Vibration analysis of FG rotating plate using nonlinear-FEM

2019 ◽  
Vol 15 (1) ◽  
pp. 26-49 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Mathematical Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Content Type ◽  
Non Linear ◽  
Rotating Plate

Purpose The purpose of this paper is to investigate the linear and non-linear free vibration of a functionally graded material (FGM) rotating cantilever plate in the thermal environment. The study employs the development of a non-linear mathematical model using the higher order shear deformation theory in which the traction free condition is applied to derive the simplified displacement model with seven field variables instead of nine. Design/methodology/approach A mathematical model is developed based on the higher order shear deformation theory using von-Karman type non-linearity. The rotating plate domain has been discretized into C0 eight-noded quadratic serendipity elements with node wise 7 degrees of freedom. The material properties are considered temperature dependent and graded along the thickness direction obeying a simple power law distribution in terms of the volume fraction of constituents, based on Voigt’s micromechanical method. The governing equations are derived using Hamilton’s principle and are solved using the direct iterative method. Findings The importance of the present mathematical model developed for numerical analysis has been stated through the comparison studies. The results provide an insight into the vibration response of FGM rotating plate under thermal environment. The influence of various parameters like setting angle, volume fraction index, hub radius, rotation speed parameter, aspect ratio, side-thickness ratio and temperature gradient on linear and non-linear frequency parameters is discussed in detail. Originality/value A non-linear mathematical model is newly developed based on C0 continuity for the functionally graded rotating plate considering the 1D Fourier equation of heat conduction. The present findings can be utilized for the design of rotating plates made up of a FGM in the thermal environment under real-life situations.

Mechanical behaviour of functionally graded plates under static and dynamic loading

2010 ◽  
Vol 225 (2) ◽  
pp. 326-333 ◽  
Author(s):  
A H Akbarzadeh ◽  
S K Hosseini Zad ◽  
M R Eslami ◽  
M Sadighi
Keyword(s):  
Shear Deformation ◽  
Dynamic Loading ◽  
Mechanical Behaviour ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Fourier Series Expansion ◽  
Inversion Method

This article presents an analytical solution for the mechanical behaviour of rectangular plates made of functionally graded materials (FGMs) based on the first-order shear deformation theory (FSDT) and the third-order shear deformation theory (TSDT). The FGM plate is assumed to be graded across the thickness. The material properties of the FGM plate are assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituent materials, except Poisson's ratio, which is assumed to be constant. The plate is subjected to a lateral mechanical load on its upper surface. The equations of motion are written based on displacement fields. The partial differential equations have been solved by the Fourier series expansion. Using the Laplace transform, unknown variables are obtained in the Laplace domain. The resulting formulations enable one to perform the static, dynamic, and free vibration analysis for both FSDT and TSDT plates. Employing the analytical Laplace inversion method and numerical time integration technique based on the Newmark method, time function solution of the problem is obtained and the unknown parameters are derived for a dynamic loading situation. Finally, the natural frequencies of the plate are obtained and dynamic responses are presented in the form of combinations of different frequencies. The results are verified with those reported in the literature.

scholarly journals A COMBINED STRAIN ELEMENT TO FUNCTIONALLY GRADED STRUCTURES IN THERMAL ENVIRONMENT

2020 ◽  
Vol 60 (6) ◽  
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Element Analysis ◽  
First Order ◽  
Graded Structures

Functionally graded materials are commonly used in a thermal environment to change the properties of constituent materials. They inherently withstand high temperature gradients due to a low thermal conductivity, core ductility, low thermal expansion coefficient, and many others. It is essential to thoroughly study mechanical responses of them and to develop new effective approaches for an accurate prediction of solutions. In this paper, a new four-node quadrilateral element based on a combined strain strategy and first-order shear deformation theory is presented to achieve the behaviour of functionally graded plate/shell structures in a thermal environment. The main notion of the combined strain strategy is based on the combination of the membrane strain and the shear strain related to tying points as well as bending strain with respect to a cell-based smoothed finite element method. Due to the finite element analysis, the first-order shear deformation theory (FSDT) is simple to implement and apply for structures, but the shear correction factors are used to achieve the accuracy of solutions. The author assumes that the temperature distribution is uniform throughout the structure. The rule of mixtures is also considered to describe the variation of material compositions across the thickness. Many desirable characteristics and the enforcement of this element are verified and proved through various numerical examples. Numerical solutions and a comparison with other available solutions suggest that the procedure based on this new combined strain element is accurate and efficient.

Temperature influences on shear stability of a nanosize plate with piezoelectricity effect

2018 ◽  
Vol 14 (1) ◽  
pp. 125-142 ◽  
Author(s):  
Mohammad Malikan
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Electric Voltage ◽  
Content Type ◽  
Shear Stability ◽  
First Order ◽  
First Time

Purpose The purpose of this paper is to predict the mechanical behavior of a piezoelectric nanoplate under shear stability by taking electric voltage into account in thermal environment. Design/methodology/approach Simplified first-order shear deformation theory has been used as a displacement field. Modified couple stress theory has been applied for considering small-size effects. An analytical solution has been taken into account for various boundary conditions. Findings The length scale impact on the results of any boundary conditions increases with an increase in l parameter. The effect of external electric voltage on the critical shear load is more than room temperature effects. With increasing aspect ratio the critical shear load decreases and external electric voltage becomes more impressive. By considering piezoelectric nanoplates, it is proved that the temperature rise cannot become a sensitive factor on the buckling behavior. The length scale parameter has more effect for more flexible boundary conditions than others. By considering nanosize, the consideration has led to much bigger critical load vs macro plate. Originality/value In the current paper for the first time the simplified first-order shear deformation theory is used for obtaining governing equations by using nonlinear strains for shear buckling of a piezoelectric nanoplate. The couple stress theory for the first time is applied on the nonlinear first-order shear deformation theory. For the first time, the thermal environment effects are considered on shear stability of a piezoelectric nanoplate.

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

2019 ◽  
Vol 50 (9-11) ◽  
pp. 267-290
Author(s):  
Ali Bakhsheshy ◽  
Hossein Mahbadi
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Scale Parameter ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
The Third

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

scholarly journals New Shape Function for the Bending Analysis of Functionally Graded Plate

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2381 ◽  
Author(s):  
Dragan Čukanović ◽  
Aleksandar Radaković ◽  
Gordana Bogdanović ◽  
Milivoje Milanović ◽  
Halit Redžović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shape Function ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Transverse Load ◽  
Shape Functions ◽  
Bending Analysis ◽  
Pasternak Elastic Foundation

The bending analysis of thick and moderately thick functionally graded square and rectangular plates as well as plates on Winkler–Pasternak elastic foundation subjected to sinusoidal transverse load is presented in this paper. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. This paper presents the methodology of the application of the high order shear deformation theory based on the shape functions. A new shape function has been developed and the obtained results are compared to the results obtained with 13 different shape functions presented in the literature. Also, the validity and accuracy of the developed theory was verified by comparing those results with the results obtained using the third order shear deformation theory and 3D theories. In order to determine the procedure for the analysis and the prediction of behavior of functionally graded plates, the new program code in the software package MATLAB has been developed based on the theories studied in this paper. The effects of transversal shear deformation, side-to-thickness ratio, and volume fraction distributions are studied and appropriate conclusions are given.

Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory

2018 ◽  
Vol 233 (6) ◽  
pp. 2056-2073 ◽  
Author(s):  
S Parida ◽  
SC Mohanty
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Graded Material

In the present article, a higher order shear deformation theory is used to develop a finite element model for the free vibration analysis of a rotating functionally graded material plate in the thermal environment. The model is based on an eight-noded isoparametric element with seven degrees-of-freedom per node. The material properties are temperature dependent and graded along its thickness according to a simple power law distribution in terms of volume fraction of the constituents. The general displacement equation provides C0 continuity, and the transverse shear strain undergoes parabolic variation through the thickness of the plate. Therefore, the shear correction factor is not used in this theory. The obtained results are compared with the published results in the literature to determine the accuracy of the method. The effects of various parameters like hub radius, rotation speed, aspect ratio, thickness ratio, volume fraction index, and temperature on the frequency of rotating plate are investigated.

scholarly journals Free Vibration Response of Four-Parameter Functionally Graded Thick Spherical Shell Formulation on Higher-Order Shear Deformation Theory

2020 ◽  
Vol 9 (3) ◽  
pp. 464-473
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Power Law ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Skew Angle

This paper emphasizes on the free vibration (FV) responses of functionally graded thick spherical shell in rectangular form using traditional mathematical formulation on finite element method and governed by Higher order shear deformation theory (HOSDT). A functionally graded spherical shell made up of metal-rich on the top surface and in contrast, base surface of the model is ceramic-rich. The FG volume fraction of four-parameter power-law material constituents assumed in the thickness direction. To highlight the potential for the current method, convergence studies, and validation tests performed to establish the stability and accuracy attained by the current approach. The parametric studies presented to scrutinize the influence of choice of four parameters employed through power-law distribution. The eminence effect of spherical shell geometrical properties, and different types of support conditions, skew angle on the FV behavior of non-dimensional frequency responses examined in detail.

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