Free vibration analysis of functionally graded double-beam system using Haar wavelet discretization method

Kim, Kwanghun; Han, Poknam; An, Kwangil; Choe, Dongson; Ri, Yonguk; Ri, Hyonil

doi:10.1016/j.jestch.2020.07.009

Cited by 12 publications

(7 citation statements)

References 44 publications

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“…Some researchers studied the static and dynamic behaviors of various structures like beams, [66][67][68] plates, [69][70][71] and shells [71][72][73][74][75][76][77] by using the Haar wavelet. Recently, Kim et al [78][79][80][81] studied the free vibration of various composite material structures by using HWDM. Therefore, in this paper, FSDT and HWDM are applied to analyze the free vibrations of multi-stepped FG curved beams with generalized boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Kim¹,

Kwak²,

Jang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, a Haar wavelet discretization method (HWDM) for analyzing the free vibration of the multi-stepped functionally graded (FG) curved beam with general boundary conditions is presented. It is assumed that the material properties of the beam change continuously in the thickness direction according to the distribution characteristics of the material determined by four parameters. The individual steps of the multi-stepped functionally graded curved beam are combined by a continuous condition. For generalization of boundary conditions, the artificial elastic spring technique is introduced. The displacement fields are determined by the first-order shear deformation theory (FSDT) and the motion equation is obtained by using Hamilton’s principle. All displacement functions including boundary and continuity conditions are expressed in the form of a Haar wavelet series and its integral, and a characteristic equation discretized based on the Haar wavelet is obtained. The reliability and accuracy of the proposed method are confirmed through convergence and validation studies. The results indicate that this method has high accuracy and reliability, also a higher convergence rate in attaining the frequencies of the multi-stepped FG curved beam. Then, the frequency parameters and mode types of the multi-stepped FG curved beam obtained by the proposed method are given with numerical examples. These new numerical results can be used as benchmark data for research in this field.

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Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Kim¹,

Kwak²,

Jang

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Many experts have conducted a large number of studies on the vibration characteristics of multi-beam systems [ 13 , 14 , 15 , 16 , 17 , 18 ]. Kim et al [ 19 , 20 ] established a double-beam system and analyzed the free vibration characteristics of a system. Deng et al [ 21 ] studied the vibration characteristics of a double-functionally-graded (FG) beam system on an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of a Graphene-Platelet-Reinforced, Porous, Two-Cylindrical-Panel System

Sun

Chi

Luo³

2022

Materials

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In this study, a novel, dynamic model of a graphene-platelet-reinforced, porous (GPLRP) double-cylindrical-panel system is proposed. The material properties of a graphene-platelet-reinforced, porous, double-cylindrical-panel system were determined by the Halpin–Tsai micromechanics model and the typical mechanical properties of open-cell metal foams. Different types of porosity distribution and graphene platelet (GPL) distribution patterns were considered. Love’s shell theory was utilized to derive the theoretical formulation, and the Rayleigh–Ritz method was used to calculate the natural frequencies of the system. The proposed model was validated by several comparison studies with the natural frequencies in the existing literature. Finally, the effects of stiffness of Winkler springs, boundary condition, porosity coefficient, porosity distribution, GPL distribution pattern, and GPL weight fraction on the free vibration characteristics of the system were evaluated.

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“…Li et al 9 presented a state-space approach to calculate the dynamic response, mode shapes, and the frequencies of double Euler–Bernoulli beams with an elastic/viscoelastic interlayer between them. In another article, Kim et al 10 carried out the natural vibration behavior of functionally graded double beam-system (FGDBS) joined by a uniform layer. Hamilton’s principle was used to obtain the coupled governing equations of motion, and the Haar wavelet series and their integral were utilized to calculate the dimensionless frequencies of the FGDBS with arbitrary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

Sari

2022

Journal of Low Frequency Noise, Vibration and Active Control

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The free transverse vibrations of two-dimensional functionally graded double Euler–Bernoulli beam system connected through a variable Winkler elastic layer are presented. The Modulus of elasticity and the density of the material of the beams are assumed to vary along the thickness and the length of the beams according to power-law and exponential functions, respectively. The governing differential equations of motion are established by the means of Hamilton’s principle. The Chebyshev Spectral Collocation Method (CSCM) is used to calculate the natural frequencies of the two-dimensional functionally graded (2D-FG) double beams. The effects of several parameters such as the height ratio of the beams, the stiffness of the coupling layer, the axial and transverse functionally graded indexes, and the boundary conditions on the natural frequencies of the 2D-FG double beams have been investigated. The frequencies obtained from the CSCM have been validated by comparing them with those available in previous literature.

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Free vibration analysis of functionally graded double-beam system using Haar wavelet discretization method

Cited by 12 publications

References 44 publications

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Free vibration analysis of a multi-stepped functionally graded curved beam with general boundary conditions

Free Vibration Analysis of a Graphene-Platelet-Reinforced, Porous, Two-Cylindrical-Panel System

Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

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