A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution

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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.

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

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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

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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.

“…To overcome the disadvantages of the original DQFEM, the virtual spring technique is introduced. The virtual spring technique has been used widely in simulation of the elastic boundary conditions as well as the coupling conditions [31,32]. Thus, the connection relationships between elements can be easily modified just by setting the stiffness of the virtual springs.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Plate with Irregular Cracks by Differential Quadrature Finite Element Method

Xu¹,

Chen²

2017

A universal method combining the differential quadrature finite element method with the virtual spring technique for analyzing the free vibration of thin plate with irregular cracks is proposed. Translational and rotational springs are introduced to restrain the vertical displacement and orientation of the plate. The mass matrix and stiffness matrix for each element are deduced involving the effects of the virtual springs. The connection relationships between elements can be modified by setting the stiffness of the virtual springs. The vibration of two rectangular plates with three irregular shaped cracks and different boundary conditions are presented. The results are compared with those obtained by ANSYS, where the good agreement between the results validates the accuracy and efficiency of the present method.