Longitudinal Impact of a Semi-Infinite Elastic Cylindrical Shell

1963 ◽  
Vol 30 (3) ◽  
pp. 347-354 ◽  
Author(s):  
H. M. Berkowitz
Keyword(s):  
Cylindrical Shell ◽  
Asymptotic Expansion ◽  
Elastic Cylindrical Shell ◽  
Longitudinal Impact ◽  
Axially Symmetric ◽  
Membrane Theory ◽  
Pressure Signal ◽  
Rigid Obstacle ◽  
Leading Term

The axially symmetric pressure signal produced by the longitudinal impact of a semi-infinite elastic cylindrical shell upon a rigid obstacle is determined by using membrane theory. Using this simplified theory, it is possible to obtain not only the leading term of an asymptotic expansion for large values of time, but also additional terms.

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.

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

scholarly journals An Evaluation of Active Noise Control in a Cylindrical Shell

1989 ◽  
Vol 111 (3) ◽  
pp. 337-342 ◽  
Author(s):  
R. J. Silcox ◽  
H. C. Lester ◽  
S. B. Abler
Keyword(s):  
Cylindrical Shell ◽  
Analytical Model ◽  
Noise Control ◽  
Active Noise Control ◽  
Effective Control ◽  
Elastic Cylindrical Shell ◽  
Noise Sources ◽  
Active Noise ◽  
Fixed Array ◽  
Forced Responses

This paper examines the physical mechanisms governing the use of active noise control in an extended volume of a cylindrical shell. Measured data were compared with computed results from a previously derived analytical model based on infinite shell theory. For both the analytical model and experiment, the radiation of external monopoles is coupled to the internal acoustic field through the radial displacement of the thin, elastic, cylindrical shell. An active noise control system was implemented inside the cylinder using a fixed array of discrete monopole sources, all of which lie in the plane of the exterior noise sources. Good agreement between measurement and prediction was obtained for both internal pressure response and overall noise reduction. Attenuations in the source plane greater than 15 dB were recorded along with a uniformly quieted noise environment over an indicative length inside the experimental model. Results indicate that for forced responses with extended axial distributions, axial arrays of control sources may be required. Finally, the Nyquist criteria for the number of azimuthal control sources is shown to provide for effective control over the full cylinder cross section.

scholarly journals Elastic Response of Acoustic Coating on Fluid-Loaded Rib-Stiffened Cylindrical Shells

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Christopher Gilles Doherty ◽  
Steve C. Southward ◽  
Andrew J. Hull
Keyword(s):  
Cylindrical Shell ◽  
Cylindrical Shells ◽  
Coupled System ◽  
Elastic Response ◽  
System Response ◽  
Elastic Cylindrical Shell ◽  
Fluid Environment ◽  
Reinforcing Ribs ◽  
Double Index ◽  
Stress Boundary Conditions

Reinforced cylindrical shells are used in numerous industries; common examples include undersea vehicles, aircraft, and industrial piping. Current models typically incorporate approximation theories to determine shell behavior, which are limited by both thickness and frequency. In addition, many applications feature coatings on the shell interior or exterior that normally have thicknesses which must also be considered. To increase the fidelity of such systems, this work develops an analytic model of an elastic cylindrical shell featuring periodically spaced ring stiffeners with a coating applied to the outer surface. There is an external fluid environment. Beginning with the equations of elasticity for a solid, spatial-domain displacement field solutions are developed incorporating unknown wave propagation coefficients. These fields are used to determine stresses at the boundaries of the shell and coating, which are then coupled with stresses from the stiffeners and fluid. The stress boundary conditions contain double-index infinite summations, which are decoupled, truncated, and recombined into a global matrix equation. The solution to this global equation results in the displacement responses of the system as well as the exterior scattered pressure field. An incident acoustic wave excitation is considered. Thin-shell reference models are used for validation, and the predicted system response to an example simulation is examined. It is shown that the reinforcing ribs and coating add significant complexity to the overall cylindrical shell model; however, the proposed approach enables the study of structural and acoustic responses of the coupled system.

scholarly journals Some axially symmetric potential problems

1972 ◽  
Vol 18 (1) ◽  
pp. 55-76 ◽  
Author(s):  
F. G. Leppington ◽  
H. Levine
Keyword(s):  
Integral Equation ◽  
Asymptotic Expansion ◽  
Integral Equations ◽  
Asymptotic Estimate ◽  
Axially Symmetric ◽  
Primary Interest ◽  
Symmetric Potential ◽  
Approximate Integral ◽  
Potential Problems ◽  
Higher Order Terms

AbstractSome axially symmetric boundary value problems of potential theory are formulated as integral equations of the first kind. In each case the kernel admits an expansion, for small values of a parameter of the problem, that leads to an approximate integral equation whose solution provides a direct asymptotic estimate for the physical quantity of primary interest. A manipulation of the original and modified integral equations provides an efficient formula for calculating higher order terms in the asymptotic expansion.

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

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