SPECTRAL DENSITY OF A NONLINEAR SINGLE-DEGREE-OF-FREEDOM SYSTEMS RESPONSE TO A WHITE-NOISE RANDOM-EXCITATION - A UNIQUE CASE OF AN EXACT SOLUTION

A SDOF vibro-impact system with a one-sided rigid barrier is considere d for the case of a perfectly elastic impact and stationary zero-mean Gaussian white-noise excitation. Special piecewise-linear transformati on of the system's state variables is applied, which effectively reduc es the original problem to one without impacts. Moreover, for the spec ial case, where position of the barrier coincides with that of the sys tem's static equilibrium, the transformed equation of motion is found to be linear, implying Gaussian transition probability densities of th e transformed state variables. Thus, the non-linear random vibration p roblem is reduced to one with ''inertialess'' non-linearity only. The above transformation is used to obtain an exact explicit expression fo r the response autocorrelation function, thus leading to quadrature ex pression for spectral density of the response.