Moving Element Method for Dynamic Analyses of Functionally Graded Plates Resting on Pasternak Foundation Subjected to Moving Harmonic Load

Luong, Van Hai; Cao, Tan Ngoc Than; Lieu, Qui X.; Nguyen, Xuan Vu

doi:10.1142/s0219455420500030

Cited by 20 publications

(4 citation statements)

References 31 publications

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“…Eyvazian [23] investigated dynamic behavior of cylindrical shells reinforced by GPLs excited by a moving harmonic force applying FSDT by considering various boundary conditions. Luong et al [24] used moving element technique based on FSDT to survey linear dynamic response of FGM rectangular plates supporting on Pasternak elastic foundation excited by moving force. Based on FSDT and by employing dynamic relaxation method, linear dynamic behavior of two directionally FGM porous rectangular plates excited by a moving load was presented by Esmaeilzadeh and Kadkhodayan [25].…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Nazari

Babaei²,

Kiarasi³

et al. 2021

SN Appl. Sci.

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In this study, we present a numerical solution for geometrically nonlinear dynamic analysis of functionally graded material rectangular plates excited to a moving load based on first-order shear deformation theory (FSDT) for the first time. To derive the governing equations of motion, Hamilton’s principle, nonlinear Von Karman assumptions and FSDT are used. Finally, the governing equations of motion are solved by employing the generalized differential quadratic method as a numerical solution. Natural frequencies, dynamic bending behavior and stresses of the plate for linear and nonlinear type of geometrically strain–displacement relations and different factors, including the magnitude and velocity of moving load, length ratio, power law exponent and various edge conditions are obtained and compared. Article highlights Developing generalized differential quadrature method (GDQM) solution based on FSDT for dynamic analysis of FGM plate excited by a moving load for the first time. Comparison of linear and nonlinear dynamic response of plate by considering Von-Karman assumption. Observing considerable difference between linear and nonlinear results

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Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Nazari

Babaei²,

Kiarasi³

et al. 2021

SN Appl. Sci.

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“…In this study, a Kirchhoff plate resting on a viscoelastic foundation is employed to model the pavement system and the moving plate element stiffness matrix was formulated in a coordinate system which was attached to the moving load. More recently, the extensions of MEM for investigating the static and dynamic responses of homogenous Mindlin plates and functionally graded plates supported by a viscoelastic foundation subjected to moving loads were performed in the research works of Luong et al (2018, 2020). Furthermore, the MEM has been also successfully developed by Cao et al (2018b) for the dynamic analysis of laminate composite plates.…”

Section: Introductionmentioning

confidence: 99%

A multi-layer moving plate method for dynamic analysis of viscoelastically connected double-plate systems subjected to moving loads

Cao

Reddy

Lieu

et al. 2021

Advances in Structural Engineering

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This article aims to firstly introduce a computational approach, named multi-layer moving plate method (MMPM), to dynamic analysis of viscoelastically connected infinitely long double-plate systems subjected to moving loads. The Reissner-Mindlin plate theory is utilized to describe the displacement field through the thickness of each plate, whilst quadratic serendipity shape functions are employed to represent unknown fields in finite element analyses (FEAs). The governing equations of motion of connected double-plate system are established in a moving coordinate system attached to the moving load. As a consequence, the paradigm can absolutely eradicate the update process of force vector since the applied load is taken into account as “stationary” in its coordinate system. First, several numerical examples for static, free vibration and dynamic analyses are exhibited to verify the accuracy of the proposed MMPM. Then, the influences of various parameters such as load’s velocity, damping coefficient, stiffness coefficient, and plate thickness on the dynamic responses of double-plate system are examined in great detail.

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“…Luong et al. 13 utilized the moving element method to compute the eigenvalues of P-FG plate supported on an elastic foundation subjected to moving harmonic load.…”

Section: Introductionmentioning

confidence: 99%

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

Ali

Azam

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

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Moving Element Method for Dynamic Analyses of Functionally Graded Plates Resting on Pasternak Foundation Subjected to Moving Harmonic Load

Cited by 20 publications

References 31 publications

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

A multi-layer moving plate method for dynamic analysis of viscoelastically connected double-plate systems subjected to moving loads

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

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