Nonlinear normal modes of a two degrees-of-freedom piecewise linear system

被引：24

作者：

Moussi, E. H. ^{[1
,2
]}

Bellizzi, S. ^{[1
]}

Cochelin, B. ^{[1
]}

Nistor, I. ^{[2
]}

机构：

[1] Aix Marseille Univ, UPR 7051, CNRS, LMA,Cent Marseille, F-13402 Marseille 20, France

[2] UMR EDF CNRS CEA 2832, LaMSID, F-92141 Clamart, France

来源：

MECHANICAL SYSTEMS AND SIGNAL PROCESSING | 2015年 / 64-65卷

关键词：

Nonlinear normal mode; Piecewise linear system; Periodic orbit; Stability; Harmonic balance method; Asymptotic numerical method; HARMONIC-BALANCE FORMULATION; MECHANICAL SYSTEMS; PERIODIC-ORBITS; MODAL-ANALYSIS; HIGH-ORDER; CONTINUATION; COMPUTATION; OSCILLATOR; DYNAMICS;

D O I：

10.1016/j.ymssp.2015.03.017

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

A study of the Nonlinear Normal Modes (NNMs) of a two degrees of freedom mechanical system with a bilateral elastic stop for one of them is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. The Harmonic Balance Method (HBM) with a large number of harmonics, combined with the Asymptotic Numerical Method (ANM), is used to solve the regularized problem. The results are validated from periodic orbits obtained analytically in the time domain by direct integration of the non-regular problem. The first NNM shows an elaborate dynamics with the occurrence of multiple impacts per period, internal resonance and instabilities. On the other hand, the second NNM presents a more simple, almost linear, dynamics. The two NNMs converge asymptotically (for an infinite energy) toward two other Linear Normal Modes, corresponding to the system with a gap equal to zero. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：266 / 281

页数：16

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