Spectral Response of a Bilinear Oscillator

Abstract An approximate analytical procedure is presented to estimate the response power spectral density of a randomly excited spring/mass/damper system having a bilinear spring. The approximate expression for the response spectrum is developed by representing the non-linear oscillator as a linear system having a natural frequency that depends on the envelope of the random response. This approximate representation of the system leads to estimates of the response spectrum that agree extremely well with those obtained by direct numerical simulation of the governing equation.