Dynamic Bergan–Wang theory for thick plates

Bergan–Wang theory for thick plates is extended from statics to dynamics. In line with static theory, kinematic assumptions are developed and explored that allow the equations of motion to be expressed in terms of the transverse displacement only. These assumptions include approximations of the shear strains in terms of spatial and temporal derivatives of the transverse displacement, as well as a simplification of the rotational inertia. The equations of motion are derived systematically through variational principles. The resulting partial differential equations are eighth-order in space and, depending on the kinematic assumptions, can be second-, fourth or sixth-order in time. An analysis of dispersive flexural waves is used to compare and contrast the various theories.