A Reduction Method for Nonhomogeneous Boundary Conditions

Abstract

A procedure is described for reducing dynamical equations in two-space variables defined in a rectangle with nonhomogeneous time dependent boundary data to equations with homogeneous boundary data. The procedure applies not only to a single equation but to systems of equations with systems of boundary conditions. One-space dimensional problems are treated separately and a condition for applicability is developed in this case. Examples are presented in which dynamical equations in one and two-space variables with nonhomogeneous time dependent boundary data are reduced to equations with homogeneous boundary data. Specific applications to problems in one-space variable include a simple beam, a laminated composite plate, and a Timoshenko beam. For two-space variable problems defined in a rectangle, the application of the procedure is made to an antisymmetric angle-ply circular cylindrical panel.