Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment

2016 ◽  
Vol 24 (3) ◽  
pp. 549-564 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Power Law ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Fields ◽  
Electric Voltage ◽  
Fg Nanobeam

In this paper, vibration characteristics of magneto-electro-thermo-elastic functionally graded (METE-FG) nanobeams is investigated in the framework of third order shear deformation theory. Magneto-electro-thermo-elastic properties of FG nanobeam are supposed to vary smoothly and continuously along the thickness based on power-law form. To capture the small size effects, Eringen’s nonlocal elasticity theory is adopted. By using the Hamilton’s principle, the nonlocal governing equations are derived and then solved analytically to obtain the natural frequencies of METE-FG nanobeams. The reliability of proposed model and analytical method in predicting natural frequencies of METE-FG nanobeam is evaluated with comparison to some cases in the literature. Numerical results are provided indicating the influences of several parameters including magnetic potential, external electric voltage, temperature fields, power-law exponent, nonlocal parameter and slenderness ratio on the frequencies of METE-FG nanobeams. It is found that the vibrational behavior of METE-FG nanobeams is significantly impressed by these effects.

scholarly journals Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams

2017 ◽  
Vol 28 (15) ◽  
pp. 2007-2022 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Elastic Foundation ◽  
Power Law ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Electric Voltage ◽  
Electro Magnetic ◽  
Functionally Graded Nanobeam

This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index, and slenderness ratio on the frequencies of the embedded magneto-electro-elastic functionally graded nanobeams are studied.

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

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.

Characteristics of Power Law and Sigmoid FGMs Models in Thermal Effect

2016 ◽  
Vol 829 ◽  
pp. 90-94
Author(s):  
Seok Hyeon Kang ◽  
Ji Hwan Kim
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Virtual Work Principle ◽  
Temperature Dependent Properties

In thermal environment, vibration behavior of Functionally Graded Materials (FGMs) plates is investigated, and the materials are developed with mixing ceramic and metal. Present study is based on the first-order shear deformation theory of plate. Then, mixture methods such as Power law (P-) and Sigmoid (S-) models are chosen. According to a volume fraction, the material properties are assumed to vary continuously through the thickness direction and to be temperature dependent properties. Further, thermal effects are considered as uniform temperature rise and one dimensional heat transfer. For the structure analysis, FEM is used to obtain the natural frequencies based on the virtual work principle.

scholarly journals Finite Element Analysis of Functionally Graded Beams using Different Beam Theories

2020 ◽  
Vol 6 (11) ◽  
pp. 2086-2102
Author(s):  
Farshad Rahmani ◽  
Reza Kamgar ◽  
Reza Rahgozar
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Power Law ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Material Distribution ◽  
Beam Theories

The present study deals with buckling, free vibration, and bending analysis of Functionally Graded (FG) and porous FG beams based on various beam theories. Equation of motion and boundary conditions are derived from Hamilton’s principle, and the finite element method is adopted to solve problems numerically. The FG beams are graded through the thickness direction, and the material distribution is controlled by power-law volume fraction. The effects of the different values of the power-law index, porosity exponent, and different boundary conditions on bending, natural frequencies and buckling characteristics are also studied. A new function is introduced to approximate the transverse shear strain in higher-order shear deformation theory. Furthermore, shifting the position of the neutral axis is taken into account. The results obtained numerically are validated with results obtained from ANSYS and those available in the previous work. The results of this study specify the crucial role of slenderness ratio, material distribution, and porosity condition on the characteristic of FG beams. The deflection results obtained by the proposed function have a maximum of six percent difference when the results are compared with ANSYS. It also has better results in comparison with the Reddy formulae, especially when the beam becomes slender. Doi: 10.28991/cej-2020-03091604 Full Text: PDF

scholarly journals Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Seyyed Amirhosein Hosseini1 ◽  
O. Rahmani2
Keyword(s):  
Size Effect ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Power Index ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Opening Angle ◽  
Simply Supported ◽  
Fg Nanobeam ◽  
Good Agreement

The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam.  The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

scholarly journals Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

2016 ◽  
Vol 33 (1) ◽  
pp. 23-33 ◽  
Author(s):  
F. Ebrahimi ◽  
M. R. Barati
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Higher Order ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Beam Model ◽  
Thickness Direction ◽  
Power Law Distribution

AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

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.

Effect of In-Plane Load and Thermal Environment on Buckling and Vibration Behavior of Two-Dimensional Functionally Graded Tapered Timoshenko Nanobeam

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Roshan Lal ◽  
Chinika Dangi
Keyword(s):  
Thermal Environment ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Energy Principle

Abstract In this work, buckling and vibration characteristics of two-dimensional functionally graded (FG) nanobeam of nonuniform thickness subjected to in-plane and thermal loads have been analyzed within the frame work of Timoshenko beam theory. The beam is tapered by linear variation in thickness along the length. The temperature-dependent material properties of the beam are varying along thickness and length as per a power-law distribution and exponential function, respectively. The analysis has been presented using Eringen’s nonlocal theory to incorporate the size effect. Hamilton’s energy principle has been used to formulate the governing equations of motion. These resulting equations have been solved via generalized differential quadrature method (GDQM) for three combinations of clamped and simply supported boundary conditions. The effect of in-plane load together with temperature variation, nonuniformity parameter, gradient indices, nonlocal parameter, and slenderness ratio on the natural frequencies is illustrated for the first three modes of vibration. The critical buckling loads in compression have been computed by putting the frequencies equal to zero. A significant contribution of in-plane load on mechanical behavior of two-directional functionally graded nanobeam with nonuniform cross section has been noticed. Results are in good accordance.

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