Unified approach for vibration analyses of annular sector and annular plates with general boundary conditions

2017 ◽  
Vol 22 (4) ◽  
pp. 449-458 ◽  
Author(s):  
Xianjie Shi ◽  
Chunli Li ◽  
Fayuan Wei
Keyword(s):  
Boundary Conditions ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Unified Approach ◽  
Annular Plates ◽  
Annular Sector

Free In-Plane Vibration Analysis of Annular Plates with General Boundary Conditions

2013 ◽  
Vol 572 ◽  
pp. 189-192
Author(s):  
Dong Yan Shi ◽  
Xian Jie Shi ◽  
Wen L. Li ◽  
Zheng Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Current Method ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Series Solutions ◽  
Plane Vibration ◽  
Annular Plates ◽  
Special Cases

An analytical method is derived for the free in-plane vibration analysis of annular plates with general boundary conditions. Under this framework, all the classical homogeneous boundary conditions can be treated as the special cases when the stiffness for each restraining springs is equal to either zero or infinity. The improved Fourier series solutions for the in-plane vibrations are obtained by employing the Rayleigh-Ritz method. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

scholarly journals A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xue-Qin Li ◽  
Wei Zhang ◽  
Xiao-Dong Yang ◽  
Lu-Kai Song
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Unified Approach ◽  
Stiffened Cylindrical Shell

A unified approach of free vibration analysis for stiffened cylindrical shell with general boundary conditions is presented in this paper. The vibration of stiffened cylindrical shell is modeled mathematically involving the first-order shear deformation shell theory. The improved Fourier series is selected as the admissible displacement function while the arbitrary boundary conditions are simulated by adjusting the equivalent spring stiffness. The natural frequencies and modal shapes of the stiffened shell are obtained by solving the dynamic model with the Rayleigh-Ritz procedure. Various numerical results of free vibration analysis for stiffened cylindrical shell are obtained, including natural frequencies and modes under simply supported, free, and clamped boundary conditions. Moreover, the effects of stiffener on natural frequencies are discussed. Compared with several state-of-the-art methods, the feasibility and validity of the proposed method are verified.

scholarly journals A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

2017 ◽  
Vol 4 (1) ◽  
pp. 189-220 ◽  
Author(s):  
Fuzhen Pang ◽  
Haichao Li ◽  
Xuhong Miao ◽  
Xueren Wang
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Radial Line ◽  
Solution Approach ◽  
Present Solution ◽  
Annular Sector ◽  
Benchmark Solutions

Abstract In this paper, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problem of moderately thick composite laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports. In this solution approach, regardless of boundary conditions, the displacement and rotation components of the sector plate are written in the form of the trigonometric series expansion in which several auxiliary terms are added to ensure and accelerate the convergence of the series. Each of the unknown coefficients is taken as the generalized coordinate and determined using the Raleigh- Ritz method. The accuracy and reliability of the present solution are validated by the comparison with the results found in the literature, and numerous new results for composite laminated annular sector plates considering various kinds of boundary conditions are presented. Comprehensive studies on the effects of elastic restraint parameters, layout schemes and locations of line/arc supports are also made.New results are obtained for laminated annular sector plates subjected to elastic boundary restraints and arbitrary internal radial line and circumferential arc supports in both directions, and they may serve as benchmark solutions for future researches.

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