一类振动问题中阻尼矩阵的等效方法及应用

A Damping Matrix Equivalent Method and Its Application in a Kind of Vibration Problems

多自由度振动系统中,很多问题的阻尼矩阵是确定的,但系统的模态关于这些阻尼矩阵不具有正交性,如果采用模态变换,由于阻尼矩阵不能化为对角矩阵的形式,因此不便于采用实模态迭加法进行振动分析.针对这一问题,本文提出一种阻尼矩阵的等效方法,即采用模态阻尼比对这类系统的实际阻尼进行等效,并考察其有效性,以便于采用模态迭加法对复杂多自由度系统进行随机振动分析.最后,采用该等效方法对某型号汽车进行随机振动分析,为改善该型号汽车的平顺性提供了建议.

In some Multiple Degrees of Freedom (MDOF) vibration systems, the damping matrices of the systems are definitive, but the modes of the systems are not orthogonal with respect to the damping matrices. So this kind of matrices can not be converted into diagonal matrices when the mode transformation is employed, and the real mode superposition technique can not be used to perform the vibration analysis of the systems. In order to use the mode superposition technique to perform the random vibration analysis of complex MDOF systems, this paper proposed a damping matrix equivalent method, which adopted the concept of modal damping ratio, and examined its validity. By using the above equivalent method, the random vibration analysis of a type of truck was carried out, and some suggestions for improving its riding qualities were given.