Guided wave propagation in porous functionally graded doubly curved nano-shells with different boundary conditions

Kuineng Chen , Zipan Yang , Wubin Shan

Abstract

Despite significant interest in the mechanics of nanostructures, the propagation behavior of guided waves in porous functionally graded (FG) doubly-curved nanoshells remains unexplored, particularly concerning the influence of different boundary constraints. The present study is therefore dedicated to addressing this void by developing a comprehensive analytical model for this problem. Based on the nonlocal strain gradient theory (NSGT) framework and incorporating the effect of moment of inertia, the governing equations of motion for porous functionally graded doubly curved shells are derived. The Galerkin technique is employed to eliminate the spatial variables from the partial differential equation system, thereby converting it into an ordinary differential equation with respect to time. By applying the boundary conditions and solving the characteristic equation, the dispersion characteristics of porous functionally graded strain gradient doubly curved shells with different boundary conditions are determined. The results indicate that the phase velocity of the hyperbolic curved plate is the smallest, followed by the cylindrical curved plate, then the ellipsoidal curved plate, with the spherical shell exhibiting the maximum phase velocity. Clearly, the spherical shell has the highest stiffness, naturally resulting in the maximum phase velocity. Additionally, at low wave numbers, the effects of nonlocal and strain gradient parameters on the dispersion relation are negligible.

Key Words

functionally graded porous material; guided wave; nanoshells; nonlocal strain gradient theory

Address

Kuineng Chen — Hunan Vocational Institute of Technology, Xiangtan 411104, China
Zipan Yang — Xiangtan Hengxin Industrial Co., Ltd., Xiangtan, 411300, China
Wubin Shan — College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China

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