一种求解振动方程的递推方法

A Recursion Method for Vibration Equations

提出了一种简便的求解结构振动方程的递推方法。该方法类似于有限元方法对空间进行离散处理的做法,把时间域离散成一系列小区间,在每一小区间对动力学方程进行简化处理以便求出其解析解,然后利用连续性条件导出递推关系式。与传统的数值积分法(如差分法、Wilsonθ及Newmarkβ法等)只是从数学角度进行近似处理不同的是:该方法充分利用了原动力学方程的信息,具有明确的物理意义。就线性和非线性振动方程进行了数值模拟运算,结果表明了该方法在动力响应分析中的有效性。

A simple recursion method was presented for the discretization to the space domain in finite element solving structure vibration equations. Similar with method, the time domain was divided into a series of small time segment. At every time segment, the vibration equation was simplified so that its analytic solution can be easily obtained. And then, the recursion expression was derived by using the continuity conditions. Different from the conventional direct integration methods, such as difference method, Wilson θ method and Newmark β method, which dealt with the differential operator from the pure mathematical aspect, the present method makes full use of the physical information of original vibration equation. Numerical examples of linear and nonlinear vibration equations were performed, the results demonstrate that this method is efficient in dynamic analysis.