Free vibration analysis of mindlin plates with parabolically varying thickness

Al-Kaabi, Saif; Aksu, G.

doi:10.1016/0045-7949(89)90481-1

Cited by 7 publications

(4 citation statements)

References 5 publications

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“…In addition, these authors assumed that the thickness of these FG structures was taken to constant. In this comparison, the material properties and geometry parameters of the shallow shells are used in the following: 3 , r m = 2702kg=m 3 and a=b = 1, h=a = 0:1. From the Table 1, the numerical results show an excellent agreement with the above papers.…”

Section: Validation Of Present Studymentioning

confidence: 99%

“…As the main results, the numerical examples will be presented for the FG shallow shells with porosities in this section. The material parameters of FG shallow shells are assumed as: E c = 348:43GPa, r c = 2370kg=m 3 , E m = 201:04GPa, r c = 8166kg=m 3 , v = 0:3.…”

Section: Parametric Studymentioning

confidence: 99%

“…Case study (3). The goal of this case study is to characterize the influence of porosities, which can occur during the fabrication of FGMs on the fundamental frequencies of the shallow shells.…”

Section: Parametric Studymentioning

confidence: 99%

“…In which, the orthotropic plates were assumed to have a variable thickness in one direction. A Mindilin isotropic plate model with the variable thickness in linear distribution was presented by Aksu and Al-kaabi 2,3 for the free vibration problem. Also, Lim and Liew applied a numerical solution for analyzing the free flexural vibration of rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of functionally graded shallow shells with variable thickness and physical neutral surface effects

Thang,

Do,

Nguyen-Thoi

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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The study and manufacture of functionally graded (FG) shallow shells with the variable thickness are essential for the actual application of these types of structures. Previously, many researchers have developed different approaches to analyzing the mechanical behaviors of the FG structures, in which the thickness parameter has been assumed to be constant. Moreover, studies on these types of structures with the variable thickness are still quite limited. For this reason, this paper provides an effective and simple approach via mathematical formulations for analyzing the free vibrational responses of FG shallow shells with the variable thickness. Also, the presence of porosities that can occur during the fabrication of FG materials is considered. One of the highlights here is to consider the influence of the physical neutral surface. Before conducting the analysis of these FG structures, firstly, it is important to establish governing equations based on the classical shell theory. These essential equations are used for the FG shallow shells. Then, by setting the Navier solution with the help of simply supported boundary conditions, the natural frequencies are obtained. Finally, the numerical examples will be given to illustrate the effects of porosity coefficient, material and geometry parameters as well as the physical neutral surface on the natural frequencies. In addition, two numerical examples for verification will also be performed and thereby show the accuracy of the current method and model. It is hoped that the main results of this study can be useful not only to designers and researchers but also to be extended to more complex problems.

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Section: Validation Of Present Studymentioning

confidence: 99%

Section: Parametric Studymentioning

confidence: 99%

Section: Parametric Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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