Nonlinear vibrations and mode interactions for a continuous rod with microstructure

被引：12

作者：

Andrianov, Igor V. ^{[1
]}

Danishevskyy, Vladyslav V. ^{[2
]}

Markert, Bernd ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Inst Gen Mech, D-52062 Aachen, Germany

[2] Pydniprovska State Acad Civil Engn & Architecture, Dept Struct Mech & Strength Mat, UA-49600 Dnepropetrovsk, Ukraine

来源：

JOURNAL OF SOUND AND VIBRATION | 2015年 / 351卷

关键词：

SPATIALLY CONTINUOUS SYSTEMS; ELASTIC-WAVE SPECTROSCOPY; INTERNAL RESONANCES; COMPOSITE-MATERIALS; ASYMPTOTIC THEORY; BEAM EQUATION; BUCKLED BEAMS; PROPAGATION; HOMOGENIZATION; MEDIA;

D O I：

10.1016/j.jsv.2015.04.011

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

Natural longitudinal vibrations of a periodically heterogeneous rod embedded into a nonlinear elastic matrix are considered. The governing macroscopic dynamical equation was obtained by the higher order asymptotic homogenization method. An asymptotic solution is developed by the method of multiple time scales. The effects of internal resonances and modes coupling are predicted. The specific objective of the paper is to analyse how the presence of the microstructure influences on the processes of mode interactions. It is shown that depending on a scaling relation between the amplitude of the vibrations and the size of the unit cell different scenarios of the modes coupling can be realized. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：268 / 281

页数：14

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