No abstract

A simple linear single‐mass oscillator with one or two rigid barriers is considered for the cases of external or parametric white‐noise random excitation. This problem is treated by using a certain piecewise‐differentiable transform of the dependent variable. For the special case of external and elastic impact the solution of the corresponding Fokker‐Planck‐Kolmogorov equation is straightforward, leading to Gaussian and truncated Gaussian stationary distributions of the velocity and displacement respectively. The general case is treated in “quasiconservative” approximation by averaging energy. This leads to a first‐oder stochastic equation for the energy and to a closed‐form solution for the stationary probability density p(E). In the case of parametric excitation necessary and sufficient conditions for the existence of p(E) are obtained.

No abstract

No abstract

No abstract