Boundary value problems for anisotropic plates with internal line hinges

Abstract

This paper deals with the formulation of an analytical model for the dynamic behaviour of anisotropic plates, with an arbitrary located interal line hinge with elastics supports and piecewise-smooth boundaries elastically restrainded against rotation and translation among other complicating effects. The equations of motion and its associated boundary and transition conditions are derived using Hamilton?s principle. By introducing an adequate change of variables, the energies which correspond to the different elastic restraints, are handled in a general framework. The concept of transition conditions and the determination of the analytical expressions are presented. Analytical examples are worked out to illustrate the range of applications of the developed analytical model. One of the essential features of this work is to demonstrate how the commonly for<span>mal derivations, used in the applications of the calculus of variations, can be made rigorous.