Geodesics, nonlinear normal modes of conservative vibratory systems and decomposition method

Zhang, Xinhua

doi:10.1016/j.jsv.2004.03.053

Cited by 7 publications

(10 citation statements)

References 16 publications

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“…More precisely, for those who use the definition of NNMs as a family of periodic orbits, numerous analytical methods have been proposed based on the use of the synchronicity of the motion [2,26,35], the extremum points of the energies [27] or the fact that those orbits are geodesics of selected subspaces [36]. A special class of methods derives from the idea of using a non-smooth temporal transformation (NSTT), proposed by Pilipchuk [37,38].…”

Section: Introductionmentioning

confidence: 99%

On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems

Blanc

Touzé

Mercier

et al. 2013

Mechanical Systems and Signal Processing

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Numerical computation of Nonlinear Normal Modes (NNMs) for conservative vibratory systems is addressed, with the aim of deriving accurate reduced-order models up to large amplitudes. A numerical method is developed, based on the center manifold approach for NNMs, which uses an interpretation of the equations as a transport problem, coupled to a periodicity condition for ensuring manifold's continuity. Systematic comparisons are drawn with other numerical methods, and especially with continuation of periodic orbits, taken as reference solutions. Three different mechanical systems, displaying peculiar characteristics allowing for a general view of the performance of the methods for vibratory systems, are selected. Numerical results show that invariant manifolds encounter folding points at large amplitude, generically (but not only) due to internal resonances. These folding points involve an intrinsic limitation to reduced-order models based on the center manifold and on the idea of a functional relationship between slave and master coordinates. Below that amplitude limit, numerical methods are able to produce reduced-order models allowing for a precise prediction of the backbone curve.

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Section: Introductionmentioning

confidence: 99%

On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems

Blanc

Touzé

Mercier

et al. 2013

Mechanical Systems and Signal Processing

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show abstract

“…Zhang (2005aZhang ( , 2005b assumed further that the NNMs pass through the equilibrium point in the configuration space. With this assumption, which is natural for systems with cubic nonlinearities, he also obtained the relation a 0.…”

Section: Application Of Adm To Nnms Of Spring-mass-pendulum Systemmentioning

confidence: 99%

“…In the context of nonlinear normal modes, Zhang (2005aZhang ( , 2005b recently applied the Adomian decomposition method to calculate nonlinear normal modes of conservative systems, though the applications are limited to discrete systems with only cubic geometric nonlinearities. Zhang approached the problem of constructing NNMs through the solution of the boundary value problems defining the existence of the NNMs in configuration space.…”

Section: Introductionmentioning

confidence: 99%

Adomian Decomposition Method Applied to Nonlinear Normal Modes of an Inertially Coupled Conservative System

Wang

Bajaj

2008

Journal of Vibration and Control

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In this work, the nonlinear normal modes (NNMs) of a conservative spring-mass-pendulum system with quadratic inertial nonlinearity are determined by applying the Adomian decomposition method. The technique is applied to the governing boundary value problem that determines the nonlinear normal modes of the two degrees-of-freedom system in configuration space. The NNMs of this system are non-similar and such that the modal curves do not pass through the origin in the configuration space. Both the low energy and the high energy cases are considered, and nonlinear normal modes near 1:2 and 1:1 internal resonances in the two linear modes of vibration of the system are developed. It is seen that the ADM polynomial approximation approach, where the model nonlinearities are approximated by polynomials in the neighborhood of center-center equilibrium, greatly reduces algebraic calculations, and improves the convergence speed and the accuracy of the results obtained. The method also captures the possible multiple nonlinear normal modes that exist near internal resonance conditions. The advantages and disadvantages in using the Adomian decomposition method to construct the nonlinear normal modes of the system are discussed.

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“…There are many researches on the modal characteristics of motorcycle frame at home and abroad, but less on the modal characteristics of ATV frame. [3][4][5] For ATV, frame is the bearing skeleton, which not only affects the vibration of the entire vehicle but also has a close connection with the safety and fatigue lifetime of the vehicle.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis and improvement of the frame for all-terrain vehicle

Feng

Xie

2018

Noise & Vibration Worldwide

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Frame is the bearing skeleton of the all-terrain vehicle, and its modal characteristics have a direct influence on the vibration and riding comfort of the entire vehicle. This article intends to investigate a certain domestic all-terrain vehicle whose frame is lengthened on the basis of benchmark vehicle, but this alteration leads to worse modal characteristics. Analytical method and experimental research are adopted for investigating the modal characteristics of this all-terrain vehicle frame. The response of the frame to different terrain roughness and various engine excitations is also discussed with the concluded results of modal analysis. It is found that these two factors are both likely to cause frame resonance. On the basis of the vibration pattern diagrams plotted, three improvement solutions are proposed, including adding transverse supporting beams, increasing the wall thickness of the longitudinal beam, and expanding the thickness of the rear vertical supporting beams. The modal characteristics of these three improvement schemes are also presented with analytical methods, confirming that the measures of adding transverse supporting beams and increasing the wall thickness of the longitudinal beam are feasible. Finally, the modal characteristics of the frame and the vibration of the entire vehicles are obviously improved.

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Geodesics, nonlinear normal modes of conservative vibratory systems and decomposition method

Cited by 7 publications

References 16 publications

On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems

On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems

Adomian Decomposition Method Applied to Nonlinear Normal Modes of an Inertially Coupled Conservative System

Modal analysis and improvement of the frame for all-terrain vehicle

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