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Dynamic Bergan–Wang theory for thick plates

Harm Askes and Alexandra R. Wallace

Vol. 10 (2022), No. 2, 191–204
Abstract

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.

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Keywords
thick plate theory, wave dispersion, rotational inertia
Mathematical Subject Classification
Primary: 74J05
Secondary: 35A15, 74B05
Milestones
Received: 14 March 2022
Revised: 14 July 2022
Accepted: 29 September 2022
Published: 25 October 2022

Communicated by Victor A. Eremeyev
Authors
Harm Askes
Department of Civil and Structural Engineering
University of Sheffield
Sheffield
United Kingdom
Faculty of Engineering Technology
University of Twente
Enschede
Netherlands
Alexandra R. Wallace
Department of Civil and Structural Engineering
University of Sheffield
Sheffield
United Kingdom