Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

Ebrahimi, Farzad; Naei, Mohammad Hasan; Rastgoo, Abbas

doi:10.1007/s12206-009-0358-8

Cited by 45 publications

(9 citation statements)

References 37 publications

(38 reference statements)

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“…By Substituting Eqs. (9), (12) and (14) into Eq. (7) and setting the coefficients of du, dw and d ow ox to zero, the following Euler-Lagrange equation can be obtained:…”

Section: Kinematic Relationsmentioning

confidence: 99%

“…Thus, FGMs have received wide applications in modern industries including aerospace, mechanical, electronics, optics, chemical, biomedical, nuclear, and civil engineering to name a few during the past two decades. Motivated by these engineering applications, FGMs have also attracted intensive research interests, which were mainly focused on their static, dynamic and vibration characteristics of FG structures [11,12]. Since functionally graded structures are most commonly used in high temperature environment, in the last decade, beams and plates made of FGMs have found wide applications as structural elements in modern industries such as aeronautics/astronautics manufacturing industry, mechanical engineering and engine combustion chamber, nuclear engineering and reactors.…”

Section: Introductionmentioning

confidence: 99%

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Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities

2015

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In this study, thermo-mechanical vibration analyzes of functionally graded (FG) beams made of porous material subjected various thermal loadings are carried out by presenting a Navier type solution and employing a semi analytical differential transform method (DTM) for the first time. Three types of thermal loadings, namely, uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-mechanical material properties of FGM beam are supposed to vary continuously along the thickness direction according to the powerlaw form, which is modified to approximate the material properties with the porosity phases. The material properties of FG porous beam are assumed to be temperature-dependent. The governing equations of motion are derived through Hamilton's principle and they are solved applying DTM. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG beams as compared to analytical results and also some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies of the temperature-dependent FG beams in detail. It is explicitly shown that the vibration behaviour of porous FGM beams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM beams with porosity phases.

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“…By Substituting Eqs. (9), (12) and (14) into Eq. (7) and setting the coefficients of du, dw and d ow ox to zero, the following Euler-Lagrange equation can be obtained:…”

Section: Kinematic Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities

2015

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“…Hence, FGMs have received wide engineering applications in modern industries including aerospace, nuclear energy, turbine components, rocket nozzles, and critical furnace parts [1][2][3][4]. The advantages of using FGM structures in general engineering structures have been increasingly recognized in recent decades so it is important to understand behaviors of engineering structures made of FGM such as vibration, static, and dynamic behavior of the FG beams and plates often found in general engineering structures [5,6].…”

Section: Introductionmentioning

confidence: 99%

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

Ebrahimi

Jafari

2016

Journal of Engineering

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In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

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“…A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and for an associated eigenvector of spline coefficients. Ebrahimi 13 studied geometrically nonlinear vibration of a piezoelectrically actuated FGM plate with an initial large deformation, based on Kirchhoff's-Love hypothesis with Von-Karman-type geometrical large nonlinear deformation. Recently, Kermani, Ghayour, and Mirdamad 14 reported a free vibration analysis of multi-directional FG circular and annular plates using a semi analytical/numerical method called state space-based differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Free Axisymmetric Vibrations Analysis of Thin Circular Functionally Graded Plates Using Iterative and Explicit Analytical Solution

Kaak¹,

Bikri²,

Benamar³

2016

IJAV

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This paper deals with nonlinear free axisymmetric vibrations of functionally graded (FG) thin circular plates whose properties vary in thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young's modulus and mass density of the material along the thickness direction, whereas Poisson's ratio is assumed to be constant. The theoretical model is based on Hamilton's principle and spectral analysis using a basis of admissible Bessel's functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of nonlinear algebraic equations, is solved numerically. The nonlinear to linear frequency ratios are presented for various values of the volume fraction index n showing a hardening type nonlinearity. The distribution of the radial bending stresses associated to the nonlinear mode shape is also given for various vibration amplitudes and compared with those predicted by the linear theory. Then, explicit analytical solutions are presented, based on the semi-analytical model previously developed by El Kadiri et al. for beams and rectangular plates. This model allows direct and easy calculation for the first nonlinear axisymmetric mode shape with its associated nonlinear frequencies and nonlinear bending stresses of FG circular plates, which are expected to be very useful in engineering applications and in further analytical developments. An excellent agreement is found with the results obtained by the iterative method.

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Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

Cited by 45 publications

References 37 publications

Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities

Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

Geometrically Nonlinear Free Axisymmetric Vibrations Analysis of Thin Circular Functionally Graded Plates Using Iterative and Explicit Analytical Solution

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