Free vibration of axially functionally graded Euler-Bernoulli beams

Kukla, Stanisław; Rychlewska, Jowita

doi:10.17512/jamcm.2014.1.05

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…This analysis is based on the approximation of the functionally graded beam by piecewise exponentially varying geometrical and material properties. They extended their studies by considering a simply supported beam with an arbitrary number of segments [6]. Some numerical examples are tabulated and they mentioned that the accuracy of the eigenfrequencies improves as the number of segments increases.…”

Section: Introductionmentioning

confidence: 99%

Optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the longitudinal direction

Alkan

2019

Sādhanā

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In this study, optimal design of the transversely vibrating Euler-Bernoulli beams segmented in the longitudinal direction is explored. Mathematical formulation of the beams in bending vibration is obtained using transfer matrix method, which is later coupled with an eigenvalue routine using the ''fmincon solver'' provided in Matlab Optimization Toolbox. Characteristic equations, namely frequency equations, for determining natural frequencies of the segmented beams for all end conditions are obtained and for each case, square of this equation is selected as a fitness function together with constraints. Due to the explicitly unavailable objective functions for the natural frequencies as a function of segment length and volume fraction of the materials, especially for the beams made of a large number of segments, initially, prescribed value is assumed for the natural frequency and then the variables minimizing objective function and satisfying the constraints are searched. Clamped-free, clamped-clamped, clamped-pinned and pinned-pinned boundary conditions are considered. Among the end conditions, maximum increment in the fundamental natural frequency is more pronounced for the case of clamped-clamped end condition and for this case, maximum increment up to 17.3274% is attained. Finally, the beam configurations maximizing fundamental natural frequencies will be presented. adhana(0123456789().,-volV)FT3 ](0123456789().,-volV)

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Section: Introductionmentioning

confidence: 99%

Optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the longitudinal direction

Alkan

2019

Sādhanā

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“…Critical buckling loads are determined from the existence condition of a non-trivial solution in the system of algebraic equations obtained here. The proposed approach is based on these presented by Kukla and Rychlewska in [9] and Rychlewska in [10].…”

Section: Introductionmentioning

confidence: 99%

A new approach for buckling analysis of axially functionally graded beams

Rychlewska

2015

J. Appl. Math. Comput. Mech.

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Abstract. The object of considerations are axially functionally graded (FG) beams, which are loaded by an axial force varying along the length of the beam. The main idea presented here is to approximate FG beams by an equivalent beam with piecewise exponentially varying material properties, geometrical properties and axial load. Numerical solutions of the buckling analysis are obtained for four various types of boundary conditions associated with pinned and clamped ends. The usefulness of the proposed method is confirmed by comparing numerical results with those available for graded beams of special polynomial non-homogeneity.

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Numerical method for stability analysis of functionally graded beams on elastic foundation

Shvartsman

Majak

2016

Applied Mathematical Modelling

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Free vibration of axially functionally graded Euler-Bernoulli beams

Cited by 5 publications

References 6 publications

Optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the longitudinal direction

Optimal design of the transversely vibrating Euler–Bernoulli beams segmented in the longitudinal direction

A new approach for buckling analysis of axially functionally graded beams

Numerical method for stability analysis of functionally graded beams on elastic foundation

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