Random vibrations with impacts: a review (Q2493152)

The review paper is devoted to random vibrations of systems with lumped parameters. The authors present various analytical methods concerning such systems with impacts. Differential equations of motion for a vibroimpact (VI) system are supplemented by impact conditions. In general, VI problems are nonlinear or contain Dirac delta function to describe relevant instantaneous event(s). Such specific features of VI systems require special methods of analysis. These methods are illustrated in the paper for VI system with offset barrier. It is pointed out that differential equation serves as a mathematical model of this system between impacts, and a stepwise integration is an obvious approach to the solution of this problem. As soon as external force is a random process, stochastic methods of analysis should be applied. One of the approaches is based on linearisation of pointwise mapping, and the solution to the linearized stochastic problem is straightforward. Another approach is a quasistatic one, whereby the random processes are slowly varying. The authors also present methods which use Fokker-Planck-Kolmogorov equation for joint probability density function. A nonsmooth transformation of state variables reduces the VI problem to a problem without impacts. The transformed equation permits analytical study by the method of averaging. The cases of white noise or broadband random excitation are considered for single-degree-of-freedom and multi-degree-of-freedom systems. Several problems are treated by energy balance method. Finally, the authors give examples of investigation of impact damper devices.