It is well-known that flexible structures like suspension bridges or overhead power transmission lines can be subjected to oscillations due to windforces or other causes. Simple models for such oscillations are described with second-and fourth-order partial differential equations. Usually asymptotic methods can be used to construct approximations for the solutions of these wave, beam or plate equations. For a long time initial boundary value problems for weakly nonlinear wave equations have been studied. The analysis becomes more compliceted for beam equations [1], [2]. Even less is known about weakly nonlinear plate equations. However, plates of various geometries, i.e. circular, rectangular etc are extensively used in engineering applications. These plates are widely used in modern aerospace technology, aircraft structures and flexible structures like suspension bridges. The majority of the literature deals with classical boundary conditions representing clamped, simply supported or free edges, and only a small number deals with edges which are restrained against translation or/and rotation, or with other nonclassical boundary conditionsA simple way to model the behavior of a suspension bridge is to describe it as a vibrating onedimensional beam with simply supported edges [3]- [4]. However, to study wind-induced oscillations of suspension bridges one can of course use plate equations to describe the displacement of the deck of the bridge [9].The deck of the bridge is modeled as a rectangular plate, and the cabels are modeled as springs. Such a model can be described by the following initially boundary value problemwhere p 2 represents the linear restoring force of the springs, is a small parameter, d and l are width and length of the plate correspondently. The initial displacement and the initial velocity of the plate in z-direction are given by u 0 (x, y) and u 1 (x, y) respectively.In this paper the following subproblems will be studied in detail• a linear problem with f (x, t, u, u t ) = 0, and g(u, u t ) = 0;• a nonlinear problem for u tt + u xxxx + 2u xxyy + u yyyy + p 2 u = u 2 , where p 2 u − u 2 represents the restoring force of the springs;• a linearized problem with f (x, t, u, u t ) = u t , and g(u, u t ) = αu t , where is α-damping parameter.
