Thermal vibration of functionally graded porous beams with classical and non-classical boundary conditions using a modified Fourier method

Eiadtrong, Suppakit; Wattanasakulpong, Nuttawit; Vo, Thuc P.

doi:10.1007/s00707-022-03401-5

Cited by 7 publications

(1 citation statement)

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“…These analytical investigations have captured the interest of researchers as they contribute to revealing the unique properties of FGBs and provide fundamental insights for future engineering applications. Therefore, using analytical methods, numerous studies have emerged that analyze the effect of porosity on one-directional FGBs' static, free vibration, and buckling behaviors [23][24][25][26][27][28][29][30][31][32][33]. As a continuation of these studies, research has been presented that examines the effect of porosity on the mechanical behaviors of bi-directional FGBs using analytical methods.…”

Section: Introductionmentioning

confidence: 99%

Mixed series solution for vibration and stability of porous bi-directional functionally graded beams

Turan

2024

Arch Appl Mech

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A new analytical solution based on the Ritz method is presented in this paper for analyzing the free vibration and buckling behavior of porous bi-directional functionally graded (2D-FG) beams under various boundary conditions. The solution is based on first-order shear deformation theory (FSDT). The selection of solution functions used in Ritz methods distinguishes the methods from each other and determines the accuracy of the analytical solution. To accurately capture the system's behavior and achieve the desired results, these functions have been carefully selected as a combination of polynomial and trigonometric expressions tailored as mixed series functions for each boundary condition. The study considers three types of porosity, namely PFG-1, PFG-2, and PFG-3. The equations of motion are derived using Lagrange's principle, taking into account the power-law variation of the beam material components throughout the volume. The non-dimensional fundamental frequencies and critical buckling loads are calculated for different boundary conditions, gradation exponents in the x and z directions (px, pz), slenderness (L/h), porosity coefficient (e), and porosity types. Initially, the accuracy of the mixed series functions is investigated for non-porous bi-directional functionally graded beams, and the numerical results are compared with existing literature to validate the proposed solution. Subsequently, the paper focuses on analyzing the influence of porosity on the free vibration and buckling behavior of bi-directional functionally graded beams using the developed solution method.

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