Vibration Analysis of Thin Plates Resting on Pasternak Foundations by Element free Galerkin Method

Bahmyari, Ehsan; Banatehrani, Mohammad Mahdi; Ahmadi, Mohammad; Bahmyari, Marzieh

doi:10.1155/2013/532913

Cited by 22 publications

(7 citation statements)

References 23 publications

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“…Table 1 shows the calculated first six non-dimensional frequencies of the plates for various foundation stiffnesses. It can be seen from Table 2 that the calculated results well agree with Bahmyari et al (2013) and ANSYS. Secondly, the frequencies parameters are computed for the plates on the viscoelastic foundation by varying the order of the derivative.…”

Section: Free Vibrationsupporting

confidence: 64%

“…This can be generalized with two parameters to include the shear modulus of the foundation, leading to the elastic Pasternak foundation (Nazarimofrad et al 2018). Bahmyari et al (2013) investigated the free transverse vibration of thin plates with elastic Winkler and Pasternak foundations, for different possible classical boundary conditions, using the meshless Galerkin's method. Huang et al (2008) presented the analytical solution of a functionally-graded plate resting on the Winkler-Pasternak elastic foundation, using the three-dimensional theory of elasticity.…”

Section: Introductionmentioning

confidence: 99%

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On the transient response of plates on fractionally damped viscoelastic foundation

Praharaj

Datta

2020

Comp. Appl. Math.

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This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin-Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

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Section: Free Vibrationsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

On the transient response of plates on fractionally damped viscoelastic foundation

Praharaj

Datta

2020

Comp. Appl. Math.

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“…It should be stressed that the Lamé parameters given in (2) are determined by the adopted orthogonal curvilinear coordinate system. Consequently, the strains given in (1) depend on the adopted coordinate system as well.…”

Section: Kinematic Relations and Stressmentioning

confidence: 99%

“…The literature on this subject is vast. In the literature, many of the studies are based on the thin-shell theories (such as Donnell's, Love's, and Sanders' shell theories), which are developed on the basis of the Kirchhoff-Love's simplifying assumptions [1][2][3][4][5][6][7][8][9][10]. Much more information on thin-shell theories is available in an influential monograph published by Leissa [11] in 1973.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

Jin

Shi

2015

Shock and Vibration

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This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.

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“…Kulachenko and his coworkers [2,3] studied nonlinear dynamics problem; the stability of transverse vibration of the web was studied by finite element method. The elementfree Galerkin method was used to analyze free vibration of thin plates resting on Pasternak elastic foundations with all possible types of classical boundary conditions by Bahmyari et al [4]. Nguyen et al [5,6] analyzed the stability and the control of transverse vibration of web by changing axial velocity and axial tension, respectively.…”

Section: Introductionmentioning

confidence: 99%

Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction

Shao

Wang

et al. 2017

Shock and Vibration

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The vibration model of moving membrane with variable density distribution is established, and the density distribution of the moving membrane varies along the lateral direction. The transverse vibration differential equations of moving membrane are established based on D' Alembert's principle and discretized by using the differential quadrature method (DQM). The relationships of the first three dimensionless complex frequencies between dimensionless speed, density coefficient, and tension ratio of the membrane are analyzed by numerical calculation. The effects of the density coefficient and the tension ratio on transverse vibration characteristics of the membrane are investigated. The relationship between density coefficient and critical speed is obtained. The numerical results show that the density coefficient and the tension ratio have important influence on the stability of moving membrane. So the study provides a theoretical basis for improving the working stability of the membrane in the high-speed printing process.

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Vibration Analysis of Thin Plates Resting on Pasternak Foundations by Element free Galerkin Method

Cited by 22 publications

References 23 publications

On the transient response of plates on fractionally damped viscoelastic foundation

On the transient response of plates on fractionally damped viscoelastic foundation

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction

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