The Transient Motion of a Cylindrical Shell of Arbitrary Cross Section in an Acoustic Medium

1977 ◽  
Vol 44 (3) ◽  
pp. 482-486 ◽  
Author(s):  
B. S. Berger ◽  
M. E. Palmer
Keyword(s):  
Cylindrical Shell ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Acoustic Medium ◽  
Fluid Equation ◽  
Fluid Medium ◽  
Transient Motion ◽  
Fluid Field ◽  
The Laplace Transform ◽  
Difference Form

A solution has been constructed for the transient motion of a viscoelastic cylindrical shell of the arbitrary cross section, surrounded by a fluid medium. The fluid region external to the shell is mapped into the interior of a rectangle. The transformed fluid equation together with the shell equations are expressed in finite-difference form and the time variable suppressed through the application of the Laplace transform. Shell displacements and acoustic pressures are found over the fluid field and at the fluid solid interface.

Graphical-Numerical Solution of Problems of Saint-Venant Torsion and Bending

1953 ◽  
Vol 20 (3) ◽  
pp. 321-326
Author(s):  
B. A. Boley
Keyword(s):  
Cross Section ◽  
Stress Function ◽  
Arbitrary Cross Section ◽  
Successive Approximations ◽  
Shear Stresses ◽  
Shearing Stress ◽  
First Approximation ◽  
Difference Form ◽  
Bending Of Beams

Abstract A simple successive-approximations procedure for the solution of the problems of Saint-Venant torsion and bending of beams of arbitrary cross section is presented. The shear stresses in a cross section of the beam are first calculated from the formulas valid for thin-walled sections, on the basis of an assumed set of lines of shearing stress. From these a first approximation to the stress function of either the torsion or the bending problem is found. The second approximation to the stress function is then obtained from the governing equation of the problem, expressed in finite-difference form; this in turn allows the determination of an improved set of lines of shearing stress, and hence of the shearing stress itself. The procedure can be repeated until the results of two successive steps are sufficiently close. Applications are presented for a beam cross section for which the exact solutions are known, and it is shown that no further difficulties arise in applications to more complicated shapes.

scholarly journals Interaction of a Ring-Reinforced Shell and a Fluid Medium

1968 ◽  
Vol 35 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Jerry W. Berglund ◽  
Jerome M. Klosner
Keyword(s):  
Circular Cylindrical Shell ◽  
Salt Water ◽  
Power Series Expansion ◽  
Cylindrical Wave ◽  
Acoustic Medium ◽  
Steel Shell ◽  
Fluid Medium ◽  
Transient Dynamic ◽  
Wave Approximation ◽  
Fluid Field

This work is concerned with the transient dynamic response of a periodically ring-reinforced, infinitely long, circular cylindrical shell to a uniform pressure suddenly applied through the surrounding acoustic medium. The incident particle velocity is zero, and the rings are assumed to be slightly flexible. A classical theory of the Donnell type is used to analyze the shell while the fluid is described by the linear acoustic field equation. The solution is obtained by assuming a power series expansion in the ring stiffness parameter and utilizing a technique which reduces the transient dynamic problem to an equivalent steady-state formulation. Numerical results are presented for a steel shell immersed in salt water for different ring spacings. For the case of rigid rings, a cylindrical and plane wave approximation was also used to represent the fluid field. It is shown that the cylindrical wave approximation yields reasonably accurate results. Flexible ring results, although limited, indicate that undamped or nonradiating components of the shell vibration are activated.

Deformation Equations for Non-Circular Cylinders

1960 ◽  
Vol 64 (600) ◽  
pp. 765-766 ◽  
Author(s):  
D. S. Houghton ◽  
D. J. Johns
Keyword(s):  
Cylindrical Shell ◽  
Cross Section ◽  
Explicit Solution ◽  
Lateral Pressure ◽  
Arbitrary Cross Section ◽  
Circular Cylinders ◽  
Pressure Loading ◽  
Elastic Shells ◽  
Linear Problems ◽  
Arbitrary Curvature

As far as is known, no explicit solution exists in the literature for the displacement equations in u, v and w, for a uniform cylinder of arbitrary cross section subjected to a lateral pressure loading. However, the advent of Ref. 1 now makes available an admirable treatise devoted entirely to the analysis of thin elastic shells. The equations developed in this reference apply only to linear problems, i.e. the displacements are assumed to be small in comparison with the thickness of the shell, but they are general enough to include all shells of arbitrary curvature. Unfortunately the generality of these equations inhibits their immediate use to cylindrical shell problems, and it is the purpose of this note to present the essential features of the theory for non-circular cylinders.

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.

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