Within the framework of Kirchhoff-type prestressed plate theory, the steady-state response of a viscoelastic plate strip on a nonlinear dissipative foundation to the action of general traveling loads is considered. Since an hereditary integral-type viscoelastic constitutive model is employed, the governing field equation is of the nonlinear integropartial-differential type. To solve the stated problem, a modified perturbation procedure is employed. To remove the occurrence of secular terms, since the governing field equation is nonholonomic, a local potential operator is used to develop a hierarchy of integral constraints. Based on this approach, arbitrary traveling loads, hereditary-type viscoelastic modeling and foundation nonlinearity can be handled. Employing the solution, the results of several numerical experiments are presented. These emphasize the effects of dissipation, foundation nonlinearity as well as the action of periodic traveling loads.

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