A CENTRAL DIFFERENCE VIRTUAL INITIAL CONDITION METHOD FOR SEISMIC RESPONSE ANALYSIS OF SYSTEMS WITH HYSTERETIC DAMPING

A central difference virtual initial condition method is proposed to address the instability of the solution of hysteretic damping system. The proposed method develops virtual initial conditions associated with the real initial conditions, which generates the direct integration solution eliminating the divergence term of complementary solution and converges to the exact solution. Then, the procedure of central difference virtual initial condition method is established based on central difference method which is of conditional stability. Numerical examples of three different natural frequency systems under three different seismic excitations are analyzed by the central difference virtual initial condition method, the analytical solution and the frequency domain method, respectively. The results show that the frequency domain analysis results only contain the steady state solutions, which will lead to significant errors in the initial stage of vibration of low natural frequency system; the central differential virtual initial condition method is stable for different conditions, and it will converge to theoretical solution including transient response.