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Dynamic Bergan-Wang theory for thick plates. (English) Zbl 1513.74108

Summary: 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.

MSC:

74J05 Linear waves in solid mechanics
35A15 Variational methods applied to PDEs
74B05 Classical linear elasticity
74K20 Plates
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References:

[1] 10.1002/cnm.1630040108 · Zbl 0627.73065 · doi:10.1002/cnm.1630040108
[2] 10.1016/0045-7949(84)90199-8 · Zbl 0549.73071 · doi:10.1016/0045-7949(84)90199-8
[3] 10.1115/1.4031965 · doi:10.1115/1.4031965
[4] 10.1016/j.jsv.2017.07.039 · doi:10.1016/j.jsv.2017.07.039
[5] ; Hassan, K.; Guirguis, S.; El-Hamouly, H., Bending of an elastic rectangular clamped plate using Bergan-Wang approach, Afr. J. Eng. Res., 5, 1, 7 (2017)
[6] 10.1590/1679-78256170 · doi:10.1590/1679-78256170
[7] 10.1023/A:1007472709175 · Zbl 0902.73047 · doi:10.1023/A:1007472709175
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