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.

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.

The Out-of-Plane Stability Analysis of Crane Jib with Two Symmetric Drawbars

2013 ◽  
Vol 446-447 ◽  
pp. 469-473
Author(s):  
Nian Li Lu ◽  
Ce Chen ◽  
Shi Ming Liu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Characteristic Equation ◽  
Critical Condition ◽  
Design Rules ◽  
Special Cases ◽  
Out Of Plane

The out-of-plane stability of the crane jib with two symmetric drawbars is studied. Differential equation with two non-conservative forces caused by the two symmetric drawbars is established in critical condition. According to the boundary conditions and proper parameter processing, the out-of-plane characteristic equation is obtained for the crane jib. Comparison with the ANSYS results verified the correctness of the method. And special cases are given to show the consistency of the method used in this paper and that with one drawbar given by the Chinese Design Rules for crane (GB3811-2008). The contribution of the angle between two symmetric drawbars to the out-of-plane stability of the crane jib is also discussed. The results show that, the crane jib with two symmetric drawbars has higher out-of-plane stability than that with one drawbar, and the increase of the angle between the two symmetric drawbars will lead to the significant increase of the out-of-plane stability of the crane jib.

scholarly journals In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianjie Shi ◽  
Dongyan Shi ◽  
Zhengrong Qin ◽  
Qingshan Wang
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Wide Spectrum ◽  
Arbitrary Boundary ◽  
Different Boundary Conditions ◽  
Plane Vibration ◽  
Arbitrary Boundary Conditions ◽  
Annular Plates ◽  
Generalized Fourier Series

In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

scholarly journals Accurate Results for Free Vibration of Doubly Curved　Shallow Shells of Rectangular Planform (Part.1)

2021 ◽  
Vol 4 (1) ◽  
pp. 29-36
Author(s):  
Daisuke Narita ◽  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Frequency Equation ◽  
Shell Shape ◽  
Comparison Study ◽  
Shallow Shells ◽  
Wide Range ◽  
Out Of Plane ◽  
Edge Conditions ◽  
Doubly Curved

A method is presented for determining the free vibration frequencies of doubly curved, isotropic shallow shells under general edge conditions and is used to obtain accurate natural frequencies for wide range of geometric parameters. Based on the shallow shell theory applicable to thin thickness shells, a method of Ritz is extended to derive a frequency equation wherein the displacement functions are modified to accommodate arbitrary sets of edge conditions for both in-plane and out-of-plane motions. In numerical computation, convergence is tested against series terms and comparison study is made with existing results by other authors. Twenty one sets of frequency parameters are tabulated for a wide range of shell shape and curvature ratio to serve as data for future comparison and practical design purpose.  

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