Vibrations of Circular Cylindrical Shells With General Elastic Boundary Restraints

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
W. L. Li
Keyword(s):  
Boundary Conditions ◽  
Solution Method ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Elastic Boundary ◽  
Special Cases ◽  
Ritz Procedure ◽  
Circular Cylindrical Shells ◽  
Elastically Restrained ◽  
Structural Engineers

Vibration of a circular cylindrical shell with elastic boundary restraints is of interest to both researchers and structural engineers. This class of problems, however, is far less attempted in the literature than its counterparts for beams and plates. In this paper, a general solution method is presented for the vibration analysis of cylindrical shells with elastic boundary supports. This method universally applies to shells with a wide variety of boundary conditions including all 136 classical (homogeneous) boundary conditions which represent the special cases when the stiffnesses for the restraining springs are set as either zero or infinity. The Rayleigh–Ritz procedure based on the Donnell–Mushtari theory is utilized to find the displacement solutions in the form of the modified Fourier series expansions. Numerical examples are given to demonstrate the accuracy and reliability of the current solution method. The modal characteristics of elastically restrained shells are discussed against different supporting stiffnesses and configurations.

scholarly journals Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading

1998 ◽  
Vol 5 (5-6) ◽  
pp. 343-354 ◽  
Author(s):  
T.Y. Ng ◽  
K.Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Axial Loading ◽  
Various Boundary Conditions ◽  
Transverse Modes ◽  
First Approximation ◽  
Ritz Procedure ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Parametric Response

In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Free vibration analysis of porous laminated rotating circular cylindrical shells

2019 ◽  
Vol 25 (18) ◽  
pp. 2494-2508 ◽  
Author(s):  
Ahmad Reza Ghasemi ◽  
Mohammad Meskini
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Equilibrium Equations ◽  
Rotating Speed ◽  
Simply Supported ◽  
Numerical Result ◽  
Love’S Shell Theory ◽  
Circular Cylindrical Shells

In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

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.

scholarly journals Free Vibration Analysis of Circular Cylindrical Shells with Arbitrary Boundary Conditions by the Method of Reverberation-Ray Matrix

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Dong Tang ◽  
Guoxun Wu ◽  
Xiongliang Yao ◽  
Chuanlong Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Traveling Wave ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Wave Form ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Circular Cylindrical Shells

An analytical procedure for free vibration analysis of circular cylindrical shells with arbitrary boundary conditions is developed with the employment of the method of reverberation-ray matrix. Based on the Flügge thin shell theory, the equations of motion are solved and exact solutions of the traveling wave form along the axial direction and the standing wave form along the circumferential direction are obtained. With such a unidirectional traveling wave form solution, the method of reverberation-ray matrix is introduced to derive a unified and compact form of equation for natural frequencies of circular cylindrical shells with arbitrary boundary conditions. The exact frequency parameters obtained in this paper are validated by comparing with those given by other researchers. The effects of the elastic restraints on the frequency parameters are examined in detail and some novel and useful conclusions are achieved.

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.

scholarly journals Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Muhmmad Nawaz Naeem ◽  
Shazia Kanwal ◽  
Abdul Ghafar Shah ◽  
Shahid Hussain Arshad ◽  
Tahir Mahmood
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Lagrangian Function ◽  
Dynamical Equations ◽  
Graded Materials ◽  
Present Technique ◽  
Circular Cylindrical Shells ◽  
Stiffened Cylindrical Shells

The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.

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.

Aerothermoelastic Stability of Functionally Graded Circular Cylindrical Shells

2010 ◽  
Author(s):  
Farhad Sabri ◽  
Aouni A. Lakis
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Shell Thickness ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Aerodynamic Pressure ◽  
Circular Cylindrical Shells

In this work, a hybrid finite element formulation is presented to predict the flutter boundaries of circular cylindrical shells made of functionally graded materials. The development is based on the combination of linear Sanders thin shell theory and classic finite element method. Material properties are temperature dependent, and graded in the shell thickness direction according to a simple power law distribution in terms of volume fractions of constituents. The temperature field is assumed to be uniform over the shell surface and along the shell thickness. First order piston theory is applied to account for supersonic aerodynamic pressure. The effects of temperature rise and shell internal pressure on the flutter boundaries of FG circular cylindrical shell for different values of power law index are investigated. The present study shows efficient and reliable results that can be applied to the aeroelastic design and analysis of shells of revolution in aerospace vehicles.

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