Article

NONLINEAR EFFECTS IN XENON SPATIAL OSCILLATIONS

Authors:

Vrije Universiteit Amsterdam

Xenon feedback can produce spatial oscillations in large power reactors. ; Depending on the reactor size, materials inventory, power, and temperature ; coefficient, these oscillations may be either transient or persistent. This ; phenomenon is treated by a modal analysis in which nonlinear terms are retained. ; The nonlinear effects are shown to limit the amplitude of the oscillation and to ; cause the position of the flux peak to precess azimuthally; a formula for ; calculating the limiting amplitude of the oscillation is derived and compared ; with analog computer results. (auth)

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Structural Modeling and Modal Analysis of Hot-line Work Across the Line Construction

January 2018 · MATEC Web of Conferences

For the nonlinear structures such as traverse and mesh spanning structure, it is very difficult to analyze the traditional calculation method. The initial shape of the structure is determined by the finite element method and the accuracy of the model is verified. Based on this model, the natural frequencies and vibration modes of the structure are analyzed and determined, which can provide ... [Show full abstract] reference for transient dynamic analysis.

Article

DYNAMIC ANALYSIS OF A SMALL RECIPROCATING COMPRESSOR V. LEAKAGE EFFECT ON INDICATOR DIAGRAMS WHEN RE...

October 1978

In reciprocating compressors, a considerable amount of gas in the cylinder leaks through the gap between the piston and the cylinder wall. The leakage affects the indicator diagrams, especially under the transient condition which exists immediately after cutting the electric power off. In order to analyze the transient vibrations at the time compressors are stopped, it is necessary to have ... [Show full abstract] accurate indication diagrams of the transient condition. In this study, transient indication diagrams have been theoretically constructed, in the form of nonlinear differential equations. Further, it has been proved that the results obtained theoretically are in good agreement with experimental results. This method of evaluation of leakage through the gap between the piston and the cylinder wall is considered to be useful not only for analyzing vibration characteristics, but also for analyzing the performance characteristics of compressors.

Article

THE OCCURENCE AND CONTROL OF SPATIAL INSTABILITIES IN LARGE REACTORS

September 1959

The reasons for the possible occurrence of regional instabilities in large reactor cores are discussed. A review of the basic behavior and control concepts of a reactor is given, and the techniques of analysis available to describe the spatial effects are considered. These techniques are illustrated with a review of a modal analysis of radial and azimuthal core behavior, involving the use of ... [Show full abstract] a large analogue computer. The importance of a suitable reactor control system is emphasized. In general, analyses show that instabilities can occur, but they are of relatively long-term time behavior and can easily be controlled using existing techniques. (auth)

Article

Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlo...

March 2018 · Physica E Low-dimensional Systems and Nanostructures

We investigate the transverse free vibration behaviour of axially moving nanobeams based on the nonlocal strain gradient theory. Considering the geometrical nonlinearity, which takes the form of von Kármán strains, the coupled plane motion equations and related boundary conditions of a new size-dependent beam model of Euler-Bernoulli type are developed using the generalized Hamilton principle. ... [Show full abstract] Using the simply supported axially moving nanobeams as an example, the complex modal analysis method is adopted to solve the governing equation; then, the effect of the order of modal truncation on the natural frequencies is discussed. Subsequently, the roles of the nonlocal parameter, material characteristic parameter, axial speed, stiffness and axial support rigidity parameter on the free vibration are comprehensively addressed. The material characteristic parameter induces the stiffness hardening of nanobeams, while the nonlocal parameter induces stiffness softening. In addition, the roles of small-scale parameters on the flutter critical velocity and stability are explained.

Article

Torsional Vibration Modal Analysis Method of Long Blade Cascade Shafting Based on Concept of Effecti...

December 2017 · Reneng Dongli Gongcheng/Journal of Engineering for Thermal Energy and Power

In this paper, the concept of effective mass is introduced firstly, then the formula of effective inertia is deduced according to its physical meaning. At last, combined with finite element technology, a method for calculating the torsional vibration frequency of shafting by using the effective mode inertia of long cascade is summarized.The rule can be used to calculate the torsional vibration ... [Show full abstract] mode of the branch system to improve the branch system's accuracy. It can also be used to the finite element model of the simplified shafting system and consume less time and resources thanfull-size nonlinear finite element model under the premise of preserving precision. © 2017, Editorial Department of "Journal of Engineering for Thermal Energy and Power". All right reserved.

Chapter

Modal and Transient Dynamic Analysis

January 2018

King Yang

In this chapter, two typical dynamic analyses, namely the modal and transient dynamic analyses, are introduced. First, the element mass matrix, not needed in static analyses, is presented. This is followed by finding the natural frequencies and mode shapes in modal analysis and adding damping to mitigate the effect of resonance. Next, two direct integration methods are derived and examples are ... [Show full abstract] given to illustrate how these methods work in a step-by-step manner. Finally, brief rationales are given regarding the selection of implicit and explicit integration schemes for various types of FEA.

Article

Full-text available

Vibrational control of nonlinear time lag systems with bounded delay: Averaging theory, stabilizabil...

June 1994 · IEEE Transactions on Automatic Control

This paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay. Averaging theory for fast oscillating, differential delay equations is presented and then applied to vibrational control. Conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also ... [Show full abstract] discussed. Illustrative examples are given which show 1) the feasibility of the theory to important applications and 2) the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations

Article

Vibration signature and modal analysis of multi-stage gear transmission

December 1991 · Journal of the Franklin Institute

An analysis is presented for multi-stage multi-mesh gear transmission systems which predicts the overall system dynamics and transmissibility to the gear box or the enclosed structure. The modal synthesis approach of the analysis treats the uncoupled lateral/torsional modal characteristics of each stage or component independently. The vibration signature analysis evaluates the global dynamics ... [Show full abstract] coupling in the system. The method synthesizes the interaction of each modal component or stage with nonlinear gear mesh dynamics and modal support geometry characteristics. The analysis simulates transient and steady state vibration events due to torque variations, speed changes, rotor imbalances and gear box support motion excitations. A vibration signature analysis scheme examines the overall dynamic characteristics of the system, and the individual modal component responses. The gear box vibration analysis also examines the spectral characteristics of the support system.

Article

Full-text available

Nonlinear normal modes and their application in structural dynamics

March 2006 · Mathematical Problems in Engineering

Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the ... [Show full abstract] system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.

Article

Static and modal analysis of wind turbine towers.

January 1970

Mark. Johnston

Thesis (Ph. D.)--De Montfort University, 1999.

Article

Full-text available

Analysis of the global second-order effects on irregular reinforced concrete structures using the na...

April 2019 · Revista IBRACON de Estruturas e Materiais

The χT parameter, a simplified method recently presented, allows to estimate the global second-order effects on reinforced concrete frames using the natural period of vibration. This parameter was developed based on the fact that both natural period of vibration and global second-order effects depend essentially on the stiffness and mass matrices of the structure, being thus related. In this ... [Show full abstract] paper, numerical analyses are conducted on nine models with different patterns of irregularity in terms of geometry in plan and stiffness. The main purpose of these analyses is to evaluate the applicability of the χT parameter in asymmetric structures as well as that can present torsional modes as the fundamental mode of vibration. In addition, different hypotheses are tested in order to verify the influence of the different modes of vibration in the structural sensitivity to global second-order effects. Results of the simplified analyses were compared to the final bending moment values obtained through a nonlinear numerical analysis considering the P-Δ effect. It is observed that the parameter χT is a promising indicator for a simplified estimation of the global second-order effects for concrete frames, especially when higher modes of vibration are taken account in the analysis.

Article

A Nonlinear Vibration Absorber for Flexible Structures

January 1998 · Nonlinear Dynamics

An approach for implementing an active nonlinear vibration absorber for flexible structures is presented. The technique exploits the saturation phenomenon exhibited by multidegree-of-freedom systems with quadratic nonlinearities possessing two-to-one autoparametric resonances. The strategy consists of introducing second-order controllers and coupling each of them with the plant through a sensor ... [Show full abstract] and an actuator, where both the feedback and control signals are quadratic. Once the structure is forced near its resonances, the oscillatory response is suppressed through the saturation phenomenon. We present theoretical and experimental results of the application of the proposed vibration absorber. The structure consists of a cantilever beam, the feedback signal is generated by a strain gage, and the actuation is achieved through piezoceramic patches. The equations of motion are developed and analyzed through perturbation techniques and numerical simulation. Then, the strategy is tested by assembling the controllers in electronic components and suppressing the vibrations of the first and second modes of two beams.