动力学问题的时域微分求积法

针对动力学问题的线性和非线性问题,提出了一种全新有效的方法——时域微分求积法.本方法直接针对动力学问题的控制微分方程,在时间域采用微分求积法(differential quadrature method),得到求解域中各时间节点处动力响应位移场为全部待定参数的方程组,只需一次求解该方程组即得到全部待定参数,进而得到各节点的动力响应位移场,再由高阶Lagrange插值得到全部求解域内的动力响应位移场,进而依据该响应位移场得到该动力学问题的响应周期.算例结果表明,本方法具有明显优于传统的数值方法(如newmark法和wilsonθ-法)的精度和计算效率,可作为一种有极好研究价值的求解动力学问题的新方法.

Differential Quadrature Method for Dynamics in Time Domain

Based on the linear and nonlinear dynamics problem, the article presented a new method, which was called time domain differential quadrature method. It adopted differential quadrature method in time domain of the dynamics differential equation, and got DQ linear or nonlinear equations for solving all parameters of the displacement-field, with that, got the dynamic response and the period of the linear or non liear dynamics problem. The solutions showed that this new method was a high accuracy and small computing effort method for dynamics problem.