An approach for free vibration analysis of axially graded beams

Kukla, Stanisław; Rychlewska, Jowita

doi:10.15632/jtam-pl.54.3.859

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…Liu et al [5] developed a model for the free transverse vibration of AFG tapered Euler−Bernoulli beam through the spline finite point method; the beam was discretized with a set of uniformly scattered spline nodes along the beam axis, and the displacement field was approximated by the particularly constructed cubic B-spline interpolation functions. Kukla et al [6] proposed an approach to free vibration analysis of functionally graded beams by approximating the beam by an equivalent beam with piece-wise exponentially varying material and geometrical properties. Cao et al [7] studied the free vibration of AFG beam using analytical method based on the asymptotic perturbation method and Meijer-Function, respectively.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Axially Functionally Graded Non-Prismatic Euler-Bernoulli Beams Using the Finite Difference Method

Fogang¹

2021

Preprint

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This paper presents an approach to the vibration analysis of axially functionally graded (AFG) non-prismatic Euler-Bernoulli beams using the finite difference method (FDM). The characteristics (cross-sectional area, moment of inertia, elastic moduli, and mass density) of AFG beams vary along the longitudinal axis. The FDM is an approximate method for solving problems described with differential or partial differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. The model developed in this paper consists of formulating differential or partial differential equations with finite differences and introducing new points (additional or imaginary points) at boundaries and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, and brutal change of stiffness). The introduction of additional points allows satisfying boundary and continuity conditions. Vibration analysis of AFG non-prismatic Euler-Bernoulli beams was conducted with this model, and natural frequencies were determined. Finally, the direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of AFG non-prismatic Euler-Bernoulli beams, considering the damping. The efforts and displacements could be determined at any time.

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Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Axially Functionally Graded Non-Prismatic Euler-Bernoulli Beams Using the Finite Difference Method

Fogang¹

2021

Preprint

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“…Xie et al [48] presented a spectral collocation approach based on integrated polynomials combined with the domain decomposition technique for free vibration analyses of beams with axially variable cross sections, moduli of elasticity, and mass densities. Kukla and Rychlewska [49] proposed a new approach to study the free vibration analysis of an AFG beam; the approach relies on replacing functions characterizing functionally graded beams with piecewise exponential functions. 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.…”

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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“…The free vibration analysis of rotating FG Timoshenko beams was made of porous materials, using the semi-analytical differential transform method, is studied by Ebrahimi and Mokhtari [26]. The free vibration problem of axially graded beams, with a non-uniform cross section, has been presented by Kukla and Rychlewska [27]. Yeh and Hsieh [28] analyzed the dynamic properties of sandwich beams, whose cores were reinforced by multi-layered nanotubes and whose surface plates were covered by carbon fiber/epoxy composites using finite components and empirical method.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded graphene-reinforced nanocomposite beams with temperature-dependent properties

Shahrjerdi

Yavari

2018

J Braz. Soc. Mech. Sci. Eng.

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A temperature-dependent vibration analysis is conducted for the functionally graded nanocomposite beams which are reinforced by graphene. Material properties are assumed to change along the beams in five different types based upon the graphene distribution with a specific function. The differential equations of motion are extracted and solved using the spectral numerical method for the beams under various boundary conditions. The effect of distribution of functionally graded nanocomposite in the thickness direction of beams on the frequency response of vibration, and the effect of various parameters on the vibration response has been examined, such as the distribution function of nanographene plates, weight percentage, dimensions of nanographene plates, temperature changes, and thickness ratio. The results are compared and validated with numerical and analytical results reported in references for manifold boundary conditions. It is seen that the increase of graphene weight percentage in all boundary conditions will cause an increase in the natural frequency of the beams.

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An approach for free vibration analysis of axially graded beams

Cited by 6 publications

References 16 publications

Vibration Analysis of Axially Functionally Graded Non-Prismatic Euler-Bernoulli Beams Using the Finite Difference Method

Vibration Analysis of Axially Functionally Graded Non-Prismatic Euler-Bernoulli Beams Using the Finite Difference Method

Free Vibration of Axially Functionally Graded Beam

Free vibration analysis of functionally graded graphene-reinforced nanocomposite beams with temperature-dependent properties

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