Excitation of an Elastic Cylindrical Shell by a Transient Acoustic Wave

1969 ◽  
Vol 36 (3) ◽  
pp. 459-469 ◽  
Author(s):  
T. L. Geers
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Wave ◽  
Circular Cylindrical Shell ◽  
Elastic Cylindrical Shell ◽  
Sandwich Shell ◽  
Governing Equations ◽  
Fluid Medium ◽  
Method Of Solution ◽  
Plane Step ◽  
Strain Responses

An infinite, elastic, circular cylindrical shell submerged in an infinite fluid medium is engulfed by a transverse, transient acoustic wave. The governing equations for modal shell response are reduced through the application of a new method of solution to two simultaneous equations in time; these equations are particularly amenable to solution by machine computation. Numerical results are presented for the first six modes of a uniform sandwich shell submerged in water and excited by a plane step-wave. These results are then used to evaluate the accuracy of a number of approximations which have been employed previously to treat this and similar problems. The results are also used to compute displacement, velocity, and flexural strain responses at certain points in the sandwich shell.

Nonlinear Response of an Elastic Cylindrical Shell to a Transient Acoustic Wave

1981 ◽  
Vol 48 (1) ◽  
pp. 15-24 ◽  
Author(s):  
T. L. Geers ◽  
C.-L. Yen
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Wave ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Elastic Cylindrical Shell ◽  
Fluid Medium ◽  
Energy Functionals ◽  
Potential Formulation ◽  
Rigorous Treatment ◽  
Residual Potential

Governing equations are developed for the nonlinear response of an infinite, elastic, circular cylindrical shell submerged in an infinite fluid medium and excited by a transverse, transient acoustic wave. These equations derive from circumferential Fourier-series decomposition of the field quantities appearing in appropriate energy functionals, and from application of the “residual potential formulation” for rigorous treatment of the fluid-structure interaction. Extensive numerical results are presented that provide understanding of the phenomenology involved.

Acoustic wave diffraction by an elastic cylindrical shell with viscous filling

1989 ◽  
Vol 25 (7) ◽  
pp. 662-667 ◽  
Author(s):  
O. B. Kachaenko ◽  
L. S. Pal'ko ◽  
N. A. Shul'ga
Keyword(s):  
Cylindrical Shell ◽  
Acoustic Wave ◽  
Wave Diffraction ◽  
Elastic Cylindrical Shell

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 an elastic cylindrical shell near the lowest cut-off frequency

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150753 ◽  
Author(s):  
J. Kaplunov ◽  
L. I. Manevitch ◽  
V. V. Smirnov
Keyword(s):  
Cylindrical Shell ◽  
Dispersion Relation ◽  
Ad Hoc ◽  
Circular Cylindrical Shell ◽  
Dynamic Modelling ◽  
Elastic Cylindrical Shell ◽  
Two Dimensional ◽  
Membrane Theory ◽  
Thin Walled Structures ◽  
Shell Equations

A new asymptotic approximation of the dynamic equations in the two-dimensional classical theory of thin-elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. At a fixed circumferential wavenumber, the latter corresponds to the eigenfrequency of in-plane vibrations of a thin almost inextensible ring. It is stressed that the well-known semi-membrane theory of cylindrical shells is not suitable for tackling a near-cut-off behaviour. The dispersion relation within the framework of the developed formulation coincides with the asymptotic expansion of the dispersion relation originating from full two-dimensional shell equations. Asymptotic analysis also enables refining the geometric hypotheses underlying various ad hoc set-ups, including the assumption on vanishing of shear and circumferential mid-surface deformations used in the semi-membrane theory. The obtained results may be of interest for dynamic modelling of elongated cylindrical thin-walled structures, such as carbon nanotubes.

Stresses Around an Elliptic Hole in a Cylindrical Shell

1969 ◽  
Vol 36 (1) ◽  
pp. 39-46 ◽  
Author(s):  
M. V. V. Murthy
Keyword(s):  
Cylindrical Shell ◽  
Stress Distribution ◽  
Theoretical Analysis ◽  
Circular Cylindrical Shell ◽  
Elliptic Hole ◽  
Major Axis ◽  
Axial Tension ◽  
Method Of Solution ◽  
Bending Stresses ◽  
Curvature Parameter

A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in a long, thin, circular cylindrical shell with the major axis of the hole parallel to the axis of the shell. The analysis has been carried out for the case of axial tension. The method of solution involves a perturbation in a curvature parameter and the results obtained are valid, if the hole is small in size compared to the shell. Formulas, from which the complete stress distribution at the hole can be calculated, are presented.

Transient Response of a Periodically Supported Cylindrical Shell Immersed in a Fluid Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 562-568 ◽  
Author(s):  
Harry Herman ◽  
J. M. Klosner
Keyword(s):  
Cylindrical Shell ◽  
Integral Transform ◽  
Circular Cylindrical Shell ◽  
Fourier Integral ◽  
Cylindrical Wave ◽  
Acoustic Medium ◽  
Steel Shell ◽  
Fluid Medium ◽  
Wave Approximation ◽  
Fourier Integral Transform

The dynamic response of a periodically simply supported, infinitely long, circular cylindrical shell to a pressure suddenly applied through the surrounding acoustic medium is investigated. The incident particle velocity is zero, and the pressure is assumed to have a harmonic spatial variation parallel to the shell axis. The exact solution is obtained by use of a Fourier integral transform, and the resulting inversion integral is evaluated by numerical and asymptotic integration. Two solutions to the same problem are obtained by using a plane and cylindrical wave approximation for the radiated field. The range of their applicability is investigated. For a steel shell in water ccs2=0.08815 it is found that, when the supports are placed three shell diameters apart, the use of the cylindrical wave approximation results in a 5-percent underestimation of the maximum deflection, while when the supports are placed one sixth of a shell diameter apart, the approximations are invalid.

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.

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