Free vibration analysis of rotating axially functionally graded-tapered beams using Chebyshev–Ritz method

Fang, Jianshi; Zhou, Ding

doi:10.1179/1432891714z.0000000001289

Cited by 9 publications

(5 citation statements)

References 15 publications

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Section: Introductionmentioning

confidence: 99%

“…In addition, the spectral method [29][30][31][32][33][34] is used in beam section optimization and vibration analysis because of its rapid convergence and high accuracy. Fang et al [29,30] studied the free vibration of rotating tapered beams made of axially functional graded materials by using the Chebyshev-Ritz method. Soltani et al [31] presented a new hybrid approach for stability and free vibration analyses of axially functionally graded non-uniform beams resting on a constant Winkler-Pasternak elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Liu,

Huang,

Zhao

2023

Aerospace

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Structures with inhomogeneous materials, non-uniform cross-sections, non-uniform supports, and subject to non-uniform loads are increasingly common in aerospace applications. This paper presents a simple and unified numerical dynamics model for all beams with arbitrarily axially varying cross-sections, materials, foundations, loads, and general boundary conditions. These spatially varying properties are all approximated by high-order Chebyshev expansions, and discretized by Gauss–Lobatto sampling. The discrete governing equation of non-uniform axially functionally graded beams resting on variable Winkler–Pasternak foundations subjected to non-uniformly distributed loads is derived based on the Euler–Bernoulli beam theory. A projection matrix method is employed to simultaneously assemble spectral elements and impose general boundary conditions. Numerical experiments are performed to validate the proposed method, considering different inhomogeneous materials, boundary conditions, foundations, cross-sections, and loads. The results are compared with those reported in the literature and obtained by the finite element method, and excellent agreement is observed. The convergence, accuracy, and efficiency of the proposed method are demonstrated.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Liu,

Huang,

Zhao

2023

Aerospace

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“…Zhao et al [50] introduced a new approach based on Chebyshev polynomial theory to investigate the free vibration of AFG Euler-Bernoulli and Timoshenko beams with nonuniform cross sections. Fang and Zhou [51,52] researched the modal analysis of rotating AFG-tapered Euler-Bernoulli and Timoshenko beams with various boundary conditions employing the Chebyshev-Ritz method. Li et al [53,54] obtained the exact solutions for the free vibration of FGM beams with material profiles and cross-sectional parameters varying exponentially in the axial direction, where assumptions of Euler-Bernoulli and Timoshenko beam theories have been applied, respectively.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Axially Functionally Graded Beam

Cao¹,

Wang²,

Hu³

et al. 2020

Mechanics of Functionally Graded Materials and Structures

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Axially functionally graded (AFG) beam is a special kind of nonhomogeneous functionally gradient material structure, whose material properties vary continuously along the axial direction of the beam by a given distribution form. There are several numerical methods that have been used to analyze the vibration characteristics of AFG beams, but it is difficult to obtain precise solutions for AFG beams because of the variable coefficients of the governing equation. In this topic, the free vibration of AFG beam using analytical method based on the perturbation theory and Meijer G-Function are studied, respectively. First, a detailed review of the existing literatures is summarized. Then, based on the governing equation of the AFG Euler-Bernoulli beam, the detailed analytic equations are derived on basis of the perturbation theory and Meijer G-function, where the nature frequencies are demonstrated. Subsequently, the numerical results are calculated and compared, meanwhile, the analytical results are also confirmed by finite element method and the published references. The results show that the proposed two analytical methods are simple and efficient and can be used to conveniently analyze free vibration of AFG beam.

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“…11 discussed the effect of the structural gravitational force as well as the tilt and pitch angle of the blade relative to the generator shaft on the structural deformation and dynamic stability characteristics of wind turbine blades. Fang and Zhou 12 studied the free vibration problem of the rotating axially functionally graded-tapered beam.…”

Section: Introductionmentioning

confidence: 99%

“…One key component of such a model is an accurate description of the geometric stiffening effect. Several modelling methods have been proposed, such as (1) the method that directly provides the axial centrifugal loads, [1][2][3][4] (2) the method that considers the foreshortening effect in the longitudinal deformation, [5][6][7][8][9][10][11][12] and (3) absolute nodal coordinate formulation (ANCF). 13,14 Likins et al 1 and Simo and Vu-Quoc 2 developed the first method.…”

Section: Introductionmentioning

confidence: 99%

Effects of steady-state axial deformation on bending frequency of rotating cantilever beam

Zhao

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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A coupling dynamic model of a rotating cantilever beam is established by considering the effect of steady-state axial deformation on transverse bending deformation. The present method uses fully nonlinear Green strain–displacement relationship to derive the coupling terms in the equations of motion. The steady-state axial deformation is derived by analysing the equation of axial motion. An expression of the rotational speed limit is also obtained. The numerical results indicate that the steady-state axial deformation has a considerable effect on the transverse bending frequencies. A comparison of the present model with the absolute nodal coordinate formulation indicates that the two models are in good agreement, which proves the effectiveness and rationality of the present model.

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Free vibration analysis of rotating axially functionally graded-tapered beams using Chebyshev–Ritz method

Cited by 9 publications

References 15 publications

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Free Vibration of Axially Functionally Graded Beam

Effects of steady-state axial deformation on bending frequency of rotating cantilever beam

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