Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction

Based on the Ritz method, this paper focused on the free vibration of functionally graded (FG) spherical torus with uniform variable thickness along axial direction under different boundary conditions. The first-order shear deformation theory (FSDT) is employed to formulate the analytical model. The...

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Main Authors: Cong Gao, Xuhong Miao, Lin Lu, Ruidong Huo, Qiaolin Hu, Yanhe Shan
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.1155/2019/2803841
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spelling doaj-2269b10bd3e24a3cae970c3282351a602020-11-25T02:15:21ZengHindawi LimitedShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/28038412803841Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial DirectionCong Gao0Xuhong Miao1Lin Lu2Ruidong Huo3Qiaolin Hu4Yanhe Shan5College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaJinan Vocational College, Jinan 250014, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaBased on the Ritz method, this paper focused on the free vibration of functionally graded (FG) spherical torus with uniform variable thickness along axial direction under different boundary conditions. The first-order shear deformation theory (FSDT) is employed to formulate the analytical model. The method involves partitioning of the spherical torus structure into proper shell segments in order to satisfy the computing requirement of high-order vibration responses according to the domain decomposition method. The two adjacent segments are connected by using the penalty method, where penalty parameters are defined by the artificial springs; the continuity condition and different boundary conditions can be obtained by assigning the appropriate values of springs. The displacement functions’ components are double mixed series, in which Fourier series and unified Jacobi polynomials, respectively, represent displacement function along circumferential direction and axial direction. Then the Ritz method is used to obtain final solutions. The numerical results obtained by the proposed method show great agreement with previously published literatures and those from the finite element program ABAQUS. The effects of boundary conditions and geometric parameters on the vibration responses of the structure are also presented. The most novelty of this paper is to generalize the selection of admissible displacement functions by using Jacobi polynomial.http://dx.doi.org/10.1155/2019/2803841
collection DOAJ
language English
format Article
sources DOAJ
author Cong Gao
Xuhong Miao
Lin Lu
Ruidong Huo
Qiaolin Hu
Yanhe Shan
spellingShingle Cong Gao
Xuhong Miao
Lin Lu
Ruidong Huo
Qiaolin Hu
Yanhe Shan
Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction
Shock and Vibration
author_facet Cong Gao
Xuhong Miao
Lin Lu
Ruidong Huo
Qiaolin Hu
Yanhe Shan
author_sort Cong Gao
title Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction
title_short Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction
title_full Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction
title_fullStr Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction
title_full_unstemmed Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction
title_sort free vibration analysis of functionally graded spherical torus structure with uniform variable thickness along axial direction
publisher Hindawi Limited
series Shock and Vibration
issn 1070-9622
1875-9203
publishDate 2019-01-01
description Based on the Ritz method, this paper focused on the free vibration of functionally graded (FG) spherical torus with uniform variable thickness along axial direction under different boundary conditions. The first-order shear deformation theory (FSDT) is employed to formulate the analytical model. The method involves partitioning of the spherical torus structure into proper shell segments in order to satisfy the computing requirement of high-order vibration responses according to the domain decomposition method. The two adjacent segments are connected by using the penalty method, where penalty parameters are defined by the artificial springs; the continuity condition and different boundary conditions can be obtained by assigning the appropriate values of springs. The displacement functions’ components are double mixed series, in which Fourier series and unified Jacobi polynomials, respectively, represent displacement function along circumferential direction and axial direction. Then the Ritz method is used to obtain final solutions. The numerical results obtained by the proposed method show great agreement with previously published literatures and those from the finite element program ABAQUS. The effects of boundary conditions and geometric parameters on the vibration responses of the structure are also presented. The most novelty of this paper is to generalize the selection of admissible displacement functions by using Jacobi polynomial.
url http://dx.doi.org/10.1155/2019/2803841
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