Dynamic Vibrations and Stresses in Elastic Cylinders and Spheres

1966 ◽  
Vol 33 (4) ◽  
pp. 825-830 ◽  
Author(s):  
G. Cinelli
Keyword(s):  
Circular Cylindrical Shell ◽  
Hankel Transform ◽  
Dynamic Loads ◽  
Torsional Motion ◽  
Spherical Shells ◽  
Symmetric Motion ◽  
Line Load ◽  
Elastic Cylinders ◽  
Finite Hankel Transform ◽  
Cylinders And Spheres

A new finite Hankel transform [1] is used to find the transient displacement and stresses in thick elastic cylinders and spheres when the surfaces are subjected to dynamic loads for the following problems: (a) Pure radial and torsional motion of an infinitely long circular cylindrical shell; (b) radially symmetric motion of a spherical shell. The loads applied to both surfaces of the cylindrical and spherical shells are completely arbitrary functions of space (for the torsional case) and time. Employing the solutions obtained for the arbitrary loads, the spatial and temporal positions of these loads are then specialized to standard forms, such as a line load, band load, impulse, and so on, and the corresponding motion and stresses are found.

Cylindrical Shells Under Line Load

1957 ◽  
Vol 24 (4) ◽  
pp. 553-558
Author(s):  
R. M. Cooper
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Transverse Shear Deformation ◽  
System Of Equations ◽  
Principle Of Superposition ◽  
Line Load ◽  
Simply Supported ◽  
Shell Equations ◽  
Shell Geometry

Abstract The problem of a line load along a segment of a generator of a simply supported circular cylindrical shell is treated using shallow cylindrical shell equations which include the effect of transverse-shear deformation. The line load is first treated as a sinusoidally-varying edge load over the length of the shell, with boundary conditions prescribed along the loaded generator such that the continuity of the shell is maintained. The solution for the problem of a uniform line load over a segment of a generator is obtained from the preceding solution, using the principle of superposition. By means of a numerical example it is shown that the results predicted by the Donnell equations for the stresses are in excellent agreement with those obtained from the system of equations employed here. However, the radial displacement predicted by the Donnell equations is in error by as much as 20 per cent in the range of shell geometry considered.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

Practical numerical considerations for the Alekseev–Mikhailenko method

1990 ◽  
Vol 27 (8) ◽  
pp. 1023-1030 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Radial Symmetry ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Integral ◽  
Finite Hankel Transform ◽  
Difference Methods ◽  
New Generation

Programs that utilize the Alekseev–Mikhailenko method are becoming viable seismic interpretation aids because of the availability of a new generation of supercomputers. This method is highly numerically accurate, employing a combination of finite integral transforms and finite difference methods, for the solution of hyperbolic partial differential equations, to yield the total seismic wave field.In this paper two questions of a numerical nature are addressed. For coupled P–Sv wave propagation with radial symmetry, Hankel transforms of order 0 and 1 are required to cast the problem in a form suitable for solution by finite difference methods. The inverse series summations would normally require that the two sets of roots of the transcendental equations be employed, corresponding to the zeroes of the Bessel functions of order 0 and 1. This matter is clarified, and it is shown that both inverse series summations may be performed by considering only one set of roots.The second topic involves providing practical means of determining the lower and upper bounds of a truncated series that suitably approximates the infinite inverse series summation of the finite Hankel transform. It is shown that the number of terms in the truncated series generally decreases with increasing duration of the source pulse and that the truncated series may be further reduced if near-vertical-incidence seismic traces are avoided.

Generalized finite Hankel transform

2006 ◽  
Vol 17 (1) ◽  
pp. 39-44 ◽  
Author(s):  
Moustafa El-shahed ◽  
M. Shawkey
Keyword(s):  
Hankel Transform ◽  
Finite Hankel Transform

The second-order deformation of a finite compressible isotropic elastic annulus subjected to circular shearing

1993 ◽  
Vol 442 (1916) ◽  
pp. 621-639 ◽  
Keyword(s):  
Hankel Transform ◽  
Outer Edge ◽  
Kernel Functions ◽  
Second Order ◽  
Cylindrical Hole ◽  
Angular Deformation ◽  
Interior Boundary ◽  
Order Deformation ◽  
Finite Hankel Transform

This work investigates the second-order deformation of a uniformly thick compressible isotropic elastic annulus with an axial cylindrical hole. The annulus is clamped at its outer edge and is subjected to a constant angular deformation on the interior boundary of the hole. The implicit m athematical solution is formulated in term s of finite Hankel transform s with Weber-Orr kernel functions which are then numerically inverted.

On a generalized finite Hankel transform

2007 ◽  
Vol 190 (1) ◽  
pp. 705-711 ◽  
Author(s):  
Mridula Garg ◽  
Alka Rao ◽  
S.L. Kalla
Keyword(s):  
Hankel Transform ◽  
Finite Hankel Transform
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