Free Vibration of a Circular Cylindrical Shell Elastically Restrained by Axially Spaced Springs

1983 ◽  
Vol 50 (3) ◽  
pp. 544-548 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Muramoto
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Circular Cylindrical Shell ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Governing Equations ◽  
Structure Matrix ◽  
The Matrix ◽  
Circular Cylindrical Shells ◽  
Elastically Restrained

An analysis is presented for the free vibration of a circular cylindrical shell restrained by axially spaced elastic springs. The governing equations of vibration of a circular cylindrical shell are written as a coupled set of first-order differential equations by using the transfer matrix of the shell. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrices and the point matrices at the springs, and the frequency equation is derived with terms of the elements of the structure matrix under the boundary conditions. The method is applied to circular cylindrical shells supported by axially equispaced springs of the same stiffness, and the natural frequencies and the mode shapes of vibration are calculated numerically.

Analysis of Fiberglass Winding Angle on Natural Frequency of Cylindrical Shell with Symmetric Boundary Conditions

2013 ◽  
Vol 765-767 ◽  
pp. 106-109
Author(s):  
Zhi Wei Wang ◽  
Yan Fu Wang ◽  
Bai Qin
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Circular Cylindrical Shell ◽  
Glass Fiber Reinforced Plastic ◽  
Glass Fiber Reinforced ◽  
Reinforced Plastic ◽  
Circular Cylindrical Shells ◽  
Winding Angle

In order to obtain approximate solution of natural frequencies for the free vibration of anisotropic circular cylindrical shells made of GFRP (glass fiber-reinforced plastic) with symmetric boundary conditions, Loves theory and energy method are used. Computation results show that the fundamental natural frequency comes from different vibration modes while the winding angle varies, the effect of number of axial half waves is stronger than number of circumferential waves on natural frequency of free vibration of anisotropic circular cylindrical shell.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

2019 ◽  
Vol 19 (08) ◽  
pp. 1950084 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Young's Modulus ◽  
Mass Density ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Governing Equations ◽  
Direct Integral

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

Parametric Resonance of Liquid Storage Axisymmetric Shell Under Horizontal Excitation

1991 ◽  
Vol 113 (4) ◽  
pp. 511-516 ◽  
Author(s):  
M. Takayanagi
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Parametric Resonance ◽  
Circular Cylindrical Shell ◽  
Translational Motion ◽  
Harmonic Balance Method ◽  
Vibration Modes ◽  
Liquid Storage ◽  
Axisymmetric Shell ◽  
Axisymmetric Shells

A procedure for analyzing parametric resonance of liquid storage axisymmetric shells is proposed that is an extension of the procedure presented at PVP-89 for parametric resonance of empty axisymmetric shells with lumped weights. Free vibration modes of axisymmetric shells containing liquid are calculated considering the effect of initial stress due to static liquid pressure by using a conical shell finite element. The calculated free vibration modes are used to expand the free vibration modes of the axisymmetric shell with lumped weights and internal liquid. A type of Mathieu equation is derived considering the effects of the translational motion of the attached weight in the radial direction or the effects of the beam-type motion of the shell without lumped weight. The harmonic balance method is used to obtain the parametric resonance regions. Principal resonance of a circular cylindrical shell with an attached weight and combination resonance of a liquid storage circular cylindrical shell without attached weights are analyzed. Analytical results show good agreement with experimental results.

Free vibration of bi-material cylindrical shells

2016 ◽  
Vol 230 (15) ◽  
pp. 2637-2649 ◽  
Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi
Keyword(s):  
Exact Solution ◽  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Thin Shell ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Space Technique ◽  
Thin Shell Theory

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

Influence of Boundary Conditions on the Active Control of Vibration and Sound Radiation for a Circular Cylindrical Shell

2011 ◽  
Vol 66-68 ◽  
pp. 1270-1277
Author(s):  
Lu Dai ◽  
Tie Jun Yang ◽  
Yao Sun ◽  
Ji Xin Liu
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Active Control ◽  
Structural Engineering ◽  
Acoustic Radiation ◽  
Circular Cylindrical Shell ◽  
Acoustic Power ◽  
Fourier Series Method ◽  
Vibration And Sound Radiation ◽  
Elastically Restrained

Vibration and acoustic radiation of circular cylindrical shells are hot topics in the structural engineering field. However for a long period, this sort of problems is only limit to classical homogeneous boundary conditions. In this paper, the vibration of a circular cylindrical shell with elastic boundary supports is studied using modified Fourier series method, and the far-field pressure for a baffled shell is calculated by Helmholtz integral equation. Active control of vibration and acoustic radiation are carried out by minimizing structural kinetic energy and radiated acoustic power respectively. The influence of boundary conditions on the active control is investigated throughout several numerical examples. It is shown that the active control of vibration and acoustic for an elastically restrained shell can exhibit unexpected and complicated behaviors.

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