emphasis is put on the uncertainty, which characterizes the problem and a s...

The aim of the paper is to present a control law for feedback active controlled structures in which a control algorithm is proposed to identify the external excitation with a time delay. The time duration in which the external excitation acts on the structure is devised into subintervals. In each subinterval the external excitation is identified an...

The purpose of the paper is to present a closure technique based on the representation of the non-linear system response process to a random excitation by a polynomial function of Gaussian process. It is shown that for the unimodal and bimodal situations of the Duffing oscillator, the proposed technique can give good approximate response moments as...

A solution technique based on the representation of the response of the non-linear system by a polynomial of the response of the linearized system is presented. The relation between the original non-linear system and the linearized system is introduced by considering the so-called extended moment equations and their closed set is to be solved to de...

A solution technique based on the representation of the response of the non-linear system by a polynomial in the response of the linearized system is presented. Extended moment equations are developed and their closed set is to be solved to determine unknowns. For the Duffing oscillator subject to white noise excitation, the technique gives good ap...

Since the effect of some nonlinear terms is lost during the first order averaging procedure, the higher order stochastic averaging method is developed to predict approximately the response of linear and lightly nonlinear systems subject to weakly external excitation of second order colored noise random processes. Application to Duffing oscillator i...

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process.

In the paper the higher order stochastic averaging method is developed to a class of colored noise excitations when the corresponding forming filter has only finite negative eigenvalues. The second approximate probability density function to the Duffing system subject to the exponentially correlated process is obtained. Numerical application is car...

Aerodynamic response prediction of structures due to the turbulent-induced forces usually burdens a lot of computational difficulties of which the turbulent loading projection on the structural modes. The stochastic decomposition must be required to decouple the multi-variant turbulent loading process into the uncoupled turbulent loading modes whic...