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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.

i.e., the j-modal damping ratio increases as the natural frequency increases. In other words, higher modes are increasingly more damped than lower modes. The response for each modal coordinate satisfying the modal Eqn. Mq Dq Kq Qj j jj jj j j n , 1,2... is obtained in the same way as for a single DOF system (See Handout 2).

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