Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment

2018 ◽  
Vol 18 (01) ◽  
pp. 1850013 ◽  
Author(s):  
Ankit Gupta ◽  
Mohammad Talha
Keyword(s):  
Free Vibration ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Future Studies ◽  
Graded Material ◽  
Vibration Responses ◽  
Free Vibration Response

This paper examines the influence of porosities on the flexural and free vibration response of functionally graded material (FGM) plates based on the authors’ recently developed non-polynomial higher-order shear and normal deformation theory. The theory accommodates the nonlinear variation in the in-plane and transverse displacements in the thickness coordinates. It also contains the hyperbolic shear strain shape function in the displacement field with only four unknowns. A new mathematical model has also been proposed to incorporate the effects of porosity in the FGM plate. Various numerical examples have been solved to ascertain the accuracy, efficiency, and applicability of the present formulation. The effects of porosity, volume fraction index, plate thickness, aspect ratio, boundary conditions and temperature have been discussed in details. The obtained results can be treated as a benchmark for future studies.

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.

Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect

2017 ◽  
Vol 232 (12) ◽  
pp. 2244-2262 ◽  
Author(s):  
Suman Pal ◽  
Debabrata Das
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Coriolis Effect ◽  
Governing Equations

The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.

Nonlinear Analysis of a Thin Circular Functionally Graded Plate and Large Deflection Effects on the Forces and Moments

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
A. Allahverdizadeh ◽  
A. Rastgo ◽  
M. H. Naei
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Functionally Grade ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Harmonic Vibrations ◽  
Graded Material

Nonlinear analysis of a thin circular functionally grade plate is formulated in terms of von Karman’s dynamic equations. The plate thickness is constant and temperature-dependent functionally graded material (FGM) properties vary through the thickness of the plate. Forces and moments of the plate, due to large vibration amplitudes, are developed in this paper by solving the governing equations for harmonic vibrations. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is influential in forces, moments, and FGM properties.

Free Vibration Responses of Functionally Graded Spherical Shell Panels Using Finite Element Method

2013 ◽  
Author(s):  
Vishesh Ranjan Kar ◽  
Subrata Kumar Panda
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Spherical Shell ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Vibration Responses ◽  
Support Conditions

Free vibration responses of functionally graded spherical shell panels are investigated in the present article. A general mathematical model is developed based on higher order shear deformation theory mid-plane kinematics. The effective material properties are graded in the thickness direction according to a power-law distribution and it varies continuously from metal (bottom surface) to ceramic (top surface). The model is discretized using a nine noded quadrilateral Lagrangian element. A convergence test has been done with different mesh refinement and compared with the available published results. In addition to that the present study includes an ANSYS model check with the developed mathematical model to show the efficacy. New results are computed for different parameters such as volume fraction, thickness ratio, curvature ratio and support conditions which indicates the effect of parametric study on non-dimensional frequency parameters.

Free Vibration Analysis of Cylindrical Micro/Nano-Shell Reinforced with CNTRC Patches

2021 ◽  
pp. 2150040
Author(s):  
Yaser Heidari ◽  
Mohammad Arefi ◽  
Mohsen Irani-Rahaghi
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Nonlocal Elasticity Theory ◽  
Metal Core ◽  
Vibration Responses

This paper studies free vibration analysis of cylindrical micro/nano shell made from a mixture of ceramic/metal, reinforced with some carbon-nanotube-reinforced (CNTRC) patches, based on shear deformation theory and nonlocal elasticity theory. Extended rule of mixture and power law model are utilized to find effective properties of composite patches and the ceramic/metal core, respectively. The main aim of this work is to investigate the effect of characteristics of attached CNTRC patches on the free vibration responses. It is concluded that some important parameters such as number and angle of composite patches as well as their volume fraction, and some geometric parameters have significant influence on the free vibration responses.

FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

2013 ◽  
Vol 13 (01) ◽  
pp. 1350004 ◽  
Author(s):  
D. K. JHA ◽  
TARUN KANT ◽  
R. K. SINGH
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Normal Deformation ◽  
Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

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.

FREE VIBRATION OF FUNCTIONALLY GRADED ARBITRARY STRAIGHT-SIDED QUADRILATERAL PLATES RESTING ON ELASTIC FOUNDATIONS

2011 ◽  
Vol 03 (04) ◽  
pp. 825-843 ◽  
Author(s):  
A. ALIBEYGI BENI
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Computational Domain ◽  
Fg Plates

The free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates rested on two-parameter elastic foundation and in thermal environment is presented. The formulation is based on the first-order shear deformation theory (FSDT). The material properties are assumed to be temperature-dependent and graded in the thickness direction. The solution procedure is composed of transforming the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. After studying the convergence of the method, its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for isotropic rectangular and FG rectangular and skew plates. Then, the effects of thickness-to-length ratio, elastic foundation parameters, volume fraction index, geometrical shape and the boundary conditions on the frequency parameters of the FG plates are studied.

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