Mode superposition is a widely used method for solving the dynamic equilibrium equation in structural dynamic analysis. However, the accuracy of this method may be reduced when the dynamic equilibrium equations are set up using displacement excitation. A new method for developing solutions for dynamic equilibrium equations based on displacement excitation is introduced. The dynamic equilibrium equation is decomposed into two parts, namely displacement excitation and velocity excitation, and precise integration and mode superposition methods are combined to solve the equation. Ritz vectors are then used to calculate the static response of the truncated modes of the structure, and a method for determining the number of participating modes is obtained. Using multi-degree-of-freedom systems as two computational examples, the differences in the structural responses obtained from the displacement excitation and acceleration excitation are compared and analyzed. It is shown that the new solution method generates consistent accuracy between the displacement excitation and acceleration excitation.

中文翻译：

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基于位移激励的动力平衡方程求解方法

模式叠加是解决结构动力分析中动力平衡方程的一种广泛使用的方法。但是，当使用位移激励建立动态平衡方程时，该方法的精度可能会降低。介绍了一种基于位移激励的动态平衡方程解求解方法。将动平衡方程分解为位移激励和速度激励两部分，并结合精确积分和模式叠加方法进行求解。然后，使用Ritz向量计算结构的截断模态的静态响应，并获得一种确定参与模态数的方法。使用多自由度系统作为两个计算示例，比较分析了位移激励和加速度激励得到的结构响应的差异。结果表明，新的求解方法在位移激励和加速度激励之间产生了一致的精度。