Perturbed motion of viscoelastic columns: a variational approach

In the past, the stability of viscoelastic columns has been analysed by solving the integro-differential equations of equilibrium under static or dynamic type disturbances. The solution of these is usually difficult and the authors intend to provide an alternative formulation of variational type. By using a convolution bilinear form, the operator governing the problem becomes symmetric and a functional, which is stationary at the solution of classical equations, is obtained. This formulation makes it possible both to use the classical approximation methods of the variation calculus and to pose the problem on more natural functional spaces. Some applications show the potential of the Ritz classical spectral method in the numerical solution and introduce the problem of columns subjected to variable load history.