On the dynamic plane problem of a rectangle

An analytical solution for the elastic plane dynamic problem of a rectangle is presented. The following boundary conditions were considered: two free edges, arbitrary normal pressure and shear displacement on the two other edges. By means of space and time Fourier transform, the solution is reduced to a set of fundamental solutions which are related to different symmetries. The solutions are expressed by means of infinite summation series involving implicit real roots. The inversion of the time Fourier transform and the numerical convergence of the solutions are discussed. As regards the applications, the solution is a tool for computations involving some kind of shock-absorber.