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对于非比例阻尼线性结构体系,利用体系无阻尼实模态来形成模态响应方程时,得到的模态方程组是关于模态阻尼矩阵耦合的。非比例阻尼可以分成两部分:耗散能量的比例阻尼和转换能量的非比例阻尼。基于这种概念,本文采用了一种拟力实模态叠加法来求解非比例阻尼体系的动力分析,即把前述耦合模态方程中代表非比例阻尼的耦合项作为虚力,放到方程的右端,再运用迭代法进行求解。这种方法综合了经典模态叠加法和拟力法的优点。数值算例表明,此方法具有很好的收敛特性,所得结果精度高。我们认为,这种方法可应用于实际工程分析。
For a non-proportionally damped linear structure system, when the modal response equation is formed using the undamped real mode of the system, the resulting modal equations are related to the modal damping matrix coupling. Non-proportional damping can be divided into two parts: proportional damping of dissipated energy and non-proportional damping of conversion energy. Based on this concept, a pseudo-real mode superposition method is used to solve the dynamic analysis of the non-proportional damping system. That is, the coupling term representing the non-proportional damping in the aforementioned coupled modal equations is used as a virtual force and put into the equation. At the right end, iterative method is used for solving. This method combines the advantages of the classical modal superposition method and the pseudo-force method. The numerical example shows that this method has good convergence characteristics and the obtained results have high accuracy. We believe that this method can be applied to practical engineering analysis.