Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load

Nguyen, Dinh Kien; Nguyen, Quang Huan; Tran, Thi Thom; Bui, Van Tuyen

doi:10.1007/s00707-016-1705-3

Cited by 109 publications

(55 citation statements)

References 35 publications

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“…Regardless of the grading index , the table shows a good agreement between the result of the present work with that obtained by using a semianalytical method in [39] and the different transformation method in [40]. In addition, the deflections evaluated by the present beam element are in excellent agreement with the finite element solution in [30], where the beam element based on Kosmatka's shape functions was used. Note that the result in Table 6 has been obtained by using the geometric and material data stated in [39].…”

Section: Forcedsupporting

confidence: 81%

“…The convergence of the present solution, as seen from Table 1, is fast, and it is capable of giving accurate frequency parameter with just sixteen elements. The rate of convergence of the present element is comparable with that of the beam element using Kosmatka shape functions as reported in [30], where the convergence of the element in evaluating the fundamental frequency of transverse FGM beams is achieved by using fourteen elements. In addition, the beam element derived in the present work is free of the shear locking, and it is able to evaluate accurately the frequency of the beam having a high aspect ratio, /ℎ = 100.…”

Section: Free Vibration the Equation For Free Vibration Analysis Of supporting

confidence: 65%

“…The element with eleven degrees of freedom employs Lagrange polynomials to interpolate the displacements and rotation. Recently, Nguyen et al [30] employed Kotsmatka's polynomials to formulate a beam element for studying the dynamic behaviour of bidirectional FGM Timoshenko beams excited by a moving load.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Nguyen¹,

Bui

2017

Mathematical Problems in Engineering

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A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.

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Section: Forcedsupporting

confidence: 81%

Section: Free Vibration the Equation For Free Vibration Analysis Of supporting

confidence: 65%

See 1 more Smart Citation

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Nguyen¹,

Bui

2017

Mathematical Problems in Engineering

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“…The development of FGMs with effective material properties varying in two or three directions to withstand severe general loadings is of great importance in practice, especially in development of structural elements for space structures [12,13]. Studies on the static and dynamic behavior of beams formed from two-directional functionally graded materials (2-D FGMs) have been recently reported by several researchers.…”

Section: Introductionmentioning

confidence: 99%

“…The numerical investigations by the authors show that the variation of material properties has a strong influence on the natural frequencies, and there is a critical frequency at which the natural frequencies have an abrupt jump when they across the critical frequency. Based on a finite element procedure, Nguyen et al [13] studied the forced vibration of 2-D FGM Timoshenko beams excited by a moving load. The material properties in [13] were assumed to vary in both the thickness and longitudinal directions by a power-law function.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Two-Directional FGM Beams Using a Higher-Order Timoshenko Beam Element

Thom

Kien²

2018

JST

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Abstract. Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted.

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Vibration and the cancellation phenomenon of a nanobeam under a moving load via the strain gradient theory

Wang

Zhu

2020

Math Methods in App Sciences

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Forced and free transverse vibrations of a nanobeam under a moving load are investigated in this work. Through the strain gradient theory, high‐order governing partial differential equations of the nanobeam are established by the extended Hamilton's principle, which incorporates its material, geometrical, and nanoscale parameters. The dynamic response of the nanobeam is obtained from spatially discretized equations via the Galerkin's method. Effects of material, geometrical, and nanoscale parameters on the forced transverse vibration of the nanobeam are discussed. Results show that material and nanoscale length parameters play a very important role in determining the amplitude of the forced transverse vibration of the nanobeam. The cancellation velocity of the moving load is determined from the rigorous initial displacement and velocity of the free transverse vibration of the nanobeam, and an approximate expression of the cancellation velocity is presented by means of its first‐mode response. Effects of geometrical and nanoscale parameters on the cancellation velocity are also discussed. It is shown that amplitudes of all modal responses of the nanobeam are not simultaneously equal to zero at the cancellation velocity.

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Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load

Cited by 109 publications

References 35 publications

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Free Vibration of Two-Directional FGM Beams Using a Higher-Order Timoshenko Beam Element

Vibration and the cancellation phenomenon of a nanobeam under a moving load via the strain gradient theory

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