On the design of external excitations in order to make nonlinear oscillators respond as free oscillators of the same or different type

被引：12

作者：

Rakaric, Zvonko ^{[1
]}

Kovacic, Ivana ^{[1
]}

Cartmell, Matthew ^{[2
]}

机构：

[1] Univ Novi Sad, Ctr Excellence Vibroacoust Syst & Signal Proc, Fac Tech Sci, Novi Sad 21000, Serbia

[2] Univ Strathclyde, Dept Mech & Aerosp Engn, Glasgow G1 1XJ, Lanark, Scotland

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2017年 / 94卷

关键词：

Nonlinear oscillator; Exact solution; Jacobi elliptic function; External excitation;

D O I：

10.1016/j.ijnonlinmec.2016.06.012

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

This study deals with nonlinear oscillators whose restoring force has a polynomial nonlinearity of the cubic or quadratic type. Conservative unforced oscillators with such a restoring force have closed-form exact solutions in terms of Jacobi elliptic functions. This fact can be used to design the form of the external elliptic-type excitation so that the resulting forced oscillators also have closed-form exact steady-state solutions in terms of these functions. It is shown how one can use the amplitude of such excitations to change the way in which oscillators behave, making them respond as free oscillators of the same or different type. Thus, in cubic oscillators, a supercritical or subcritical pitchfork bifurcation can appear, whilst in quadratic oscillators, a transcritical bifurcation can take place. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：323 / 333

页数：11

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