Decoupled Time-Invariant Forms of Linear Parametrically Excited Structural Systems

Abstract In this study, decoupled time-invariant forms of linear parametrically excited structural systems are constructed. First, equations of motion are temporarily written in the state-space form to apply the Lyapunov-Floquet transformation. Next, the resulting time-invariant equation is subjected to a decoupling transformation to yield a new equation that can be expressed as a set of decoupled second-order time-invariant equations. Such equations are generated for linear systems with and without external excitations. Examples are provided, and the results thus obtained are verified by numerical simulation.