The variational theory of complex rays for medium-frequency vibrations of shells

Abstract

This chapter focuses on a new approach that is called the “variational theory of complex rays” (VTCR) that is developed to calculate the vibrations of slightly damped elastic structures in the medium-frequency range. It is a predictive tool for dealing with this kind of problems. Numerical examples of structures made of plates and shells demonstrate the possibilities of the VTCR. The calculation of medium-frequency vibrations is a key aspect of the design of car chassis or satellites and represents a real challenge. The first characteristic feature of the VTCR is the use of a new variational formulation of the problem to allow the approximations within the substructures to be a priori independent.In other terms, these approximations do not necessarily satisfy a priori the transmission conditions with respect to displacements or to stresses at the interfaces between substructures. The chapter also puts an emphasis on the extension of this theory to shells of relatively small curvature.