Free Vibrations Of Cylindrical Shells Research Articles

Analysis of free vibration of cylindrical shells on the basis of three dimensional exact elasticity theory

In this paper we present a study of free vibration of cylindrical shells on the basis of three dimensional exact theory. The studied boundary condition is simple-simple supported boundary condition. Extensive frequency parameters have been obtained through resolving frequency equations. The results of frequency parameters have been obtained by computers programs and have been compared with the results of classical theories. Keywords: Free vibration, Cylindrical shells, Frequencies, Exact elasticity theory

Free vibrations of cylindrical shells with elastic-support boundary conditions

This paper concerns the free vibrations of cylindrical shells with elastic boundary conditions. Based on the Flügge classical thin shell theory, the equations of motion for the cylindrical shells are solved by the method of wave propagations. The wave numbers are obtained by directly solving an eighth order equation. The elastic-support boundary conditions can be arbitrarily specified in terms of 8 independent sets of distributed springs. All the classical homogeneous boundary conditions can be considered as the special cases when the stiffness for each set of springs is equal to either infinity or zero. The present solutions are validated by the results previously given by other researchers and/or obtained using finite element models. The effects on the frequency parameters of elastic restraints are investigated for shells of different geometrical characteristics.

Nonlinear free vibration of cylindrical shells with delamination using high order shear deformation theory:-A finite element approach

A dynamic analysis method has been developed to investigate and characterize embedded delamination on the dynamic response of composite laminated structures. A nonlinear finite element model for geometrically large amplitude free vibration intact shallow cylindrical and delamination shell analysis is presented using higher order shear deformation theory where the nonlinearity was introduced in the Green-Lagrange sense. The governing equation of the vibrated shell were derived using the Variational approach. The effect of different orthotropicity ratio, and delamination size on the non-dimenational fundamental frequency and frequency ratios of plate for different stacking sequences. Finally the results were compared with those available in literatures where the discrepancy of the results was (15.8022 % with considering the nonlinearity).

On one approach to studying free vibrations of cylindrical shells of variable thickness in the circumferential direction within a refined statement

We used the spline collocation method for finding the frequencies of free vibrations of circular closed cylindrical shells of variable thickness in the circumferential direction. The problem was formulated within the framework of Mindlin’s refined theory. We studied the influence of change in the shell thickness on the distribution of its natural frequencies. Our calculations were carried out for different geometrical parameters of the shell and different boundary conditions. The validity of results obtained was verified by increasing the number of collocation points in our calculations and by comparing them with the results of computations according to the three-dimensional theory.

Free vibration characteristics of cylindrical shells partially buried in elastic foundations

Free vibrations of cylindrical shells partially buried in elastic foundations based on the finite element method were examined. The shells are discretized into cylindrical finite elements and the distribution of the foundation in the circumferential direction is defined by the expansion of Fourier series. The present formulation can be simply applied to consider non-uniformities in the foundation both in the circumferential and longitudinal directions. Convergence issues with the present method are explained. Numerical results of the natural frequency and mode for various shell geometries and foundation parameters are given to provide a clearer picture of the shell characteristics in linear vibrations. The relative stiffness ratio of foundation and shell is discussed. The results of free vibration analysis for partially suspended shells on elastic foundations are also presented.

A comparative study of axisymmetric finite elements for the vibration of thin cylindrical shells conveying fluid

AbstractA comparative study of the relative performance of several different axisymmetric finite elements, when applied to the dynamic problem of thin cylindrical shells conveying fluid, is presented. The methods used are based on (1) the Sanders' theory of thin shells and the potential flow theory, and (2) the theory of elasticity and the Euler equations. The elements studied are: linear, paralinear, parabolic and cubilinear. Extensive comparison with experiment is carried out for the free vibration of cylindrical shells in the absence of, and containing, quiescent and flowing fluid. The analysis of the relative competence of these elements is presented for shell length‐to‐radius ratios 1.95≤L/R≤32, shell radius‐to‐thickness ratios 10≤R/h≤375 and boundary conditions: clamped–clamped, clamped–free and simply supported. We show that natural frequencies of thin cylindrical shells in the absence of, and containing, quiescent and flowing fluid can be assessed accurately when using two‐ and eight‐noded elements, and the latter are also applicable to the dynamic problem of thick cylindrical shells. Copyright © 2002 John Wiley & Sons, Ltd.

Free Vibrations of Cylindrical Shells with Non-Axisymmetric Mass Distribution on Elastic Bed

The free vibrations of circular cylindrical shells partiallyloaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction,while they are considered to be uniformly distributed in longitudinaldirection on the entire shell length. Therefore, the problem is notaxisymmetric. The solution is obtained by using the development of theflexural mode shapes in a Fourier series, whose coefficients are determinedby rendering the Rayleigh quotient stationary, so a Galerkin equation isobtained. The proposed method is independent of the boundary conditionsat the shell ends. The results are satisfactorily compared to FEM results.Finally, the influence of the mass-load and of the bed stiffness on thenatural frequencies and mode shapes of a simply supported shell is shownand discussed.

Free vibration of cylindrical shells filled with liquid

A theoretical analysis for the free vibration of vertical simply supported cylindrical shells filled with ideal liquid has been investigated. The vibrations of the shell are examined by using the Donnell shell theory. The fluid is considered to be non-viscous and incompressible. The shell dynamic response function is obtained by applying Hamilton's principle. The Galerkin method is used to simplify the differential equations into algebraic equations in order to obtain the natural frequencies and corresponding modes. The method shows its great advantage in saving of computing time. The results are compared with those available in the literature and excellent agreement is found between them.

Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

Bifurcation buckling and free vibrations of cylindrical shells under pressure

This paper presents asymptotic solutions for the free vibrations of a circular cylindrical shell subjected to uniform pressure. A simple formula is derived for the natural frequency, which is valid for all possible combinations of the boundary conditions characterizing simply supported, clamped, and free ends. The formula can also be used to evaluate the buckling pressure. It is shown that both the free-vibration and the buckling characteristics depend on whether the ends of the cylinder are free or supported and on whether or not the supported ends are axially constrained.

A perturbation solution of free vibration of cylindrical shells with ring-stiffeners

In this paper, the free vibration of cylindrical sheel with ring-stiffeners is studied in detail by using the PLK method in singular perturbation and the general Hale's law, and the formulas calculating natural frequencies of cylindrical sheel with ring-stiffeners are expressed. Finally, the FEM solution is also given to prove the perturbation solution to be seemly, and this comparison shows that the method yields very good results.

High-precision finite element analysis of cylindrical shells

This paper presents the finite element formulation to study the free vibration of cylindrical shells. The displacement function for the high-precision shell element with 16 degrees of freedom is approximated by a Hermitian polynomial of beam function type. The explicit formulation for the high-precision element is extremely efficient. For the purpose of comparison, the subject element is used to study the sample case of free vibration of a shell structure. The results are in good agreement with those published. The study shows that solution accuracy with fewer elements is assured and that accurate solutions are obtainable in the high-frequency range.

Free vibrations of cylindrical shells reinforced with elastic rings

Free vibrations of cylindrical shells reinforced with elastic rings

The free vibrations of cylindrical shells with various end closures

The natural frequencies of vibration of cylindrical shells clamped at one end and closed at the other by different types of shells of revolution (cones, hemispheres, ellipsoids, etc.) were determined using programs written for the digital computer. The principal numerical methods investigated were variational finite-differences and finite elements. However, some results obtained by numerical integration of the differential equations of motion, together with some obtained from series solutions, are also given for purposes of comparison. For L D = 0.5 , h D = 0.01 the lowest four natural frequencies for all the cylinder/end closures investigated were concentrated in a band such that ω 4 ω 1 ⋍ 1.7 . Thus, changing the head shape does not cause radical changes in the natural frequencies for these geometric ratios. Results for other values of the geometric parameters are also given in the paper. Again for L D = 0.5 , h D = 0.01 , the effect of not equating to zero the in-plane circumferential displacement at the base of the cylinder caused a marked reduction in the n = 1 natural frequencies. In many of the cases studied, the n = 1 frequency was either the fundamental one or was close to it. Insofar as dynamic analyses are concerned, designers ought to be aware of the influence that the in-plane boundary conditions at the cylinder base can have on the natural frequencies. With regard to the main two numerical methods studied, the authors found both of them to be very effective for the natural frequency and mode shape predictions. For pointed shells (e.g. cones) it appears that for n = 0 and n = 1, the conditions employed at the apex in some of the programs need re-examination.

Free Vibrations of Fluid-Conveying Cylindrical Shells

This paper treats the free vibrations of cylindrical shells conveying fluid. The shell motion is described by the Flu¨gge’s equations, whereas the hydrodynamic forces are described by the linearized potential flow theory. Frequency spectra are presented for symmetric and asymmetric modes and the effects of flow velocity and other parameters are discussed. In the low-frequency range, a modified water-hammer theory and an approximate bending frequency equation including the effect of the flowing fluid are developed.

Free vibration of cylindrical shells partially filled with liquid

A theory is presented for the determination of the free vibration characteristics of vertical, thin, circular cylindrical shells, partially or completely filled with stationary liquid. The shell may be uniform or non-uniform, provided it is axially symmetric. This is a finite-element theory, using cylindrical finite elements, but the displacement functions are determined by using classical shell theory. The inertial loading of the fluid is taken into account by incorporating the virtual mass of the fluid into the mass matrix of those finite elements which are below the liquid free-surface. Calculations of the natural frequencies and eigenvectors were conducted for one such shell, for which experimental data were available. Agreement between theory and experiment was found to be quite good.