Free vibration characteristics of a functionally graded beam by finite element method

Abstract This paper presents an analytical investigation on the free vibration characteristics of symmetric sandwich conical shell with functionally graded material (FGM) face sheets using finite element method. Sandwich-type structures offer higher stiffness to weight ratio with excellent thermal barrier in high temperature application extending the operational life of the component. The sandwich-type conical structure used in the advanced supersonic and hypersonic space vehicles. The material properties of FGM face sheets are considered to be varied in thickness direction as per simple power law distribution in terms of the volume fractions of the FGM constituents. The core layer is considered as homogeneous and made of an isotropic material (Titanium alloy-Ti–6Al–4V). A finite element method is used to reduce the governing equations of vibration problem. The QR iteration algorithm used to solve the standard eigen value problem for determine the natural frequencies. Convergence studies are performed in respect of mesh sizes to substantiate the accuracy of the proposed method. Computer codes developed to obtain the numerical results for the combined effects of twist angle and rotational speed on the free vibration characteristics of symmetric sandwich conical shell with FGM face sheets. A detailed numerical study is carried out to examine the influence of the sandwich plate type, volume fraction index on the free vibration characteristics. The typical mode shapes are also illustrated for different cases.

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An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

Mathematical Problems in Engineering ◽

10.1155/2020/7520209 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

The-Van Tran ◽

Tuan-Duy Tran ◽

Quoc Hoa Pham ◽

Trung Nguyen-Thoi ◽

Van Ke Tran

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Vibration ◽

Mass Density ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Dispersion Pattern ◽

Strain Smoothing ◽

Triangular Elements ◽

Element Method

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young’s modulus estimated via the Halpin–Tsai model and Poisson’s ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.

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