Free vibration of functionally graded parabolic and circular panels with general boundary conditions

Zhang, Hong; Shi, Dongyan; Wang, Qingshan; Qin, Bin

doi:10.1515/cls-2017-0006

Cited by 16 publications

(4 citation statements)

References 69 publications

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“…For validation of the panel's analysis, the toro circular panel is analyzed. Then, the results were compared with [30]. The obtained results are explained in Table 7.…”

Section: Numerical Analysis and Discussionmentioning

confidence: 99%

Free vibration response of functionally graded carbon nanotubes double curved shell and panel with piezoelectric layers in a thermal environment

2019

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This paper presents free vibration of the double-curved shells and panels with piezoelectric layers in a thermal environment. Vibration characteristics of elliptical, spherical, cycloidal, and toro circular shells of revolution are studied in detail. These structures are made of a based carbon nanotubes (CNTs) core and piezoelectric layers at the upper and lower surfaces. It is supposed that temperature changes linearly through the thickness direction. Reissner-Mindlin and the first order shear deformation (FSDT) theories are implemented to derive the governing equations of the considered structures. The distribution of nanotubes is assumed to be linear along the thickness direction. For solving the equation, the General Differential Quadrature (GDQ) method is implemented to investigate the dynamic behavior of the structures. Finally, the effects of the boundary conditions, the thickness of piezoelectric layers, the functional distribution of CNTs, thermal environment and kinds of the circuit (opened-circuit and closedcircuit) are analyzed. Eigenvalue system is solved to obtain natural frequencies. It is delineated that the obtained fundamental frequency by the closed -circuit is smaller than those obtained by the opened-circuit. Another interesting result is that the natural frequency is decreased by increasing temperature.

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“…For validation of the panel's analysis, the toro circular panel is analyzed. Then, the results were compared with [30]. The obtained results are explained in Table 7.…”

Section: Numerical Analysis and Discussionmentioning

confidence: 99%

Free vibration response of functionally graded carbon nanotubes double curved shell and panel with piezoelectric layers in a thermal environment

2019

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“…The selection of an admissible displacement function is an important factor in guaranteeing a stable convergence and accuracy of the solution. In the handling of the continuity conditions, the use of spring stiffness, which can be seen as penalty parameters, makes the selection of admissible functions very flexible [37][38][39][40][41][42][43][44][45][46][47]. Subscript is omitted here for the sake of brevity.…”

Section: Unified Solution and Solutionmentioning

confidence: 99%

Free and Forced Vibration Analysis of Airtight Cylindrical Vessels with Doubly Curved Shells of Revolution by Using Jacobi-Ritz Method

Pang

Choe³

et al. 2017

Shock and Vibration

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This paper presents free and forced vibration analysis of airtight cylindrical vessels consisting of elliptical, paraboloidal, and cylindrical shells by using Jacobi-Ritz Method. In this research, the theoretical model for vibration analysis is formulated by Flügge's thin shell theory and the solution is obtained by Rayleigh-Ritz method. The vessel structure is divided into shell components (i.e., ellipsoid, parabolic, and cylinder) and their segments, and each displacement field of shell segments is represented by the Jacobi polynomials and the standard Fourier series. The continuous conditions at the interface are modeled by using the spring stiffness technique. The reliability and the accuracy of the present method are verified by comparing the results of the proposed method with the results of the previous literature and the finite element method (FEM). Moreover, some numerical results for free and forced vibration of elliptical-cylindrical-elliptical vessel (ECE vessel) and paraboloidal-cylindrical-elliptical vessel (PCE vessel) are reported.

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“…Thus, we study the FG shallow shell vibrations based on Rayleigh-Ritz energy method [64][65][66][67] which can obtain more accurate results. The Lagrangian energy function for the shallow shell can be written as…”

Section: Energy Expressionsmentioning

confidence: 99%

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Shi

Zha

Zhang

et al. 2017

Shock and Vibration

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The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and RayleighRitz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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Free vibration of functionally graded parabolic and circular panels with general boundary conditions

Cited by 16 publications

References 69 publications

Free vibration response of functionally graded carbon nanotubes double curved shell and panel with piezoelectric layers in a thermal environment

Free vibration response of functionally graded carbon nanotubes double curved shell and panel with piezoelectric layers in a thermal environment

Free and Forced Vibration Analysis of Airtight Cylindrical Vessels with Doubly Curved Shells of Revolution by Using Jacobi-Ritz Method

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

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