Determining dynamic responses in elastic deformable systems possessing intermediate supports and affected by pulse loads

The present report is devoted to determination of the dynamic forces of interaction inshell-like systems possessing structural inhomogeneities. The principal assumptions of a computational technique based on a partition of the system and determination of the dynamic responses from a condition specifying that the individual elements are subjected to cooperative deformation are set forth. As remarked in such studies as [6.7], the preferred application of expansions in series in certain stationary states if an entire system as a whole, especially in the case of loads that vary rapidly over time, is one such deformation at one or more points belonging to the contact regions. However, in contrast to problems in statics [3,5] and in steady-state vibrations [4,5], when we wish to determine dynamic responses the latter simplications do not lead to algabraic systems, but instead to systems of integral equations with time variable. These equations are analogous to those obtained in [7] for systems of homogenous elastic elements by means of Laplace transformation and called {open_quotes}functions of dynamic pliancy{close_quotes}. In the present study equations are derived directly through application of expansions in terms of the natural vibration forms of individual elements and by writing the solutions in form of Duhamelmore » integrals. As a result of integral convolution-type Volterra equations of the first kind [2] are obtained for finding the responses, where the kernels are represented in the form of stochastic series. Through the use of special techniques it si possible to construct a stable computational algorithm for solving these systems, as will become clear from examining the examples presented below.« less