非线性结构动响应的Taylor级数解法

Taylor级数方法是结构动力分析中一种新的时间积分方法,它在求解线性问题方面的理论和应用已经比较完善和成熟.将Taylor方法进一步用于非线性结构动响应的求解,对于非线性项可以表示为多元多项式的结构动响应问题,建立了Taylor级数方法的理论,给出了递归求解通式.通过对典型方程的求解,阐述了Taylor级数方法的应用.算例表明,Taylor级数方法解决非线性结构动响应问题是行之有效的.

A Taylor Series Method in Nonlinear Structural Dynamics

A Taylor series method for solving nonlinear structural dynamics problems where nonlinear items can be expressed as a polynomial with multiple variables was established. Different from existing methods, the Taylor series method satisfies governing equations in continuous intervals rather than at discrete time instants or in an average form. It solves dynamics problems through a sequence of recursions of Taylor expansion coefficients, without the necessity of solving simultaneous equations. The method was compared with the Runge Kutta method through solving classical equations of Duffing, Van der Pol and the free vibration equation of two DOFs with quadratic nonlinear items. Numerical results indicated that the proposed Taylor series method is an excellent alternative for solving the aforementioned nonlinear dynamics problems.