MODAL-ANALYSIS OF THE STEADY-STATE RESPONSE OF A DRIVEN PERIODIC LINEAR-SYSTEM

A modal analysis method is developed that predicts the steady state re sponse of discrete linear systems that are governed by systems of ordi nary differential equations with periodic coefficients. The systems ar e excited both parametrically by periodic coefficients and directly by inhomogeneous forcing terms that have the same period. In the method, the solution for the steady state vibration is expressed as a linear combination of the Floquet eigenvectors, which are orthogonal with res pect to solutions of the associated adjoint problem. The approach is a pplicable either when the Floquet eigensolutions have been obtained nu merically through the transition matrix, or when they are found analyt ically through perturbation methods. For this reason, implementation o f the present modal analysis solution can be computationally efficient , even if the dimension of the system is large. The approach is demons trated by an application to Mathieu's equation.