Free vibration analysis of non-uniform Euler–Bernoulli beams by means of Bernstein pseudospectral collocation

Garijo, Diego

doi:10.1007/s00366-015-0401-6

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…The mode shapes of the structure were also studied, and it was found that they are sensitive to changes in the nonuniformity of the beams. Garijo (2015) proposed Bernstein pseudospectral collocation to solve the free vibration analysis of non-uniform Euler-Bernoulli beams. The accuracy and efficiency of the Bernstein pseudospectral collocation method were demonstrated through numerical examples.…”

Section: Introductionmentioning

confidence: 99%

Free Vibrational Analysis of Non-uniform Double Eulerbernoulli Beams on a Winkler Foundation Using Laplace Differential Transform Method

Usman

Hammed

Daniel³

2023

J. of Eng. Sci.

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In this study, the free vibrational analysis of non-uniform Euler-Bernoulli double beams on a Winkler foundation under simply supported and fixed-fixed boundary conditions is examined. The governing equation is solved using the Laplace Differential Transform Method, the combined form of the Laplace transform and differential transform technique (DTM). The accuracy of the method used is demonstrated by comparing the natural frequencies obtained using LDTM with previously published results available in the literature. It is discovered that for non-uniform double Euler-Bernoulli beams on a Winkler foundation with fixed-fixed end conditions, the natural frequencies are higher than those of simply supported end conditions. It is also observed that as the non-uniformity of the cross section of the beam increases, the natural frequencies reduce. Hence, it is suggested that the non-uniformity of the cross-section of the beam for a simply supported end condition be between 0 and less than 0.8. While the fixed-fixed end condition should have a value between 0 and 0.95. Journal of Engineering Science 14(1), 2023, 111-121

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Section: Introductionmentioning

confidence: 99%

Free Vibrational Analysis of Non-uniform Double Eulerbernoulli Beams on a Winkler Foundation Using Laplace Differential Transform Method

Usman

Hammed

Daniel³

2023

J. of Eng. Sci.

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“…Boiangiu et al [59] obtained the exact solutions for free bending vibrations of straight beams with variable cross section using Bessel's functions and proposed a transfer matrix method to determine the natural frequencies of a complex structure of conical and cylindrical beams. Garijo [60] analyzed the free vibration of Euler-Bernoulli beams of variable cross section employing a collocation technique based on Bernstein polynomials. Arndt et al [61] presented an adaptive generalized FEM to determine the natural frequencies of nonuniform Euler-Bernoulli beams.…”

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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“…Free vibration analysis solved for beams with continuously and stepped varying cross-sectional parameters has been reviewed in recent publications, e.g. [7][8][9]. Both analytical solutions in terms of special functions including Bessel functions, hypergeometric series, power series, Bernstein polynomials and approximate solutions obtained by using Rayleigh-Ritz approach, finite element method, dynamic stiffness method, differential quadrature method, differential transform method have been reported there.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method

et al. 2017

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Free vibration analysis of non-uniform Euler–Bernoulli beams by means of Bernstein pseudospectral collocation

Cited by 8 publications

References 21 publications

Free Vibrational Analysis of Non-uniform Double Eulerbernoulli Beams on a Winkler Foundation Using Laplace Differential Transform Method

Free Vibrational Analysis of Non-uniform Double Eulerbernoulli Beams on a Winkler Foundation Using Laplace Differential Transform Method

Free Vibration of Axially Functionally Graded Beam

Free vibration analysis of functionally graded beams with non-uniform cross-section using the differential transform method

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