Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution

Tornabene, Francesco; Viola, Erasmo

doi:10.1016/j.euromechsol.2009.04.005

Cited by 180 publications

(60 citation statements)

References 29 publications

(19 reference statements)

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“…The discretization of the system by means of the differential quadrature technique leads to the eigenvalue problem. Basing on the firstorder shear deformation theory, the paper [2] focuses on the dynamic behaviour of moderately thick functionally graded parabolic panels and shells of revolution. The generalized differential quadrature method has been used to discretize the system equations.…”

Section: Introductionmentioning

confidence: 99%

Deformation of compound shells under action of internal shock wave loading

Chernobryvko

Kruszka

Аврамов

2015

EPJ Web of Conferences

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Abstract. The compound shells under the action of internal shock wave loading are considered. The compound shell consists of a thin cylindrical shell and two thin parabolic shells at the edges. The boundary conditions in the shells joints satisfy the equality of displacements. The internal shock wave loading is modelled as the surplus pressure surface. This pressure is a function of the shell coordinates and time. The strain rate deformation of compound shell takes place in both the elastic and in plastic stages. In the elastic stage the equations of the structure motions are obtained by the assumed-modes method, which uses the kinetic and potential energies of the cylindrical and two parabolic shells. The dynamic behaviour of compound shells is treated. In local plastic zones the 3-D thermo-elastic-plastic model is used. The deformations are described by nonlinear model. The stress tensor elements are determined using dynamic deformation theory. The deformation properties of materials are influenced by the strain rate behaviour, the influence of temperature parameters, and the elastic-plastic properties of materials. The dynamic yield point of materials and Pisarenko-Lebedev's criterion of destruction are used. The modified adaptive finite differences method of numerical analysis is suggested for those simulations. The accuracy of the numerical simulation is verified on each temporal step of calculation and in the case of large deformation gradients.

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Section: Introductionmentioning

confidence: 99%

Deformation of compound shells under action of internal shock wave loading

Chernobryvko

Kruszka

Аврамов

2015

EPJ Web of Conferences

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“…Tornabene and Viola [1][2][3] studied the free vibration of the moderately thick four-parameter functionally graded conical, cylindrical shells and annular plates under some classical boundary conditions by means of the generalized differential quadrature method on the basis of the first-order shear deformation theory. Zhao and Liew [4,5] presented the element-free kp-Ritz method to investigate the free vibration analysis of mechanical and thermal buckling of functionally graded conical shell panels with classical boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Pang

et al. 2017

Mathematical Problems in Engineering

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The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

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“…Matsunaga [20] investigated a two-dimensional, higher-order theory for analyzing the thick simply supported rectangular plates resting on elastic foundations. Tornabene and Viola [21,22] investigated free vibration of three and four parameter functionally graded parabolic panels and shells of revolution. For the discretization of the system equations the Generalized Differential Quadrature (GDQ) method had been used.…”

Section: Introductionmentioning

confidence: 99%

An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

Tahouneh

2017

Period. Polytech. Mech. Eng.

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In the present work, vibration characteristics of functionally graded (FG) Keywords multiwalled carbon nanotubes, vibration, sandwich plates, modified Halpin-Tsai equation, three-dimensional elasticity solution IntroductionNowadays, the use of carbon nanotubes in polymer/carbon nanotube composites has attracted wide attention [1]. A high aspect ratio, low weight of CNTs and their extraordinary mechanical properties (strength and flexibility) provide the ultimate reinforcement for the next generation of extremely lightweight but highly elastic and very strong advanced composite materials. On the other hand, by using of the polymer/CNT composites in advanced composite materials, we can achieve structures with low weight, high strength and high stiffness in many structures of civil, mechanical and space engineering.Several researches have recently investigated the elastic properties of multiwalled carbon nanotube (MWCNT) and their composites [2,3]. Gojny et al. [4] focused on the evaluation of the different types of the CNTs applied, their influence on the mechanical properties of epoxy-based nanocomposites and the relevance of surface functionalization. Therefore, the study of the mechanical performance of CNT-based composites and the discovery of possible innovative applications has recently attracted the interest of many researchers.Several researchers have reported that mechanical properties of polymeric matrices can be drastically increased [5,6] by adding a few weight percent (wt%) MWCNTs. Montazeri et al. [5] showed that modified Halpin-Tsai equation with exponential Aspect ratio can be used to model the experimental result of MWCNT composite samples. They also demonstrated that reduction in Aspect ratio (L/d) and nanotube length cause a decrease in aggregation and above 1.5 wt%, nanotubes agglomerate causing a reduction in Young's modulus values. Thus, it is important to determine the effect Aspect ratio and arrangement of CNTs on the effective properties of carbon nanotube-reinforced composite (CNTRC). Yeh et al. [6] used the Halpin-Tsai equation to shows the effect of MWCNT shape factor (L/d) on the mechanical properties. They showed that the mechanical properties of nanocomposite samples with the higher shape factor (L/d) values were better than the ones with the lower shape factor. The reinforcement effect of MWCNTs with different aspect ratio in an epoxy matrix has been carried out by Martone et al. [7]. They showed that progressive reduction of

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Free vibrations of four-parameter functionally graded parabolic panels and shells of revolution

Cited by 180 publications

References 29 publications

Deformation of compound shells under action of internal shock wave loading

Deformation of compound shells under action of internal shock wave loading

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

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