Incremental Deformations in Orthotropic Laminated Plates Under Initial Stress

Plate equations for the incremental deformation in composite plates with orthotropic constituent layers are derived according to Trefftz’s formulation for elastic bodies under initial stress. The plate theory thus derived includes the microdeformation which can account for the heterogeneity of the plate. Flexural wave propagation under initial stress and buckling of a simply supported rectangular composite plate are investigated. In a special case of harmonic wave propagation in a free composite plate dispersion curves predicted by the plate equations are compared with the exact curve. Good agreement is observed for the complete plate theory and Approximation I, while the adequacy of the other two sets of simplified equations, Approximations II and III, depends vitally on the ratio of the transverse shear rigidities of the constituent materials.

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Band gaps for elastic flexural wave propagation in periodic composite plate structures with star-shaped, transversely isotropic, magneto-electro-elastic inclusions

Acta Mechanica ◽

10.1007/s00707-021-03050-0 ◽

2021 ◽

Author(s):

G. Y. Zhang ◽

W. Shen ◽

S. T. Gu ◽

X.-L. Gao ◽

Z.-Q. Xin

Keyword(s):

Wave Propagation ◽

Composite Plate ◽

Transversely Isotropic ◽

Band Gaps ◽

Flexural Wave ◽

Plate Structures ◽

Periodic Composite ◽

Elastic Inclusions ◽

Flexural Wave Propagation

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Flexural Wave Propagation of Double-Layered Graphene Sheets Based on the Hamiltonian System

Materials Science Forum ◽

10.4028/www.scientific.net/msf.975.121 ◽

2020 ◽

Vol 975 ◽

pp. 121-126

Author(s):

Cheng Hui Xu ◽

Jing Jing Hu ◽

Da Lun Rong

Keyword(s):

Wave Propagation ◽

Plate Theory ◽

Mechanical Systems ◽

Chemical Properties ◽

Nonlocal Elasticity Theory ◽

Flexural Wave ◽

Graphene Sheets ◽

Hamiltonian Equation ◽

New Type ◽

Flexural Wave Propagation

Double-layered graphene sheets (DLGSs) as a new type of nanocomponents, with special mechanical, electrical and chemical properties, have the potential of being applied in the nanoelectro-mechanical systems (NEMS) and nanoopto-mechanical systems (NOMS). In DLGSs structure, the two graphene sheets are connected by van der Waals (vdW) interaction. Thus, it can exhibit two vibration modes during the propagation of the flexural wave, i.e., in-phase mode and anti-phase mode. Based on the Kirchhoff plate theory and the nonlocal elasticity theory, Hamiltonian equations of the DLGSs are established by introducing the symplectic dual variables. By solving the Hamiltonian equation, the dispersion relation of the flexural wave propagation of the DLGSs is obtained. The numerical calculation indicates that the bending frequency, phase velocity and group velocity of the in-phase mode and anti-phase mode for the DLGSs are closely related to the nonlocal parameters, the foundation moduli and the vdW forces. The research results will provide theoretical basis for the dynamic design of DLGSs in micro-nanofunctional devices.

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