Exact frequency equations of free vibration of exponentially functionally graded beams

Li, Xian-Fang; Kang, Y.A.; Wu, Jingxiang

doi:10.1016/j.apacoust.2012.08.003

Cited by 116 publications

(50 citation statements)

References 24 publications

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“…The solution to the problem was obtained by applying a differential transform element method. The exact solution to free vibration of axially exponentially graded beams is presented by Li et al in reference [5]. Free vibration of axially FG beams consisting of two segments was studied in paper [6].…”

Section: Introductionmentioning

confidence: 99%

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Free vibration of axially functionally graded Euler-Bernoulli beams

Kukla

Rychlewska

2014

J. Appl. Math. Comput. Mech.

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Abstract. In this contribution, free vibration of axially functionally graded beams is analysed within the framework of the Euler-Bernoulli beam theory. The beams with uniaxial variation of the elasticity modulus and mass density are approximated by an equivalent beam with piecewise exponentially varying geometrical and material properties. A numerical example for a beam with pinned ends is presented.

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Section: Introductionmentioning

confidence: 99%

“…The free vibrations of FG beams was analyzed by using various methods in papers [1][2][3][4][5]. The finite element method to the free vibration problem of a FG beams was applied by Alshorbagy et al in paper [1].…”

Section: Introductionmentioning

confidence: 99%

Free vibration of axially functionally graded Euler-Bernoulli beams

Kukla

Rychlewska

2014

J. Appl. Math. Comput. Mech.

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“…For axially graded beams similar problems have become more complicated because of the governing equations with functional coefficients. We can mention here [4] where free vibration of exponentially graded beams is analyzed. Such problems are investigated also in [5] by using the Fredholm integral equations method.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded beams

Kukla

Rychlewska

2013

J. Appl. Math. Comput. Mech.

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“…However, analysis of the axial functionally graded (AFG) structural element is the relatively newer domain, where there exists a few papers on different aspects of such components. Li et al [14] analyzed the free vibration of axially inhomogeneous exponentially graded beams. A simple approach to calculate the critical buckling loads of beams with arbitrary axial inhomogeneity was developed by Huang and Luo [15].…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

Lohar¹,

Mitra

Sahoo³

2016

IFSL

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Abstract.A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton's principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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Exact frequency equations of free vibration of exponentially functionally graded beams

Cited by 116 publications

References 24 publications

Free vibration of axially functionally graded Euler-Bernoulli beams

Free vibration of axially functionally graded Euler-Bernoulli beams

Free vibration analysis of functionally graded beams

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

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