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摘要
Nonlinear dynamic equation is a common engineering model. There is not precise analytical solution for most of nonlinear differential equations. These nonlinear differential equations should be solved by using approximate methods. Classical perturbation methods such as LP method, KBM method, multi-scale method and the averaging method on weakly nonlinear vibration system is effective, while the strongly nonlinear system is difficult to apply. Approximate solutions of primary resonance for forced Duffing equation is investigated by means of homotopy analysis method (HAM). Different from other approximate computational method, the HAM is totally independent of small physical parameters, and thus is suitable for most nonlinear problems. The HAM provides a great freedom to choose base functions of solution series, so that a nonlinear problem may be approximated more effectively. The HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter It and the auxiliary function. Therefore, HAM not only may solve the weakly non-linear problems but also may be suitable for the strong non-linear problem. Through the approximate solution of forced Duffing equation with cubic non-linearity, the HAM and fourth order Runge-Kutta method of numerical solution were compared, the results show that the HAM not only can solve the steady state solution, but also can calculate the unsteady state solution, and has the good computational accuracy.
- 出版日期2011-5
- 单位东北大学
