VIBRATION OF MULTI-DEGREE-OF-FREEDOM SYSTEMS WITH NONPROPORTIONAL VISCOUS DAMPING

In this paper, free vibration, steady-state vibration and transient vi bration of multidegree-of-freedom systems with non-proportional viscou s damping are presented. Natural frequencies and the corresponding dam ping ratios are obtained by solving the complex eigenvalue problem wit h complex roots. Then the amplitudes of free vibration and amplitude o f steady-state solution of forced vibration are obtained by solving li near algebraic equations. The transient vibration problems are analyze d by using the superposition principle and convolutional integral. Num erical results of amplitudes of vibration and natural frequencies of t wo-degree-of-freedom systems with different values of coefficients of viscosity are presented. It is very interesting to note that in additi on to the overdamped and underdamped cases as in a single-degree-of-fr eedom system, there exists a degenerated case. Under these conditions (degenerated cases) the number of natural frequencies may be less than the number of degrees of freedom. Numerical results of forced vibrati on, steady-state solution and transient vibration under different forc ing functions are also analyzed. It is found that the effects of visco us damping are very significant in vibration.