A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach |
| |
Authors: | Dongmei Wu |
| |
Affiliation: | Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200436, P.R. China |
| |
Abstract: | According to Mickens R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as |
| |
Keywords: | 02 30 Hq 02 60 Cb 02 70 -c |
本文献已被 ScienceDirect 等数据库收录! |
|