Free vibration analysis of layered functionally graded beams with experimental validation (original) (raw)
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Science and Engineering of Composite Materials, 2015
Free vibration behavior of short beams made of axially layered functionally graded material (FGM) was investigated experimentally and numerically. Beams, which have gradation of the material properties in the axial direction, are fabricated by powder metallurgy technique using different weight fractions of aluminum and silicon carbide powders. In order to determine elasticity modulus of axially layered functionally graded (FG) beams, homogeneous beams containing different weight fractions of Al (aluminum) and SiC (silicon carbide) are produced, and these homogeneous beams are subjected to tensile tests. Density of each homogeneous layer is also calculated experimentally. After determination of the mechanical properties of each layer of the FG beams, they are modeled in a finite element program (ANSYS) according to Timoshenko beam theory, and free vibration analyses are performed. Fundamental frequencies of the axially layered FG beams produced are also calculated experimentally. FG ...
Archives of Materials Science and Engineering, 2021
In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler-Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.
Vibrational behavior of beams made of functionally graded materials by using a mixed formulation
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2020
This paper investigates the vibrational behavior of beams made of functionally graded materials using a mixed formulation. Unlike the other high order shear deformation theories (HSDTs), the proposed formulation is elaborated within a double field of displacements and stresses which offers the possibility of the development of low order linear elements with enhanced accuracy. As well as, the effect of the transverse shear strains and the zero condition of the transverse shear stresses on the top and bottom surfaces are verified. The material characteristics of the beams are described via a power law distribution in order to take into account the continuous variation of the volume fraction of its constituents along the thickness direction. Numerical simulations are conducted to show the influence of power law index, slenderness ratios, and boundary conditions on natural frequencies of functionally graded beams. Results demonstrate the efficiency and the applicability of the model bas...
Free vibration of FGM layered beams by various theories and finite elements
Composites Part B: Engineering, 2014
The Carrera Unified Formulation (CUF) is used to perform free-vibrational analyses of functionally graded (FG) structures. CUF is a hierarchical formulation for obtaining refined structural theories that account for variable kinematic description. These theories can be obtained by expanding the unknown displacement variables over the beam section axes by adopting any kind of function. The number of the terms in the expansions is a free parameter of the analysis. For Taylor-like expansions, the linear case can result in classical beam theories. For the first time in the 1D CUF framework, the Finite Element method is used to solve the governing equations of functionally graded beams which are derived in a weak form by means of the Principle of Virtual Displacements. These equations are written in terms of fundamental nuclei.¨Their forms do not depend on the expansions used. Several structures are considered, including a sandwich beam with FG core, laminated beams, thin-and thick-walled boxes as well as sandwich cylinders. The results are shown in terms of natural frequencies and compared with those available in existing literature.
Modeling and Analyzing the Free Vibration of Simply Supported Functionally Graded Beam
Journal of Aerospace Technology and Management
Euler, Timoshenko and high shear deformation theories to analyze the free vibration of the functionally graded (FG) beam were developed. The mechanical properties of this beam were assumed to differ in thickness direction according to the model of a power-law distribution. The principle of Hamilton was used to find equations of motion. For free vibration, the analytical solution of these equations was presented using the Navier method. The effect of power index, aspect ratio, modulus ratio, and deformation theories on dimensionless frequency were studied numerically by Ansys software and analytically according to different beam theories using the Fortran program. The obtained results from these programs were compared with each other and with some previous research. Results showed an excellent agreement with the previous research. The numerical and analytical results showed that the use of this new FG beam model especially based on first and high shear deformation theories leads to the reduction of dimensionless frequency. It may be concluded that, the including of shear's effect leads to a decrease in the dimensionless frequency. From the modeling and analysis of this model, it is possible to know what is the appropriate design for this FG beam model to reduce the vibration.
Vibration Analysis of Functionally Graded Sandwich Beam with Variable Cross-Section
Mathematical and Computational Applications, 2013
In this study, free vibration behavior of a multilayered symmetric sandwich beam made of Functionally Graded Material (FGM) with variable cross-section is investigated. The elasticity and density of the Functionally Graded (FG) sandwich beam vary through the thickness according to the power and exponential laws by using mixture rules and laminate theory. In order to provide this, fifty layered beam is considered. Each layer is isotropic and homogeneous although the volume fractions of the constituents of the layers are different. Furthermore, the width of the beam varies exponentially along the length of the beam with rectangular cross-section. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using theoretical procedure. The effects of material index, geometric index and slenderness ratio are also discussed. Finally, the obtained results are compared with those in literature and a finite element based commercial program ANSYS® and found to be consistent with each other.
Buckling and Vibrational Analysis of Functionally Graded Materials on Beams
With the rapid progress of advanced manufacturing technology,the functionally graded material (FGM) has emerged as a promising type of composites. By gradually varying the volume fraction of constitute materials, it not only combines the desired merits of several materials, such as the thermal resistance ability of ceramics and the strength of metals, but also eliminates the interlaminar stresses that usually exist in the traditional laminated composites. In this thesis, the analytical investigation is done by using functionally graded materials for beams and plates for their strength, vibrations and buckling behaviour. The Functionally Graded Material with metal Aluminum alloy 6061 using Ceramic as interface zone is taken for analysis. FGM's are considered for volume fractions of K=2 and K=4.Theoretical calculations are done to compute the material properties for each layer up to 10 layers.
Free Vibration Analysis of a Functionally Graded Beam with Finite Elements Method
In this study, free vibration analysis of a functionally graded (FG) beam under various boundary conditions is carried out. Natural frequencies of the FG beam are analysed by using Finite Elements method. The system of equations of motion is derived by using Lagrange's equations with the assumption of Euler-Bernoulli beam theory. The material properties of the beam are assumed to vary through thickness according to power-law form. Different boundary conditions are attained by applying different stiffness values to the springs connected at the ends. The model is validated by comparing the results with previous studies. The effects of various material distributions and spring support values on the natural frequen-cy parameters of the FG beam are discussed in detail.
Free vibration characteristics of a functionally graded beam by finite element method
Applied Mathematical Modelling, 2011
This paper presents the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law. The present model is more effective for replacing the non-uniform geometrical beam with axially or transversally uniform geometrical graded beam. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler-Bernoulli beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Numerical results are presented in both tabular and graphical forms to figure out the effects of different material distribution, slenderness ratios, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of the beam.
Effects of different shear deformation theories on free vibration of functionally graded beams
Free vibration of functionally graded (FG) beams subjected to all sets of boundary conditions is examined in the present article. Different higher-order shear deformation beam theories (SDBTs) have been incorporated for the free vibration response of FG beam. The material properties of FG beam are taken in thickness direction in power-law form and trial functions denoting the displacement components are expressed in algebraic polynomials. Rayleigh-Ritz method is used to estimate frequency parameters in order to handle to all sorts of boundary conditions at the edges by a simple way. Comparison of frequency parameters is made with the existing literature in special cases and new results are also provided after checking the convergence of frequency parameters.