The Free Vibration of a Cylindrical Shell on an Elastic Foundation

1998 ◽  
Vol 120 (1) ◽  
pp. 63-71 ◽  
Author(s):  
D. N. Paliwal ◽  
Rajesh K. Pandey
Keyword(s):  
Cylindrical Shell ◽  
Elastic Foundation ◽  
Circular Cylindrical Shell ◽  
Frequency Equation ◽  
Radial Mode ◽  
Wave Number ◽  
Wave Parameter ◽  
Longitudinal Modes ◽  
Foundation Parameters ◽  
Circumferential Wave

The frequency equation for a thin circular cylindrical shell resting on an elastic foundation is developed by using the first order shell theory of Sanders and eigenfrequencies are calculated. These eigenfrequencies are plotted against the axial wave parameter. Effects of the axial wave parameter, circumferential wave number, non-dimensional thickness and foundation parameters on eigenfrequencies are investigated. It is found that the foundation modulus chiefly affects the radial mode eigenfrequency and has no effect on torsional and longitudinal modes. On the otherhand, shear modulus does have influence on radial as well as tangential modes of vibrations. Though the effect on radial mode frequency is more pronounced.

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.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

scholarly journals Free vibration and damping analysis of the cylindrical shell partially covered with equidistant multi-ring hard coating based on a unified Jacobi-Ritz method

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110325
Author(s):  
Jian Yang ◽  
Hua Song ◽  
Dong Chen ◽  
Yue Zhang
Keyword(s):  
Cylindrical Shell ◽  
Loss Factor ◽  
Ritz Method ◽  
Rectangular Pulse ◽  
Hard Coating ◽  
Wave Number ◽  
Thickness Variation ◽  
Ring Number ◽  
Wave Numbers ◽  
Circumferential Wave

In this study, the aim was to evaluate the vibration suppression performance of the partially covered equidistant multi-ring hard coating damping treatment for the cylindrical shell structure in aviation power equipment. A continuous rectangular pulse function was presented to describe the local thickness variation of arbitrary coating proportion and arbitrary number of coating rings. A semi-analytical unified solution procedure was established by combining the rectangular pulse function, the generalized Jacobi polynomials, and the Rayleigh-Ritz method. The stiffness coefficient k = 1013 N/m2 and the truncation number N = 8 were found to be large enough to achieve an accurate and efficient solution of the vibration analysis of the shell. The modal loss factor generally increased with the increase of the coating proportion ranging from 0.0 to 1.0 for all the circumferential wave numbers. The modal loss factor increased roughly linear with the coating proportion for all the circumferential wave numbers. And the modal loss factor was increased with the circumferential wave number, and the greater the number of circumferential waves, the greater the rate of change. The increase of the ring number was not always beneficial for vibration reduction of the shell, while the modal loss factor increased roughly linear with the coating proportion. The increased ring number and coating proportion tend more to exhibit an obvious incremental damping effect under larger circumferential wave number.

scholarly journals Vibration of FG Shell Rested on Winkler Foundation

2020 ◽  
Author(s):  
Abdellatif Selmi
Keyword(s):  
Cylindrical Shell ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
Wave Number ◽  
Winkler Foundation ◽  
Shell Material ◽  
Graded Materials ◽  
Maximum Value ◽  
Graded Material ◽  
Point To Point

Abstract Love’s first a pproximation theory is employed with the combination of Winkler term for the vibration of functionally graded cylindrical shell. MATLAB software is utilized for the vibration of functionally graded cylindrical shell with elastic foundation of Winkler and t he results are verified with the open literature. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functiona lly graded material. The influence of the elastic foundation, wave number, length - and height - to - radius ratios is investigated with different boundary conditions. The frequencies of length - to - radius and height - to - radius ratio are counter part of each other . The frequency first increases and gain maximum value in the midway of the shell length and then lowers down for the variations of wave number. It is found that due to inducting the elastic foundation of Winkler, the frequencies increases.

Vibration of a Spinning Cylindrical Shell With Internal/External Ring Stiffeners

1996 ◽  
Vol 118 (2) ◽  
pp. 227-236 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Lin-Hung Chen
Keyword(s):  
Cylindrical Shell ◽  
Mass Density ◽  
Wave Number ◽  
External Ring ◽  
Spin Speed ◽  
Receptance Method ◽  
Frequency Changes ◽  
Spinning Speed ◽  
Stiffening Effect ◽  
Circumferential Wave

The paper presents an approach to the vibration analysis of a spinning cylindrical shell with internal, symmetric, or external ring stiffeners. A modified receptance method for spinning structures is employed in this analysis. Various numerical examples are demonstrated and the results are compared with the existing data. The effects of types, numbers of stiffeners and of spin speed on the shell frequencies are extensively discussed. The results show that for no spin the ring stiffeners stiffen only then > 1 modes (n–circumferential wave number), and the stiffening effect become more significant with the increasing n number. With spin, the rings stiffen the forward modes in a way similar to the non-spin cases. The backward modes are however all stiffened by the attached rings for all n values. Among the three types of rings, on backward modes, the internal rings always have a better stiffening effect, then the symmetric and the external rings. As to the forward modes, as spinning speed increases, the external rings raise the shell’s frequencies faster than the others due to the largest centrifugal force. At last, the effects of the ring’s location, stiffness, and mass density on the frequency changes are examined. Numerical results show that the sensitivity of the shell’s frequencies to these parameters increases with the spin speed. Among the shell modes, the lower n modes are affected more by these parameters.

scholarly journals Free Vibration of a Fluid-Filled Circular Cylindrical Shell with Lumped Masses Attached, Using the Receptance Method

1996 ◽  
Vol 3 (3) ◽  
pp. 159-167 ◽  
Author(s):  
Marco Amabili
Keyword(s):  
Cylindrical Shell ◽  
Analytical Study ◽  
Circular Cylindrical Shell ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Structure Interaction ◽  
Steel Tank ◽  
Receptance Method ◽  
Lumped Masses ◽  
Theory Of Shells

The receptance method is applied to the analytical study of the free vibrations of a simply supported circular cylindrical shell that is either empty or filled with an in viscid, incompressible fluid and with lumped masses attached at arbitrary positions. The receptance of the fluid-filled shell is obtained using the added virtual mass approach to model the fluid–structure interaction. The starting data for the computations is the modal properties of the cylinder that can be obtained using any theory of shells. Numerical results are obtained as roots of the frequency equation and also by considering the trivial solution. They are compared to data obtained by experimental modal analysis performed on a stainless steel tank, empty, or filled with water, with a lead mass attached.

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