Structural Optimization of an Inhomogeneous Infinite Layer in Problems on Propagation of Periodic Waves

A structural optimization problem for an infinite elastic layer inhomogeneous across its finite thickness is considered in order to find the optimum distribution functions for its elastic modulus and density that allows the propagation of a plane periodic wave with a given phase speed. The problem is mathematically formulated as a coupled system of bilinear partial differential equations of the second order with variable controlled coefficients, and the maximum absolute value of the unknown function is taken as the functional to be minimized. The optimum distribution of the elastic modulus across the layer thickness is found as a piecewise constant function. The problem is reduced to a problem of nonlinear programming under constraints of equality type. The results of numerical calculations are presented.