Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

Hussain, Muzamal; Isvandzibaei, Mohammad Reza

doi:10.1177/0954406217753459

Cited by 34 publications

(21 citation statements)

References 36 publications

(46 reference statements)

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“…The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation [9,[11][12][13][14][15][16] can be expressed as follows:…”

Section: Fundamental Equationsmentioning

confidence: 99%

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

Yuan

Yang

et al. 2020

Civ Eng J

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The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation are simplified to an independent equation of radial deflection. The independent equation of radial deflection is decomposed to two Laplace operators by intermediate variable. The R-function theory is applied to describe a shallow spherical shell on Winkler foundation with concave boundary, and then a quasi-Green's function is established by using the fundamental solution and the normalized boundary equation. The quasi-Green's function satisfies the homogeneous boundary condition of the problem. The Laplace operators of the problem are reduced to two simultaneous Fredholm integral equations of the second kind by the Green's formula. The singularity of the kernel of the integral equation is eliminated by choosing a suitable form of the normalized boundary equation. The integral equations are discretized into the homogeneous linear algebraic equations to proceed numerical computing. The singular term in the discrete equation is eliminated by the integral method. Some numerical examples are given to verify the validity of the proposed method in calculating simple boundary conditions and polygonal boundary conditions. A comparison with the ANSYS finite element (FEM) solution shows a good agreement, and it demonstrates the feasibility and efficiency of the present method.

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“…The governing differential equations of the bending problem of simply supported shallow spherical shells on Winkler foundation [9,[11][12][13][14][15][16] can be expressed as follows:…”

Section: Fundamental Equationsmentioning

confidence: 99%

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

Yuan

Yang

et al. 2020

Civ Eng J

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“…Prior to this, many techniques have been sequentially used to study the vibration of CNTs [41][42][43]. Previously, the current approach was used continuously to study the vibration of carbon nanotubes [27,29,[44][45][46][47].…”

Section: Application Of Wpamentioning

confidence: 99%

Vibration Characteristics of Single-Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory Using Wave Propagation Approach (WPA) Including Chirality

Hussain¹

2019

Perspective of Carbon Nanotubes

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This chapter deals with the vibrational properties of single-walled carbon nanotubes (SWCNTs), based on nonlocalized theory of elasticity (NLT). The nanotube pilot control with nonlinear parameters was derived from Euler's beam theory. The wave propagation (WPA) approach was used to derive the frequency equation describing the natural frequencies of vibration in SWCNTs. Complex exponentials depend on the boundary conditions given at the edges of the carbon nanotubes used. Vibration frequency spectra were obtained and evaluated for different physical parameters such as diameter ratio for single chiral carbon nanotubes and flexural strength for chiral SWCNT. The results show that the natural frequencies are significantly reduced by increasing the nonlocal parameters, but by increasing the ratio of the diameter length (aspect ratio), the natural frequency increases. The frequency of SWCNTs is calculated with the help of MATLAB computer software. These results are compared to previously known numerical simulations.

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“…Substituting equations (5)- (14) into equation (15), the discretized equation of vibration of the spherical cap can be expressed as the matrix form as…”

Section: Unified Solutions and Calculation Proceduresmentioning

confidence: 99%

“…e vibration behavior of a thin cylindrical shell with simply supported edges was studied by Wu et al [13] by means of Hamilton's principle. Lagrange principle and Hamilton's principle were utilized by Hussain et al [14] to investigate vibration of cylindrical shell resting on Winkler and Pasternak elastic foundations. Zhou et al [15] analyzed the free vibration features of cylindrical shells with elastic edge conditions.…”

Section: Introductionmentioning

confidence: 99%

A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

Sun

Miao

et al. 2019

Shock and Vibration

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The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported.

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Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

Cited by 34 publications

References 36 publications

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary

Vibration Characteristics of Single-Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory Using Wave Propagation Approach (WPA) Including Chirality

A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

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