Nonlinear free vibration of systems with inertia and static type cubic nonlinearities: An analytical approach

被引：41
作者：
Bayat, M. [1 ]
Pakar, I. [2 ]
Cveticanin, L. [3 ]
机构：
[1] Islamic Azad Univ, Mashhad Branch, Coll Engn, Dept Civil Engn, Mashhad, Iran
[2] Islamic Azad Univ, Mashhad Branch, Young Researchers & Elites Club, Mashhad, Iran
[3] Univ Novi Sad, Fac Tech Sci, Novi Sad 21000, Serbia
来源：
MECHANISM AND MACHINE THEORY | 2014年 / 77卷
关键词：
Hamiltonian Approach; Nonlinear vibration; Equivalent rigidity; APPROXIMATE ANALYTICAL SOLUTION; HAMILTONIAN APPROACH; OSCILLATION;
D O I：
10.1016/j.mechmachtheory.2014.02.009
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
The present paper deals with the new application of a powerful analytical method to a system with inertia and static type cubic nonlinearities. The free vibration of a mass grounded by linear and nonlinear springs in series is studied. A nonlinear ordinary differential equation with inertia and static type cubic nonlinearities represents the governing equation of the system. The new approach does not have the limitation of the traditional perturbation method which is valid for conservative systems with small perturbed parameters. An attempt has been made to provide simple approximate analytical expressions valid for small as well as large amplitudes of oscillation. The exact solution is also presented and discussed to validate the present analysis. In the paper the method for determining the equivalent rigidity for the serial connected nonlinear springs is developed. (c) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：50 / 58
页数：9
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