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    Perturbed motion of viscoelastic columns: a variational approach

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    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

    A variational formulation of the perturbed motion problem for a viscoelastic body

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    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
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