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.

Methods of Analysis for Very Thick-Walled Cylindrical Shells

1975 ◽  
Vol 97 (1) ◽  
pp. 175-181 ◽  
Author(s):  
J. R. Vinson
Keyword(s):  
Boundary Conditions ◽  
Wall Thickness ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Explicit Solutions ◽  
Axially Symmetric ◽  
Various Boundary Conditions ◽  
First Approximation ◽  
Methods Of Analysis ◽  
Elasticity Solutions

Methods of analysis are presented for very thick-walled cylindrical, isotropic shells subjected to axially symmetric lateral and in-plane loads. These methods are developed for shells with ratios of wall thickness to mean radius as large as 0.5, as well as being applicable for thin classical shells which involve Love’s First Approximation. The present methods are elasticity solutions and employ no shell theory assumptions. Explicit solutions are presented for the shell subject to in-plane loads and laterally distributed loads which are constant or varying linearly axially for various boundary conditions at the ends.

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.

Dynamic Stability of Transverse Axisymmetric Waves in Circular Cylindrical Shells

1974 ◽  
Vol 41 (1) ◽  
pp. 77-82 ◽  
Author(s):  
J. H. Ginsberg
Keyword(s):  
Asymptotic Expansion ◽  
Phase Velocity ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Transverse Displacement ◽  
First Approximation ◽  
Uniform Asymptotic Expansion ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Stability Limits

Previous experiments [1] have indicated that axisymmetric waves may be unstable and that nonsymmetric waves may result. To show that it is possible for such a phenomenon to occur even in perfectly cylindrical shells, a new mechanism for the coupling of the two types of waves is determined. Relationships for the phase velocity of steady-state waves as a function of the amplitude of transverse displacement are obtained. The stability of the system is shown to be defined by an equivalent nonlinear system with two degrees of freedom. It is found that the stability limits are the bifurcation points in the amplitude-phase velocity diagram for the axisymmetric and nonsymmetric waves. The solution is a uniform asymptotic expansion of the modal series for the displacement components and retains all effects significant to the first approximation of the nonlinearity.

Chebyshev Collocation Solutions for Vibration Analysis of Circular Cylindrical Shells with Arbitrary Boundary Conditions

2017 ◽  
Vol 17 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Nuttawit Wattanasakulpong ◽  
Sacharuck Pornpeerakeat ◽  
Arisara Chaikittiratana
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Chebyshev Collocation Method ◽  
Arbitrary Boundary ◽  
Chebyshev Collocation ◽  
Various Boundary Conditions ◽  
Circular Cylindrical Shells

This paper applies the Chebyshev collocation method to finding accurate solutions of natural frequencies for circular cylindrical shells. The shells with different boundary conditions are considered in the parametric study. By using the method to solve the coupled differential equations of motion governing the vibration of the shell, numerical results are obtained from the algebraic eigenvalue equation using the Chebyshev differentiation matrices. And the results satisfy both the geometric and force boundary conditions. Based on the numerical examples, the proposed method shows its capacity and reliability in predicting accurate frequency results for circular cylindrical shells with various boundary conditions as compared to some exact solutions available in the literature.

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.

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