Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations

Hosseini-Hashemi, Shahrokh; Taher, H. Rokni Damavandi; Akhavan, Hamed

doi:10.1016/j.compstruct.2009.12.016

Cited by 71 publications

(23 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To calculate basic displacement functions, the differential equations governing higher-order shear deformable beam must be solved with respect to transverse displacement of the beam, i.e., w. Since closed-form solution for governing differential equation of higher-order shear deformable beams is not attainable, it is necessary to resort application of numerical methods such as Rayleigh-Ritz method [28], differential quadrature method (DQM) [29], differential quadrature element method (DQEM) [30], least-square-based finite difference (LSFD) [31], methods based on the green functions [32] and differential transform method (DTM) [33].…”

Section: Introductionmentioning

confidence: 99%

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

et al. 2015

View full text Add to dashboard Cite

Since the accuracy of results obtained through displacement-based finite element method (FEM) considerably depends on the accuracy of shape functions used to interpolate the displacement field within an element, this paper aims at presenting a new efficient element for static and free vibration analysis of higher-order shear deformable beams using FEM with introducing basic displacement functions (BDFs). First, BDFs are introduced and computed. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions, static and free vibration behavior of the higher-order shear deformable beam is studied using FEM. The accuracy and economy of the method are demonstrated through several numerical examples.Keywords Higher-order beam theory (HOBT) · Finite element method (FEM) · Basic displacement functions (BDFs) · Free vibration B Rahmat Kazemi Firouzjaei

show abstract

Section: Introductionmentioning

confidence: 99%

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

et al. 2015

View full text Add to dashboard Cite

show abstract

“…This has been addressed by in [7][8][9] for axially graded Euler-Bernoulli and Timoshenko beams. It has also been fully discussed for radially FGM circular plates by Sahraee [10], Shariyat and Alipour [11] and Hosseini-Hashemi et al [12], [13]. However, information about rectangular plates with in-plane inhomogeneity is very limited.…”

Section: Introductionmentioning

confidence: 99%

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

Boreyri

Ketabdari

Mohtat³

et al. 2016

IJPR

View full text Add to dashboard Cite

In this research, free vibration of rectangular functionally graded (FG) plates with in-plane exponentially non-homogeneous material is investigated. Young's modulus and mass density are assumed to vary between a metal-rich and a ceramic-rich zone along one in-plane direction of the plate. The governing differential equation is derived for the case, and a truncated Taylor series expansion technique is utilized to calculate natural frequencies. A Levy-type solution is obtained for plates having two simply supported edges parallel with the material gradient direction. Results for normalized natural frequency are compared with the 4th order Runge-Kutta method, and when possible with exact solution, showing an accurate agreement. Furthermore, a comprehensive parametric study is carried out to determine the effects of different boundary conditions, aspect ratios, and material variations on the free vibration of FGM plates. Nomenclature

show abstract

“…The plate middle surface is described by the following position vector r(x, ϑ) = (R i + x) cos ϑ e 1 − (R i + x) sin ϑ e 2 (91) where x, ϑ are the principal coordinate of the surface, assuming x ∈ [0, L] and ϑ ∈ [0, 2π]. The inner radius is denoted by R i , whereas the outer one can be computed as R out = R i + L. A linear variation is applied along the radial direction to define the thickness profile…”

Section: Comparison With the Literaturementioning

confidence: 99%

“…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

View full text Add to dashboard Cite

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.

show abstract

Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations

Cited by 71 publications

References 23 publications

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

On the FEM Analysis of Higher-Order Shear Deformable Beams: Validation of an Efficient Element

Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

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

Contact Info

Product

Resources

About