A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unif...

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Main Authors: Yuan Du, Liping Sun, Xuhong Miao, Fuzhen Pang, Haichao Li, Siyu Wang
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Shock and Vibration
Online Access:http://dx.doi.org/10.1155/2019/7470460
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author Yuan Du
Liping Sun
Xuhong Miao
Fuzhen Pang
Haichao Li
Siyu Wang
author_facet Yuan Du
Liping Sun
Xuhong Miao
Fuzhen Pang
Haichao Li
Siyu Wang
author_sort Yuan Du
collection DOAJ
description The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported.
format Article
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institution Kabale University
issn 1070-9622
1875-9203
language English
publishDate 2019-01-01
publisher Wiley
record_format Article
series Shock and Vibration
spelling doaj-art-b1f36eb366914a4f929d33da90bb04212025-02-03T01:10:02ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/74704607470460A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz MethodYuan Du0Liping Sun1Xuhong Miao2Fuzhen Pang3Haichao Li4Siyu Wang5College 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, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, ChinaThe free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported.http://dx.doi.org/10.1155/2019/7470460
spellingShingle Yuan Du
Liping Sun
Xuhong Miao
Fuzhen Pang
Haichao Li
Siyu Wang
A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
Shock and Vibration
title A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
title_full A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
title_fullStr A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
title_full_unstemmed A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
title_short A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
title_sort unified formulation for free vibration of spherical cap based on the ritz method
url http://dx.doi.org/10.1155/2019/7470460
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