On derivation of model equations for nonlinear strain waves in wave guides

An approach is developed to obtain the model equations for nonlinear strain waves using the boundary conditions on the lateral surfaces of the wave guides. It allows us to reduce the dimension of an initial statement of the problem without use of any "physical" hypothesis. As a result the governing equations are obtained with required precision. The problem of long waves modeling in a free lateral surface rod is considered in detail. The use of the procedure is discussed when interaction with an external medium or a microstructure of a material of the rod are taken into account. Two dimensional problem is discussed on an example of a plate interacting with an external medium.