黏弹性梁弯曲振动的复模态分析

发展复模态分析研究黏弹性梁的弯曲振动。将梁的控制方程写作状态变量的形式，然后利用复模态的正交性可解耦为无穷多个彼此独立的常微分方程组。基于固有频率和模态函数，可以得到黏弹性梁对于任意初始条件和外激励的响应。在固支梁的边界条件下确定黏弹性梁的固有频率、衰减系数和模态函数，并计算梁受两种典型的外激励时的响应。

COMPLEX MODAL ANALYSIS OF BENDING VIBRATION OF A VISCOELASTIC BEAM

The complex modal analysis is developed to investigate bending vibration of a viscoelastic beam. The governing equation of the beam is expressed in state variables. The orthogonality of the modal functions is employed to decouple the governing equation into a set of infinite ordinary differential equations that are independent of each other. The response of the beam to arbitrary initial excitation and external excitation is derived form the natural frequencies and modal functions. For a beam with two fixed boundary conditions, the natural frequencies, the decrement coefficients, and the modal functions are determined. Its resposes to two typical external exciations are calculated.