Forced vibrations of damped systems with bilinear nonsymmetric elasticity

A single degree-of-freedom viscously damped system with bilinear, nonsymmetric restoring force is analyzed. The differential equations governing the motion of the system are solved in closed form by matching the solutions for the positive and negative parts of a cycle. The fourth order Runge-Kutta method is also employed to solve the system numerically. Steady-state response curves are plotted for several ratios of the spring constants and damping. Both force and motion inputs are considered.