Journal
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
Volume 36, Issue 11, Pages 1403-1416Publisher
SHANGHAI UNIV
DOI: 10.1007/s10483-015-1991-7
Keywords
forced vibration; quadratic nonlinearity; primary resonance; multiple-scale method; Lindstedt-Poincare method; averaging method; harmonic balance method
Categories
Funding
- State Key Program of National Natural Science Foundation of China [11232009]
- National Natural Science Foundation of China [11572182]
Ask authors/readers for more resources
The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of different analytical approximate approaches. The forced vibration of snap-through mechanism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincar, method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are compared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method predicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the LindstedtPoincar, method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available