INTEGRAL ESTIMATES IN NONLINEAR OSCILLATORY SYSTEMS

A procedure for constructing integral estimates for the wave equation with a non-linearity concentrated in a certain local region of the sys tem in question is presented. To obtain these estimates a knowledge of the solution of the linear homogeneous differential equation and the dynamics of wave propagation in the system is required. The accuracy o f the estimates depend considerably on the nature of the external load s, their intensity and duration. It makes sense to consider this type of estimate for processes whose duration is comparable with the time t aken for the wave to traverse the system, which is characteristic, for example, for explosive and shock phenomena, and also dynamic fracture . An example of the construction of wave estimates for a simple mechan ical system is considered. (C) 1996 Elsevier Science Ltd.