Effects of Dead Loads in Dynamic Plates

This paper demonstrates the effect of dead loads on the dynamic response of a uniform elastic rectangular plate and clarifies the physical factors governing the effect. First of all, the governing equation of plates, which includes the effect of dead loads, is formulated by considering the strain energy produced by conservative initial bending stresses due to dead loads. Next, an approximate solution for dynamic deflections of simply supported plates that include the effect of dead loads is presented in closed form. The proposed solution shows strong agreement with numerical results obtained using the Galerkin method. Numerical results show that dynamic displacements and stress couples produced by dynamic live loads decrease on a plate with heavyweight dead loads by considering the effect of dead loads. The reduction is given by $k_w$ a being a function of the intensity of dead loads and the thickness, span length, and bending rigidity of the plate. Finally, a method that reflects the effect of dead loads on dynamic live loads is presented by an example.