A Theoretical and Experimental Study of Vibrations of Thick Circular Cylindrical Shells and Rings

1988 ◽  
Vol 110 (4) ◽  
pp. 533-537 ◽  
Author(s):  
R. K. Singal ◽  
K. Williams
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Frequency Equation ◽  
Experimental Investigations ◽  
Resonant Frequencies ◽  
Modes Of Vibration ◽  
Circular Cylindrical Shells ◽  
Experimental Values

The free vibrations of thick circular cylindrical shells and rings are discussed in this paper. The well-known energy method, which is based on the three-dimensional theory of elasticity, is used in the derivation of the frequency equation of the shell. The frequency equation yields resonant frequencies for all the circumferential modes of vibration, including the breathing and beam-type modes. Experimental investigations were carried out on several models in order to assess the validity of the analysis. This paper first describes briefly the method of analysis. In the end, the calculated frequencies are compared with the experimental values. A very close agreement between the theoretical and experimental values of the resonant frequencies for all the models was obtained and this validates the method of analysis.

Effect of Radial Thickness on the In-Plane Free Vibrations of Circular Annular Discs

1991 ◽  
Vol 113 (4) ◽  
pp. 455-460 ◽  
Author(s):  
R. K. Singal ◽  
K. Williams ◽  
H. Wang
Keyword(s):  
Energy Method ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Experimental Models ◽  
Frequency Equation ◽  
Modes Of Vibration ◽  
Radial Thickness ◽  
Beam Type ◽  
Experimental Values

In this paper the in-plane free vibrations of both thick and thin circular annular discs are studied. The well-known energy method, which is based on the three-dimensional theory of elasticity, is used in the derivation of the frequency equation of the disc. The frequency equation yields all the natural frequencies for all the circumferential modes of vibration, including the breathing and beam-type modes. In order to assess the validity of the analysis experimental data were acquired on several models. The paper first describes briefly the energy method analysis, this is followed by a description of the various experimental models. Finally, the calculated values of frequencies are compared with the experimental values. A very close agreement between both the theoretical and experimental values of the resonant frequencies for all the models was obtained and this validates the energy method of analysis.

Propagation of Harmonic Waves in Orthotropic Circular Cylindrical Shells

1973 ◽  
Vol 40 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. E. Armena`kas ◽  
E. S. Reitz
Keyword(s):  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Longitudinal Shear ◽  
Theory Of Elasticity ◽  
Frequency Equation ◽  
Radial Coordinate ◽  
Harmonic Waves ◽  
Circular Cylindrical Shells ◽  
General Frequency

In this investigation, the general frequency equation for trains of harmonic waves having an arbitrary number of circumferential nodes, traveling in orthotropic, circular, cylindrical shells is established on the basis of the three-dimensional linear theory of elasticity, by expanding the displacement components in power series of the radial coordinate. Simpler forms of the frequency equation for axisymmetric nontorsional and torsional motion and for longitudinal-shear and plane-strain motion are established and discussed. The frequency equation has been evaluated numerically on an IBM 360/50 digital computer system and the numerical results are compared with those obtained on the basis of an approximate shell theory.

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 Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

Dispersion of flexural waves in circular cylindrical shells

1972 ◽  
Vol 329 (1578) ◽  
pp. 283-297 ◽  
Keyword(s):  
Linear Elasticity ◽  
Poisson Ratio ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Real Plane ◽  
Solid Cylinder ◽  
Flexural Waves ◽  
Circular Cylindrical Shells ◽  
The Waves ◽  
Zero Frequency

The imaginary and complex branches of the dispersion spectra corresponding to flexural waves in circular cylindrical shells of various wall thicknesses including the solid cylinder have been constructed by utilizing exact three-dimensional equations of linear elasticity. The effects of wall thickness and Poisson ratio on the cut-off frequencies have been studied. Complex branches emanate from the points of frequency extrema on the purely imaginary or purely real branches and intersect the zero frequency plane, either as purely imaginary or as complex branches. The waves associated with complex branches emerging from points on the real plane are less decaying at higher frequencies.

Dynamic Buckling and Post-buckling of Imperfect Orthotropic Cylindrical Shells Under Mechanical and Thermal Loads, Based on the Three-Dimensional Theory of Elasticity

1999 ◽  
Vol 66 (2) ◽  
pp. 476-484 ◽  
Author(s):  
M. Shariyat ◽  
M. R. Eslami
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Dynamic Buckling ◽  
Curvilinear Coordinates ◽  
Thermal Loads ◽  
Dimensional Theory ◽  
Highly Nonlinear

The three-dimensional theory of elasticity in curvilinear coordinates is employed to investigate the dynamic buckling of an imperfect orthotropic circular cylindrical shell under mechanical and thermal loads. Accurate form of the strain expressions of imperfect cylindrical shells is established through employing the general Green's strain tensor for large deformations and the equations of motion are derived in terms of the second Piola-Kirchhoff stress tensor. Then, the governing equations are properly formulated and solved by means of an efficient and relatively accurate solution procedure proposed to solve the highly nonlinear equations resulting from the above analysis. The proposed formulation is very general as it can include the influence of the initial imperfections, temperature distribution, and temperature dependency of the mechanical properties of materials, effect of various end conditions, possibility of large-deformation occurrence and application of any combination of mechanical and thermal loadings. No simplifications are done when solving the resulting equations. Furthermore, in contrast to the displacement-based layer-wise theories and the three-dimensional approaches proposed so far, the stress, force and moment boundary conditions as well as the displacement type ones, can be incorporated accurately in these formulations. Finally, a few examples of mechanical and thermal buckling of some orthotropic cylindrical shells are considered and results of the present three-dimensional elasticity approach are compared with the buckling loads predicated by the Donnell's equations, some single-layer theories, some available results of the layer-wise theory and the recently published three-dimensional approaches and the accuracy of the later methods are discussed based on the exact method presented in this paper.

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