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 alternative to the differential formulation used to date, by solving the so-called inverse problem of the calculus of variations. This paper shows how the operator ruling the problem can be made symmetric by using a convolution bilinear form to obtain four functionals which are stationary at the solution of the differential problem. In conclusion, for example, the two-dimensional equations of the perturbed motion of a viscoelastic thin plate, are derived from the stationary condition of the three-dimensional functional.