Abstract: By the Krylov-Bogoliubov method, the response computation of a forced vibration of the viscous damping bilinear hysteretic oscillator with cubic restoring force is studied. The approach is examined by fourthorder Runge-Kutta numerical integration. The Floquet theory is applied to determining the stability of periodic solutions. Through the numerical and theoretical investigation, a conclusion that the saddle-node bifurcation due to the cubic nonlinear will happen under higher level exciting is reached.

Key words: Bilinear hysteretic oscillator, Nonlinear vibration, Response computation