Natural frequency analysis of bidirectional functionally graded plates based on a refined shear theory using nonconforming finite elements

被引:4
|
作者
Bashiri, Abdullateef H. [1 ]
机构
[1] Jazan Univ, Coll Engn, Dept Mech Engn, Jazan 45142, Saudi Arabia
关键词
Bidirectional functionally graded plate; unified shear deformation theory; natural frequencies; nonconforming plate element; FREE-VIBRATION ANALYSIS; HIGHER-ORDER SHEAR; RADIAL BASIS FUNCTIONS; DEFORMATION-THEORY; RECTANGULAR PLATE; FORCED VIBRATION; FGM PLATES; COLLOCATION; STRESS;
D O I
10.1080/15376494.2023.2297390
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this study, we investigate the free vibrations of functionally graded plates using the refined shear deformation theory. These plates have material properties that vary in two directions: the z-axis and the x-axis. The variation follows a bidirectional gradation described by a power law based on the Voigt rule of mixture. The displacement field is characterized by four variables, chosen in such a way that shear strain and stress vanish, and traction is free at the upper and lower surfaces of the plate. This eliminates the need for a shear correction factor, as required in the first-order shear deformation theory. We derive the equations of motion and related boundary conditions using Hamilton's principle and a finite element approach. The proposed element ensures C1-continuity by including the first derivative of the transverse deflection in the kinematic field. For spatial discretization, we employ a rectangular element with four nodes and two interpolation schemes. Lagrangian shape functions are used for in-plane displacement, while a Hermitian scheme is employed for transverse deflection. This enables us to determine the natural frequencies of the 2D-FG plates. We demonstrate the validity, convergence, and accuracy of the proposed element through illustrative examples and compare it with previous literature. Furthermore, we conduct numerical analyses to examine the effects of transverse shear function, boundary conditions, plate aspect ratio, slenderness ratio, and gradation indices on the natural frequencies. The developed model provides insights into the significance of natural frequencies in the design of various structural elements, including 2D-FG plates.
引用
收藏
页码:10782 / 10793
页数:12
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