“…During the last few decades, fruitful work has been done in studying the nonlinearity of these systems, i.e., solving the piecewise linear equations. Exact solutions (Natsiavas, 1989;Chicurel-Uziel, 2001;Ji and Leung, 2004), which are composed of a set of transcendental equations, can be obtained for the frequency responses and stability analysis of such systems. However, the instances of time at which the displacement crosses the piecewise linear boundary needs to be determined, and thus the complete response history cannot be obtained in closed form.…”