期刊
ARCHIVE OF APPLIED MECHANICS
卷 81, 期 8, 页码 1017-1030出版社
SPRINGER
DOI: 10.1007/s00419-010-0465-0
关键词
Damped oscillators; Transient responses; Strong nonlinearity; Linearization; Harmonic balance; Analytical approximations
类别
资金
- Jilin University [200903288]
- National Natural Science Foundation of China [10926154]
An analytical approximate method for strongly nonlinear damped oscillators is proposed. By introducing phase and amplitude of oscillation as well as a bookkeeping parameter, we rewrite the governing equation into a partial differential equation with solution being a periodic function of the phase. Based on combination of the Newton's method with the harmonic balance method, the partial differential equation is transformed into a set of linear ordinary differential equations in terms of harmonic coefficients, which can further be converted into systems of linear algebraic equations by using the bookkeeping parameter expansion. Only a few iterations can provide very accurate approximate analytical solutions even if the nonlinearity and damping are significant. The method can be applied to general oscillators with odd nonlinearities as well as even ones even without linear restoring force. Three examples are presented to illustrate the usefulness and effectiveness of the proposed method.
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