A VARIATIONAL FORMULATION OF THE PERTURBED MOTION PROBLEM FOR A VISCOELASTIC BODY

The analysis of perturbed motion is often very important for studying the progress of strain and stress in viscoelastic bodies. The authors intend to provide a variational formulation of the problem as an alter native to the differential formulation used to date, by solving the so -called inverse problem of the calculus of variations. This paper show s how the operator ruling the problem can be made symmetric by using a convolution bilinear form to obtain four functionals which are statio nary at the solution of the differential problem. In conclusion, for e xample, the two-dimensional equations of the perturbed motion of a vis coelastic thin plate, are derived from the stationary condition of the three-dimensional functional.