A Comprehensive Review on Vibration Analysis of Functionally Graded Beams

2020 ◽  
Vol 20 (04) ◽  
pp. 2030002 ◽  
Author(s):  
Parham Zahedinejad ◽  
Chen Zhang ◽  
Haifeng Zhang ◽  
Shuai Ju
Keyword(s):  
Numerical Methods ◽  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Structural Components ◽  
Sensors And Actuators ◽  
Engineering Structures ◽  
Comprehensive Review ◽  
Structural Applications

Beams and beam structures are structural components commonly used in mechanical, aerospace, nuclear, and civil engineering. To meet the different engineering design limitations such as operational conditions, weight, and vibrational characteristics, these components may be made of various materials such as functionally-graded materials (FGMs), composites, and homogeneous materials. Functionally-graded (FG) beams play a key role not only in classical structural applications, but also have vast applications in thermal, electric-structural and electric-thermal-structural systems, e.g. in the form of FG beam energy harvesters, sensors and actuators. In all these applications, using new materials like FGMs can greatly improve the efficiency of the structural components and systems. Since FG beams are mostly used as moving components in engineering structures, vibration analysis of these components has been studied by numerous researchers. In order to solve the governing equation and related boundary conditions of the FG beams, powerful numerical methods with a high level of accuracy and fast rate of convergence are often required. The differential quadrature method (DQM) is a powerful and reliable numerical method which has been extensively used by researchers to perform the vibration analyses of FG structures in the last decade. In this paper, firstly various mathematical models which have been used to express the material properties of FGMs are reviewed. Secondly different elasticity theories which have been applied in vibration analysis of FG beams are summarized. In addition, a review on the DQM and its applications is presented. At the next step, a comprehensive review on free vibration analyses of FG beams based on different elasticity theories and in particular those using the DQM is performed. In continue, a brief review on the application of other numerical methods in vibration analysis of FG beams is presented. Moreover, because of the importance of nonlinear vibration analysis of FG beams, a review on the application of various numerical methods and different elasticity theories on nonlinear vibration analysis of FG beams is performed. Finally, a brief review on linear and nonlinear vibration analysis of FG microbeams, as a special type of FG beams, is presented.

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells

2021 ◽  
pp. 095440622110458
Author(s):  
Vahid Movahedfar ◽  
Mohammad M Kheirikhah ◽  
Younes Mohammadi ◽  
Farzad Ebrahimi
Keyword(s):  
Nonlinear Vibration ◽  
Material Properties ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Scale Parameters ◽  
Functionally Graded Piezoelectric ◽  
Doubly Curved

Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes.

Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface

2019 ◽  
Vol 233 (10) ◽  
pp. 2140-2159 ◽  
Author(s):  
Ehsan Arshid ◽  
Ali Kiani ◽  
Saeed Amir
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Elastic Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Neutral Surface ◽  
Sensors And Actuators

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

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