A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations

Su, Zhu; Jin, Guoyong; Wang, Yunlong; Ye, Xinmao

doi:10.1007/s00707-016-1575-8

Cited by 57 publications

(31 citation statements)

References 40 publications

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“…). Both the Voigt model and Mori-Tanaka scheme are adopted to evaluate the effective material properties [48]. In the Voigt model, it is assumed that the material properties including…”

Section: Materials Propertiesmentioning

confidence: 99%

An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner‐Mindlin Rectangular Plate with General Boundary Conditions

Liu

Pang

et al. 2018

Shock and Vibration

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This paper presents an accurate solution method for the static and vibration analysis of functionally graded Reissner-Mindlin plate with general boundary conditions on the basis of the improved Fourier series method. In the theoretical formulations, the governing equations and the general elastic boundary equations are obtained by using Hamilton’s principle. The components of admissible displacement functions are expanded as an improved Fourier series form which contains a 2D Fourier cosine series and auxiliary function in the form of 1D series. The major role of the auxiliary function is to remove the potential discontinuities of the displacement function and its derivatives at the edges and ensure and accelerate the convergence of the series representation. The characteristic equations are easily obtained via substituting admissible displacement functions into governing equations and the general elastic boundary equations. Several examples are made to show the excellent accuracy and convergence of the current solutions. The results of this paper may serve as benchmark data for future research in related field.

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“…). Both the Voigt model and Mori-Tanaka scheme are adopted to evaluate the effective material properties [48]. In the Voigt model, it is assumed that the material properties including…”

Section: Materials Propertiesmentioning

confidence: 99%

An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner‐Mindlin Rectangular Plate with General Boundary Conditions

Liu

Pang

et al. 2018

Shock and Vibration

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“…Particularly, each of the basic beam variables is mathematically described as a set of modified Fourier series including a standard cosine Fourier series as well as certain auxiliary functions [36][37][38][39][40][41]. The auxiliary terms are introduced for the purpose of removing the entire possible discontinuities with the basic beam variables and their derivatives at the edges to form a mathematically complete set and then ensure the convergence and speed up the calculation [39,[42][43][44][45]. In addition, the governing equations of the beams are derived and numerically solved by a modified variational principle for the sake of making arbitrary boundary conditions applicable.…”

Section: Modified Fourier Series Approximation the Modifiedmentioning

confidence: 99%

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Wang

Miao

et al. 2017

Shock and Vibration

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An efficient modified Fourier series-based sampling surface approach is proposed for the analytical evaluation of the vibration characteristics of thick curved beams subjected to general restraints. The theoretical models of the beams are formulated by the theory of elasticity in two dimensions, which allows arbitrary thickness configurations to be tackled. As an innovation of this work, the approach is based upon the sampling surface method combined with the use of modified Fourier series approximation. In particular, the transverse beam domain is discretized by a set of sampling surfaces with unequal spaces, and the displacement components in beam domain coinciding with these surfaces are mathematically described as a set of modified Fourier series in which certain supplementary functions are included to remove all the relevant discontinuities with the displacements and their derivatives at the boundaries to form a mathematically complete set and guarantee the results convergent to the exact solutions. The final results are numerically solved using a modified variational principle by means of Lagrange multipliers and penalty method for the sake of arbitrary boundary conditions. The influences of transverse normal and shear deformation on the vibration characteristics with respect to the geometrical dimension and boundary conditions are systematically evaluated.

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“…The use of FG materials eliminates interlaminar stress concentration and due to its unique properties provides strength and toughness of the structure [2]. A large number of studies related to vibration characteristics of intact and cracked FG uniform beams are available [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Furthermore the studies have been extended in mechanical analysis of small-sized structures [23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of cracked functionally graded non-uniform beams

Shabani

Cunedioĝlu

2020

Mater. Res. Express

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This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

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A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations

Cited by 57 publications

References 40 publications

An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner‐Mindlin Rectangular Plate with General Boundary Conditions

An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner‐Mindlin Rectangular Plate with General Boundary Conditions

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Free vibration analysis of cracked functionally graded non-uniform beams

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