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Wave propagation and free vibration of FG graphene platelets sandwich curved beam with auxetic core resting on viscoelastic foundation via DQM

Al Mukahal F. H. H., Sobhy Mohammed

Archives of Civil and Mechanical Engineering

2022

Vol. 22, no. 1

art. no. e12, 2022

A novel shear and normal deformations theory is presented in this article to illustrate the wave propagation and free vibration of three-layer sandwich curved beams subjected to elevated temperature and moisture environments and resting on viscoelastic foundation. The upper and lower layers are made of metal matrix reinforced with functionally graded (FG) graphene platelets (GPLs). While, the core layer is made of auxetic honeycomb structures. For the layers to be more bonded, the matrix of the face layers and the auxetic layer are both made of aluminum material. The volume fraction of GPLs is varied through the thickness of the face layers according to a layer-wise rule. The modified Halpin–Tsai model is used to describe the effective material properties of the face layers. Four types of GPLs distribution are considered in the present analysis. The differential quadrature method (DQM) is employed to discretize the equations of motion and then converted to a system of algebraic equations. This system can be solved to obtain the natural frequencies of the sandwich curved beams. Whereas, the wave dispersion relations are determined by solving the motion equations analytically. Convergence and comparison examples are presented to adjust and validate the present solution. In addition, comprehensive parametric studies are performed to investigate the effects of the weight fraction of GPLs, temperature, moisture concentrations, core thickness, boundary conditions, and viscoelastic foundation stiffness on the natural frequency, wave frequency and phase velocity of the honeycomb sandwich curved beams.