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.

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.

scholarly journals VIBRATIONS OF A LONGITUDINALLY STIFFENED, LIQUID-FILLED CYLINDRICAL SHELL IN LIQUID

2020 ◽  
Vol 2 (32) ◽  
pp. 112-131
Author(s):  
N. I. Alizadeh
Keyword(s):  
Cylindrical Shell ◽  
Wave Equation ◽  
Viscous Liquid ◽  
Orthotropic Cylindrical Shell ◽  
Ideal Liquid ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Characteristic Curves

In the paper we study free vibrations of a longitudinally stiffened, viscous liquid-filled orthotropic cylindrical shell in ideal liquid. The Navier – Stokеs linearized equation is used to describe the motion of the internal viscous liquid, the motion of the external liquid is described by a wave equation written in the potential by perturbed velocity. Frequency equation of a longitudinally stiffened orthotropic, viscous liquid-contacting cylindrical shell is obtained on the basis of the Hamilton – Ostrogradsky principle of stationarity of action. Characteristic curves of dependence are constructed.

Free Vibrations of Reinforced Elastic Shells

1969 ◽  
Vol 36 (4) ◽  
pp. 835-844 ◽  
Author(s):  
Hyman Garnet ◽  
Alvin Levy
Keyword(s):  
Cylindrical Shell ◽  
Wide Class ◽  
Circular Cylindrical Shell ◽  
Normal Modes ◽  
Free Vibrations ◽  
Equivalent Model ◽  
Governing Equations ◽  
Interaction Forces ◽  
Elastic Shells ◽  
Loading System

A technique is presented for the analysis of a wide class of reinforced, elastic structures undergoing free vibrations while subject to constraints imposed by the reinforcing elements. The technique consists of replacing the constrained structure by an equivalent model, a structure without reinforcing elements, undergoing free vibrations while subject to a loading system which consists of the structure-reinforcing element interaction forces. These forces are introduced as displacement-dependent loads, whose magnitudes reflect the elastic and inertial properties of the reinforcing elements. The displacements of the constrained body are expanded in terms of the normal modes of the unconstrained body. This approach leads to a set of manageable governing equations describing the behavior of the reinforced body exactly. A solution to these equations may then be obtained to any desired degree of accuracy. The technique is illustrated by computations performed for the case of a ring reinforced, circular cylindrical shell.

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 Analysis of Orthotropic Circular Cylindrical Shell Under External Hydrostatic Pressure

2002 ◽  
Vol 46 (03) ◽  
pp. 201-207
Author(s):  
Li Xuebin ◽  
Chen Yaju
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Free Vibration ◽  
Material Properties ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
External Hydrostatic Pressure ◽  
Two Parameters

An analysis is presented for the free vibration of an orthotropic circular cylindrical shell subjected to hydrostatic pressure. Based on Flügge shell theory, the equations of free vibrations of an orthotropic circular cylindrical shell under hydrostatic pressure are obtained. For shear diaphragms at both ends, the resulting characteristic equations about pressure and frequency are given. These two parameters are calculated exactly. The effect of the shell's parameters (L/R, h/R) and material properties on the free vibration characteristics are studied in detail. Differences between Love-Timoshenko, Donnell equations and that of the Flügge theory are examined as well.

Acoustic Transmission Through Cylindrical Shells Treated with FLD Mechanisms

2009 ◽  
Vol 25 (3) ◽  
pp. 299-306 ◽  
Author(s):  
K. Daneshjou ◽  
R. Talebitooti ◽  
A. Nouri
Keyword(s):  
Cylindrical Shell ◽  
Wave Equations ◽  
Analytical Study ◽  
Circular Cylindrical Shell ◽  
Impedance Method ◽  
Fluid Medium ◽  
Damping Material ◽  
Especial Case ◽  
In Series ◽  
Stiffness Loss

AbstractAnalytical study is conducted in this paper to understand the characteristics of sound transmission through cylindrical shell with free layer damping (FLD) treatment. It is assumed an infinitely long circular cylindrical shell subjected to a plane wave with uniform airflow in the external fluid medium. The damping layer applied on the surface of the shell is represented by HN model with frequency-dependent specifications. An exact solution is obtained by solving the Markus equations of FLD shells and acoustic wave equations simultaneously. As the pressure and displacement terms are expressed in series form, an iterative procedure is founded to cut them with an appropriatenumber of modes. Transmission losses obtained from the solution are compared with “modal-impedance method” for an especial case of untreated shell. Eventually, the numerical results show the effects of stiffness, loss factor and thickness of damping material, and also incident wave angles on TL curves.

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