摘要
求解有阻尼多自由度结构系统的振动微分方程,实模态分析法是得到广泛应用的一种有效方法。但随着对阻尼的深入研究,发现广泛采用的 Rayleigh 比例阻尼假设,往往不符合实际情况。但若采用非比例型的阻尼,用实模态矩阵变换结构振动微分方程时,往往不能使之完全解耦而进行求解。通常的处理方法,可将阻尼耦合项忽略,但这样有时会使计算结果的精度很差。或者转而用复模态求解,这又使方程自由度数增加一倍,计算量大增,且占用计算机内存过多,使计算难以在容量有限的小型机上进行。本文针对这一问题,提出一种新的求解方法。在实模态分析法的基础上,计入模态阻尼耦合项,对计算结果进行反复迭代修正,使其逐渐逼近精确解。本文方法经数学证明,在一定条件下收敛,且收敛条件易获满足,因而具有一定实用价值。
The dynamic response of the damping multi-DOF structural system is usually calcu- lated by the real modal analysis method.But when the real modal matrix can't uncou- ple the structural system damping matrix,it is obliged to negleet the coupled terms of modal damping in order to calculate it continuously and this often makes the result accuracy unacceptable.Or people are forced to use the complex modal analysis method to calculate dynamic response.Thus it will greatly increase the calculating difficulty and the amount of calculating work so that the calculation must be carried out in the great capacity computer.This paper has put forward a new method to calculate the dynamic response in some certain conditions when the modal damping couples.There- fore it can avoid using the complex modal analysis method and ensure the calculating accuracy.The convergence of the method in this paper has been demonstrated in maths Its characteristics are convenient to calculate,program and save the computer capucity and the calculating cost.The dynamic response of the great structural system can be expected to carry out in micro-computer.
出处
《振动与冲击》
EI
CSCD
北大核心
1991年第3期7-13,共7页
Journal of Vibration and Shock
