Interaction of Membrane and Bending Forces in Plates at Nonlinear Vibration

The subject of this paper is the analysis of the dynamic response of circular and rectangular elastic-viscoplastic plates subjected to impulsive loading. The range of what is referred to as moderately large deflections has been considered. All the displacement components and their time derivatives in the description of the kinematics are included. The equations of motion have been formulated by using the principle of virtual work. Approximate solutions are found by the orthogonalization principle. As regards the numerical aspects of this method, they are characterized by the necessity of applying typical techniques of numerical integration of the equations of motion and the constitutive relations. Principal emphasis is laid on the study of the co-operation between membrane and bending forces over a wide range of plate deflection. The influence of such factors as the type of edge support, the character of dynamic load and the kind of material of the plate have been discussed. It has been found that plates on hinged supports are more sensitive to membrane e:lfects than those with clamped edges. Intensive dynamic loads with long periods of action lead in most cases to membrane-type mechanisms of deformation. lnitial velocity pulses make the plate move with a strongly non-stationary displacement velocity field, the deformation being characterized by a flexural way of producing deformation.