Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation

Tajeddini, Vahid; Ohadi, Abdolreza; Sadighi, Mojtaba

doi:10.1016/j.ijmecsci.2011.01.011

Cited by 73 publications

(17 citation statements)

References 34 publications

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“…Although a rather large amount of work has been done on tapered beams [87][88][89] and variable thickness circular [9,10,[90][91][92][93][94] and rectangular [95][96][97] plates, but the literature on the variable thickness annular sector plates is scarce. Stability [98], vibration [99][100][101] and bending [102,103] analysis of annular sector plates M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 5 with variable thickness were investigated.…”

Section: Introductionmentioning

confidence: 99%

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Alinaghizadeh

Shariati

2016

Composites Part B: Engineering

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Section: Introductionmentioning

confidence: 99%

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Alinaghizadeh

Shariati

2016

Composites Part B: Engineering

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“…Polynomials and traditional Fourier series are commonly used. However, for the polynomial [91,92], the lower order polynomials cannot form a complete set, and the higher-order polynomials always tend to become numerically unstable due to the computer round-off errors. And for traditional Fourier series expression, it is only applicable for a few simple boundary conditions and can lead to unavoidable convergence problem for other boundary conditions, which limits the Fourier series to only a few ideal boundary conditions [58] Figure 4(a).…”

Section: Admissible Displacement Functions and Solution Procedurementioning

confidence: 99%

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Pang

Wang

et al. 2017

Shock and Vibration

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The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the powerlaw distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.

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“…Several thickness profiles, as well as volume fraction distributions, were considered. The same kind of FGM structures resting on the Pasternak elastic foundation were investigated also by Hosseini-Hashemi et al [91] and by Tajeddini et al [92]. In the first paper, the differential quadrature method was used to solve numerically the governing equations based on the classical plate theory, whereas the free vibration problem was solved by means of the polynomial-Ritz method in the second paper.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

et al. 2017

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Abstract:The main aim of the present paper is to solve numerically the free vibration problem of sandwich shell structures with variable thickness and made of Functionally Graded Materials (FGMs). Several Higher-order Shear Deformation Theories (HSDTs), defined by a unified formulation, are employed in the study. The FGM structures are characterized by variable mechanical properties due to the through-the-thickness variation of the volume fraction distribution of the two constituents and the arbitrary thickness profile. A four-parameter power law expression is introduced to describe the FGMs, whereas general relations are used to define the thickness variation, which can affect both the principal coordinates of the shell reference domain. A local scheme of the Generalized Differential Quadrature (GDQ) method is employed as numerical tool. The natural frequencies are obtained varying the exponent of the volume fraction distributions using higher-order theories based on a unified formulation. The structural models considered are two-dimensional and require less degrees of freedom when compared to the corresponding three-dimensional finite element (FE) models, which require a huge number of elements to describe the same geometries accurately. A comparison of the present results with the FE solutions is carried out for the isotropic cases only, whereas the numerical results available in the literature are used to prove the validity as well as accuracy of the current approach in dealing with FGM structures characterized by a variable thickness profile.

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Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation

Cited by 73 publications

References 34 publications

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method

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