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...
Main Authors: | , , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2019-01-01
|
Series: | Shock and Vibration |
Online Access: | http://dx.doi.org/10.1155/2019/2803841 |
id |
doaj-2269b10bd3e24a3cae970c3282351a60 |
---|---|
record_format |
Article |
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 |
work_keys_str_mv |
AT conggao freevibrationanalysisoffunctionallygradedsphericaltorusstructurewithuniformvariablethicknessalongaxialdirection AT xuhongmiao freevibrationanalysisoffunctionallygradedsphericaltorusstructurewithuniformvariablethicknessalongaxialdirection AT linlu freevibrationanalysisoffunctionallygradedsphericaltorusstructurewithuniformvariablethicknessalongaxialdirection AT ruidonghuo freevibrationanalysisoffunctionallygradedsphericaltorusstructurewithuniformvariablethicknessalongaxialdirection AT qiaolinhu freevibrationanalysisoffunctionallygradedsphericaltorusstructurewithuniformvariablethicknessalongaxialdirection AT yanheshan freevibrationanalysisoffunctionallygradedsphericaltorusstructurewithuniformvariablethicknessalongaxialdirection |
_version_ |
1724897205469315072 |