Free vibration of FGM Timoshenko beams with through-width delamination

Liu, Shirong; Fan, Liang‐Liang

doi:10.1007/s11433-013-5248-5

Cited by 10 publications

(6 citation statements)

References 20 publications

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“…It is well known that the EBBT, or the classical beam theory, is the simplest one, in which it is assumed that the cross-section is perpendicular to the bending line so that the transverse shear deformation is neglected [1][2][3][4][5][6][7][8][9] . However, in the TBT [10][11][12][13][14][15][16][17][18][19] or the first-order shear deformation beam theory, it allows a rotation between the cross-section and the bending line and takes into account rotational inertia effects. This rotation comes from a shear deformation which is considered by introducing a shear deformation correction factor.…”

Section: 2mentioning

confidence: 99%

“…In the framework of the first-order shear deformation theory, or the TBT, other researchers dealt with the dynamic response of FGM beams [10][11][12][13][14][15][16][17][18][19] . Sina et al [10] used a new beam theory different from the traditional first-order shear deformation beam theory to analyze the free vibration of FGM beams.…”

Section: Introductionmentioning

confidence: 99%

“…More recently, Rajasekaran and Tochaei [17] used both the differential transformation element method (DTEM) and the differential quadrature element method (DQEM) to carry out the free vibration analysis of axially functionally graded tapered beams. By the DQEM, Li and Fan [18] studied free vibration of FGM beams with a through-width delamination. Numerical results of the first eight natural frequencies of the delaminated FGM beam with clamped-clamped ends were presented to show the effects of the parameters of the material gradients and the size and location of the delamination on the vibration responses.…”

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of functionally graded material beams based on Levinson beam theory

Wang

Liu

2016

Appl. Math. Mech.-Engl. Ed.

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Free vibration response of functionally graded material (FGM) beams is studied based on the Levinson beam theory (LBT). Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.

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Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of functionally graded material beams based on Levinson beam theory

Wang

Liu

2016

Appl. Math. Mech.-Engl. Ed.

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“…For example, Xiang and Yang [3] carried out the free and forced vibration analysis of a laminated FGM Timoshenko beam with variable thickness under heat conduction. Li and Fan [4] proposed natural frequencies solutions for the free vibration of a FGM beam with a through-width delamination based on the Timoshenko beam theory. Leissa and Narita [5] investigated natural frequencies of a simply supported circular plate using Classical plate theory with ordinary and modified Bessel functions of the first kind.…”

Section: Introductionmentioning

confidence: 99%

Shooting method for free vibration of FGM Reissner-Mindlin circular plates resting on elastic foundation in thermal environments

Li¹,

Weidi²,

Zhu³

2017

J. vibroeng.

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This paper presents a free vibration analysis of functionally graded Reissner-Mindlin circular plates with various supported boundaries in thermal environments. A FGM consisting of metal and ceramic was considered in the study. Based on the geometric equation, physical equation and equilibrium equation of thick plate, taking into account the transverse shearing deformation, the free vibration equation of the axisymmetric FGM moderately thick circular plates was derived in terms of the middle surface angles of rotation and lateral displacement. The material properties of the plate were assumed to vary continuously in the thickness direction according a power law. By using shooting method to solve the coupled ordinary differential equations with different boundary conditions, the natural frequencies of FGM thick circular plates were obtained numerically. The effects of material gradient property, thickness ratio and boundary conditions on the natural frequencies were discussed in detail.

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“…The same authors [28] studied the flapwise bending vibration analysis of functionally graded rotating double-tapered beams. Free vibration of FG Timoshenko beams with through-width delamination have been investigated by Li and Fan [29]. Ke et al [30] coped with the non-linear vibration of edged cracked FG beams using differential quadrature method and Timoshenko beam model.…”

Section: Introductionmentioning

confidence: 99%

Quasi-3D beam models for the computation of eigenfrequencies of functionally graded beams with arbitrary boundary conditions

Fazzolari

2016

Composite Structures

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Free vibration of FGM Timoshenko beams with through-width delamination

Cited by 10 publications

References 20 publications

Free vibration analysis of functionally graded material beams based on Levinson beam theory

Free vibration analysis of functionally graded material beams based on Levinson beam theory

Shooting method for free vibration of FGM Reissner-Mindlin circular plates resting on elastic foundation in thermal environments

Quasi-3D beam models for the computation of eigenfrequencies of functionally graded beams with arbitrary boundary conditions

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