Forced vibrations of functionally graded annular and circular plates by domain‐boundary element method

Eshraghi, Iman; Dağ, Serkan

doi:10.1002/zamm.201900048

Cited by 12 publications

(6 citation statements)

References 29 publications

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“…The von Kármán assumptions are used to determine the strain components of the plate. Based on these assumptions in the cylindrical coordinate system, the strains are related to the displacements generally as [46,47]:…”

Section: Mathematical Formulationsmentioning

confidence: 99%

“…The foundation is modeled by visco-Pasternak type which consists of springs, shear layer, and dampers. So, its reaction force can be stated as [47]:…”

Section: Mathematical Formulationsmentioning

confidence: 99%

\begin{matrix} ε_{r r} & = & \frac{\partial U (r, θ, z, t)}{\partial r} + \frac{1}{2} {((), \frac{\partial W (r, θ, z, t)}{\partial r})}^{2}, \\ ε_{θ θ} & = & \frac{1}{r} \frac{\partial V (r, θ, z, t)}{\partial θ} + \frac{U (r, θ, z, t)}{r} + \frac{1}{2} {((), \frac{1}{r} \frac{\partial W ((), r, θ, z, t)}{\partial θ})}^{2}, \\ γ_{r θ} & = & \frac{1}{r} \frac{\partial U (r, θ, z, t)}{\partial θ} - \frac{V (r, θ, z, t)}{r} + \frac{\partial V (r, θ, z, t)}{\partial r} + \frac{1}{r} (\frac{\partial W ((), r, θ, z, t)}{\partial θ}) (\frac{\partial W ((), r, θ, z, t)}{\partial r}), \\ γ_{r z} & = & \frac{\partial U (r, θ, z, t)}{\partial z} + \partial W () \end{matrix}

…”

Section: Mathematical Formulationsmentioning

confidence: 99%

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Vibration characteristics of FG saturated porous annular plates integrated by piezoelectric patches on visco‐Pasternak foundation

Allah Gholi,

Khorshidvand,

Jabbari

et al. 2024

Z Angew Math Mech

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The vibrational behavior of a three‐layered annular plate is considered in the present study. The plate is composed of a functionally graded (FG) porous core which is saturated by fluid and two piezoelectric patches that are bonded to the core and are subjected to the electric field. The whole of the structure is also rested on visco‐Pasternak elastic foundation. The material properties of the FG porous core vary through the thickness direction based on different patterns which are called porosity distributions. Love‐Kirchhoff's hypothesis and Hamilton's principle is employed to extract the governing motion equations and boundary conditions and following it, they are solved by generalized differential quadrature method (GDQM) for various boundary conditions. After ensuring the validity of the results by comparing them with known data in the literature, the effect of the most important parameters on the results is considered. It is seen that the effect of the porosity coefficient on the natural frequencies is completely dependent on the pores’ distribution patterns. Also, increasing in externally applied voltage to the piezoelectric facesheets, leads the results to enhance. The outcomes of this work can help to design and create smart structures and systems such as sensors and actuators.

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Section: Mathematical Formulationsmentioning

confidence: 99%

“…The foundation is modeled by visco-Pasternak type which consists of springs, shear layer, and dampers. So, its reaction force can be stated as [47]:…”

Section: Mathematical Formulationsmentioning

confidence: 99%

\begin{matrix} ε_{r r} & = & \frac{\partial U (r, θ, z, t)}{\partial r} + \frac{1}{2} {((), \frac{\partial W (r, θ, z, t)}{\partial r})}^{2}, \\ ε_{θ θ} & = & \frac{1}{r} \frac{\partial V (r, θ, z, t)}{\partial θ} + \frac{U (r, θ, z, t)}{r} + \frac{1}{2} {((), \frac{1}{r} \frac{\partial W ((), r, θ, z, t)}{\partial θ})}^{2}, \\ γ_{r θ} & = & \frac{1}{r} \frac{\partial U (r, θ, z, t)}{\partial θ} - \frac{V (r, θ, z, t)}{r} + \frac{\partial V (r, θ, z, t)}{\partial r} + \frac{1}{r} (\frac{\partial W ((), r, θ, z, t)}{\partial θ}) (\frac{\partial W ((), r, θ, z, t)}{\partial r}), \\ γ_{r z} & = & \frac{\partial U (r, θ, z, t)}{\partial z} + \partial W () \end{matrix}

…”

Section: Mathematical Formulationsmentioning

confidence: 99%

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Vibration characteristics of FG saturated porous annular plates integrated by piezoelectric patches on visco‐Pasternak foundation

Allah Gholi,

Khorshidvand,

Jabbari

et al. 2024

Z Angew Math Mech

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“…For the analysis of the free transverse vibration characteristics of the stepped circular plate, the eigenvalues and eigenvectors can be easily obtained by solving the standard matrix of equation (21). e physical modal shape can be readily yielded by substituting the corresponding eigenvectors into equations ( 15)- (17) for the given natural frequency.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…en, Eshraghi and Dag [17] developed a new domain-boundary element formulation to investigate the axis-symmetric dynamic response of functionally graded circular and annular Mindlin plates with through-the-thickness variations of physical properties. Lam and Amrutharaj [18] employed a novel hybrid method to analyze the natural frequencies of a rectangular plate with stepped thickness variations and different edge boundary conditions, which had incorrect continuity conditions at stepped sections as was proposed by Dickinson [19].…”

Section: Introductionmentioning

confidence: 99%

Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method

Hao

Chen

Zhai

2022

Shock and Vibration

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In this investigation, free vibration of stepped circular Mindlin plate with arbitrary boundary conditions is presented by an improved Fourier–Ritz method. Based on the locations of the step variations, the stepped circular plate can be divided into different concentric annular and circular plates. The first-order shear deformation plate theory is employed to establish the theoretical model. Once all the displacements of a stepped circular plate are expanded by an improved Fourier series expansion, an exact solution can be obtained based on the Rayleigh–Ritz procedure by the energy function of the current model. The convergence and accuracy of the proposed method are proved by several numerical examples. The effects of classical boundary conditions and geometrical parameters on the frequency parameters of a stepped circular plate are also analyzed.

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A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method

Liu

Zhao

Pishbin

et al. 2021

Engineering with Computers

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Forced vibrations of functionally graded annular and circular plates by domain‐boundary element method

Cited by 12 publications

References 29 publications

Vibration characteristics of FG saturated porous annular plates integrated by piezoelectric patches on visco‐Pasternak foundation

Vibration characteristics of FG saturated porous annular plates integrated by piezoelectric patches on visco‐Pasternak foundation

Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method

A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method

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