Stationary response of bilinear hysteretic system driven by Poisson white noise

• Stochastic averaging of bilinear system to Poisson white noise is studied.
• New exponential polynomial closure expression is proposed.
• Corresponding averaged GFPK equation is derived and solved.
• Approximate solutions are validated by a pertinent Monte Carlo simulation.

Stationary response of single-degree-of-freedom (SDOF) bilinear hysteretic system driven by Poisson white noise is investigated via stochastic averaging of energy envelope in this paper. The averaged generalized Fokker–Planck–Kolmogorov (GFPK) equation for SDOF bilinear hysteretic system driven by Poisson white noise is derived and the approximate stationary solutions of the averaged GFPK equation are obtain by using a modified exponential polynomial closure method. The effectiveness and accuracy of the approximate solution are assessed by performing appropriate Monte Carlo simulations. It is found that analytical and numerical results agree well and the effect of non-Gaussianity of the excitation process on stationary probability densities of total energy and displacement of bilinear hysteretic system is predicted successfully via stochastic averaging of energy envelope.