scholarly journals Vibration Analysis of Annular Sector Plates under Different Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Dongyan Shi ◽  
Xianjie Shi ◽  
Wen L. Li ◽  
Qingshan Wang ◽  
Jiashan Han
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Current Method ◽  
Analytical Framework ◽  
Generalized Coordinates ◽  
Accelerated Convergence ◽  
Equal Importance ◽  
Annular Sector ◽  
Expansion Coefficients ◽  
Elastic Restraints

An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.

Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Shiliang Jiang ◽  
Tiejun Yang ◽  
W. L. Li ◽  
Jingtao Du
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Wide Spectrum ◽  
Current Method ◽  
Entire Solution ◽  
Shallow Shells ◽  
Special Cases ◽  
Out Of Plane ◽  
Expansion Coefficients ◽  
Doubly Curved

An analytical method is derived for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports alone its edges, a class of problems which are rarely attempted in the literature. Under this framework, all the classical homogeneous boundary conditions for both in-plane and out-of-plane displacements can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Regardless of the boundary conditions, the displacement functions are invariably expanded as an improved trigonometric series which converges uniformly and polynomially over the entire solution domain. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh–Ritz technique. Unlike most of the existing solution techniques, the current method offers a unified solution to a wide spectrum of shell problems involving, such as different boundary conditions, varying material and geometric properties with no need of modifying or adapting the solution schemes and implementing procedures. A numerical example is presented to demonstrate the accuracy and reliability of the current method.

scholarly journals Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Shi ◽  
Teijun Yang ◽  
Shiliang Jiang ◽  
W. L. Li ◽  
Zhigang Liu
Keyword(s):  
Boundary Conditions ◽  
Current Method ◽  
Vibration Characteristics ◽  
Shallow Shells ◽  
Various Boundary Conditions ◽  
Curvature Effects ◽  
Fourier Series Method ◽  
Vibration Problems ◽  
Elastic Restraints ◽  
Doubly Curved

Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

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.

Static and Dynamic Analysis of Annular Sector Plates Subjected to Arbitrary Boundary Conditions

2014 ◽  
Vol 624 ◽  
pp. 240-244
Author(s):  
Kai Peng Zhang ◽  
Cheng Yang ◽  
Han Wu
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Current Method ◽  
Displacement Function ◽  
Current Approach ◽  
Arbitrary Boundary ◽  
Static And Dynamic Analysis ◽  
Arbitrary Boundary Conditions ◽  
Annular Sector

In this investigation, an improved Fourier series method (IFSM) is employed to predict the static and dynamic characteristics of annular sector plates with arbitrary boundary conditions. Regardless of boundary supports, the displacement function is invariantly expressed as a modified two-dimensional Fourier series containing sine and cosine function. It is capable of dealing with the possible discontinuities at elastic boundary edges. The unknown Fourier coefficients are treated as generalized coordinates, and determined using Rayleigh-Ritz method. Unlike most of the existing solution techniques, the current approach can be universally applied to a variety of edge restraints including all classical cases and their combinations. The accuracy and reliability of the current method are fully illustrated through all the numerical examples.

Modified Fourier–Ritz Approximation for the Free Vibration Analysis of Laminated Functionally Graded Plates with Elastic Restraints

2015 ◽  
Vol 07 (05) ◽  
pp. 1550073 ◽  
Author(s):  
Zhu Su ◽  
Guoyong Jin ◽  
Xueren Wang ◽  
Xuhong Miao
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Lamina Thickness ◽  
Volume Fractions ◽  
Elastic Restraints ◽  
Benchmark Solutions

Free vibration analysis of moderately thick laminated functionally graded rectangular plates with elastic restraints is presented using the modified Fourier–Ritz method in conjunction with the first-order shear deformation plate theory. The material properties are assumed to change continuously through the lamina thickness according to a power-law distribution of volume fractions of the constituents. Each of the displacements and rotations of the laminated functionally graded plates, regardless of boundary conditions, is represented by a modified Fourier series which is constructed as the linear superposition of a standard Fourier cosine series and several closed-form auxiliary functions. The accuracy, convergence and reliability of the current solutions are demonstrated by numerical examples and comparison of the present results with those available in the literature. New results for free vibration of laminated functionally graded plates are presented, which may serve as benchmark solutions. The effects of the boundary conditions, volume fractions and lamina thickness ratios on the frequencies of the plates are investigated.

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Sign in / Sign up

Export Citation Format

Share Document