A method for dynamic response analysis of time-variant discrete systems

A method is proposed for analysing the transient response of structures when variation with respect to time of the stiffness and damping coefficients are taken into account. The state-variable technique is employed to formulate the dynamic equilibrium equation for the time-variant system. Excitation is represented as a series of impulses. It allows introduction of virtual initial conditions which are equivalent to the impulse excitations in the state space equations. The effective method for evaluation of a state transition matrix is used. Numerical tests of an illustrative example demonstrate the validity and effectiveness of the approach suggested in this paper. The method has great advantages when the behaviour of the semi-active system is calculated and the optimal control of the systems is simulated.