Nonlinear free and forced vibration analysis of thin circular functionally graded plates

Allahverdizadeh, A.; Naei, Mohammad Hasan; Bahrami, Mohammad

doi:10.1016/j.jsv.2007.08.011

Cited by 140 publications

(51 citation statements)

References 27 publications

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“…From this table, it is observed that the nonlinear frequency increases with increasing vibration amplitudes. It can be also observed that the results calculated via the present model exhibit a higher increase of the frequency compared with those obtained by Haterbouch and Benamar 2 with a discrepancy of 6.22% for a value of the non-dimensional amplitude w * max = 1.0 and 0.41% for a non-dimensional vibration amplitude w * max = 0.2. This may be attributed to the negligence of in-plane displacements in the present theory.…”

Section: Amplitude Frequency Dependencesupporting

confidence: 48%

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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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Section: Amplitude Frequency Dependencesupporting

confidence: 48%

“…Allahverdizadeh et al 2 investigated the nonlinear free and forced vibration of thin circular FG plates. Praveen and Reddy 3 conducted the nonlinear transient thermoelastic analysis of FG ceramic-metal plates using the finite element 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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show abstract

“…An analytical solution was proposed by Woo et al 2006 to analyzed the nonlinear vibration of functionally graded plates using classic plate theory. Allahverdizadeh et al (2008aAllahverdizadeh et al ( , 2008b have studied the non-linear forced and free vibration analysis of circular functionally graded plate in thermal environment. The p-version of the FEM has been applied to investigate the non-linear free vibration of elliptic sector plates and functionally graded sector plates by (Belalia & Houmat 2010;2012).…”

Section: Introductionmentioning

confidence: 99%

Linear and non-linear vibration analysis of moderately thick isosceles triangular FGPs using a triangular finite p-element

Belalia

2017

Mech Adv Mater Mod Process

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Background: The geometrically non-linear formulation based on Von-Karman's hypothesis is used to study the free vibration isosceles triangular plates by using four types of mixtures of functionally graded materials (FGMs -AL/ AL 2 O 3 , SUS304/Si 3 N 4 , Ti-AL-4V/Aluminum oxide, AL/ZrO 2 ). Material properties are assumed to be temperature dependent and graded in the thickness direction according to power law distribution. Methods: A hierarchical finite element based on triangular p-element is employed to define the model, taking into account the hypotheses of first-order shear deformation theory. The equations of non-linear free motion are derived from Lagrange's equation in combination with the harmonic balance method and solved iteratively using the linearized updated mode method.

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“…Therefore, many researchers have proposed the different methods to detect and localize the crack in the structures. [1][2][3][4][5][6][7] One of the inhomogeneous composite structures is FGM, which have great applications in aerospace vehicles, nuclear reactors, power generators and automobile structures. A crack has occurred in FGM structures and numerous researchers have investigated the fracture analysis of these materials.…”

Section: Introductionmentioning

confidence: 99%

“…A crack has occurred in FGM structures and numerous researchers have investigated the fracture analysis of these materials. [3][4][5][6][7] The location and size of an open edge crack has been determined in an FGM beam by Yu and Chu. 8 They utilized the p-version finite-element method to estimate the transverse vibration of an FGM beam.…”

Section: Introductionmentioning

confidence: 99%

Application of R2PSO Algorithm in Crack Detection of Functionally Graded Beams

Eftekhar¹,

Kamyab²,

Eftekhari³

et al. 2017

IJAV

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A fault diagnosis procedure based on r2PSO algorithm-a newly developed version of particle swarm optimization (PSO)-is presented for detecting crack depth and location in a functionally graded material (FGM) cantilever beam. The governing equation and boundary conditions are obtained by using the extended Hamilton's principle, and the characteristic equation is obtained as a function of position ratio and depth ratio of crack. Identification of the crack is formulated as an optimization problem. The r2PSO algorithm is used to find the optimal solution of the cost function, which is based on the summation of the absolute value of the characteristic equation for three natural frequencies. The position ratio and depth ratio of crack are computed by algorithm, when three natural frequencies of FGM beam are entered to algorithm as inputs. The obtained results confirm the applicability and efficiency of r2PSO to calculate the parameters of crack with high accuracy and suitable convergence rate.

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Nonlinear free and forced vibration analysis of thin circular functionally graded plates

Cited by 140 publications

References 27 publications

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

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

Linear and non-linear vibration analysis of moderately thick isosceles triangular FGPs using a triangular finite p-element

Application of R2PSO Algorithm in Crack Detection of Functionally Graded Beams

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