A new state-space method for exponentially damped linear systems. (February 2019) - Wu, Xinhai; He, Huan; Chen, Guoping
Abstract: A new state-space method is presented in this paper for linear systems with multiple exponential damping models. By introducing displacement vector and its derivatives as state variables, the original second-order differential equations involving convolution integrals are transformed into a state-space formulism. The iterative relationships are given to calculate all the coefficient matrices, loading vectors and initial conditions. Based on the extended state-space formulism, the eigensolutions, frequency response functions and dynamic responses can be calculated easily using mature techniques for first-order linear systems. Besides, a direct integration method for time-domain analysis based on the proposed stated-space formulism is presented. Two numerical examples are used to illustrate the proposed approach.