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.

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.

scholarly journals Study Of Three Dimensional Propagation Of Waves In Hollow Poroelastic Circular Cylinders

2015 ◽  
Vol 20 (3) ◽  
pp. 565-587
Author(s):  
S.A. Shah
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Longitudinal Shear ◽  
Frequency Equation ◽  
Circular Cylinders ◽  
Torsional Vibrations ◽  
Saturated Porous Media ◽  
Axially Symmetric ◽  
General Frequency ◽  
Propagation Of Waves

Abstract Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic circular cylinder of infinite extent are investigated. General frequency equations for propagation of waves are obtained each for a pervious and an impervious surface. Degenerate cases of the general frequency equations of pervious and impervious surfaces, when the longitudinal wavenumber k and angular wavenumber n are zero, are considered. When k=0, the plane-strain vibrations and longitudinal shear vibrations are uncoupled and when k≠0 these are coupled. It is seen that the frequency equation of longitudinal shear vibrations is independent of the nature of the surface. When the angular (or circumferential) wavenumber is zero, i.e., n=0, axially symmetric vibrations and torsional vibrations are uncoupled. For n≠0 these vibrations are coupled. The frequency equation of torsional vibrations is independent of the nature of the surface. By ignoring liquid effects, the results of a purely elastic solid are obtained as a special case.

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.

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

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.

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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