A higher order dynamic theory for viscoelastic plates and layered composites

By using a new technique proposed by the first author [1] approximate theories are developed for the dynamic response of viscoelastic plates and layered composites. The originality of the new technique lies in the fact that it permits the approximate theory to satisfy correctly the lateral boundary conditions of a plate, or the interface (continuity) conditions of a layered composite. This, in turn, enables the approximate theory to describe accurately the geometric dispersion of waves propagating in a plate or layered composite. The approximate equations of a single viscoelastic plate are first derived by making use of the new technique. To develop the approximate theory for viscoelastic layered composites made of two alternating layers it is noted that the approximate equations of a single plate already established also hold in each layer of the composite. The theory is completed by adding the continuity conditions to these equations and using a smoothing operation. The equations thus obtained constitute a continuum (homogeneous) model (CM) which simplifies the determination of the dynamic response of viscoelastic layered composites when the number of layers in the composite is large. The proposed approximate theories are open to improvement in the sense that their region of validity in the wave number-frequency plane can be enlarged as much as one wishes by increasing the orders of the theories and continuity conditions.