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Modal Analysis of MDOF Systems with Proportional Damping

MEEN 617 HD 8 Modal Analysis with Proportional Damping . L. San Andr s 2013 1 Handout 8 Modal Analysis of MDOF Systems with Proportional Damping The governing equations of motion for a n-DOF linear mechanical system with viscous Damping are: ()()ttMU+DU+KU =F (1) where andU, U,U are the vectors of generalized displacement, velocity and acceleration, respectively; and ()tF is the vector of generalized (external forces) acting on the system. M, D, Krepresent the matrices of inertia, viscous Damping and stiffness coefficients, respectively1. The solution of Eq. (1) is uniquely determined once initial conditions are specified. That is, (0)(0)at0,oot UUUU (2) Consider the case in which the Damping matrix D is of the form DM K (3) where , are constants2, usually empirical.

Handout 8 Modal Analysis of MDOF Systems with ... As in the undamped modal analysis, ... See Handout (2a) for formulas for responses corresponding to overdamped and critically damped SDOF systems. Forced response in modal coordinates For step-loads, QSj, the …

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