OSCILLATIONS OF A SYSTEM WITH NONLINEAR STIFFNESS, UNDER SIMULTANEOUS EXTERNAL AND PARAMETRIC RANDOM EXCITATIONS.

An approximate analysis is made of the expression for the stationary probability density of the oscillation amplitude of a second-order system, as obtained in the quasi-conservative approximation. The integrals appearing in this expression are taken in finite form by using an approximate procedure whose accuracy corresponds to that of the harmonic linearization (harmonic balance) method. The case of a system with a linear damping and cubically nonlinear stiffness that is simultaneously excited by external and parametric random excitations is treated in detail. A comparison with some reults of computer simulation is offered.