Finite difference computation of the dynamic motion of cylindrical shells including the effect of rotatory inertia and transverse shear

1977 ◽  
Vol 5 (4) ◽  
pp. 323-335
Author(s):  
A. F. Emery ◽  
F. J. Cupps
Keyword(s):  
Finite Difference ◽  
Transverse Shear ◽  
Cylindrical Shells ◽  
Rotatory Inertia ◽  
Dynamic Motion

A Study of Axisymmetric Vibrations of Cylindrical Shells as Affected by Rotatory Inertia and Transverse Shear

1956 ◽  
Vol 23 (2) ◽  
pp. 255-261
Author(s):  
T. C. Lin ◽  
G. W. Morgan
Keyword(s):  
Transverse Shear ◽  
Circular Tube ◽  
Cylindrical Shells ◽  
Rotatory Inertia ◽  
High Frequencies ◽  
Additional Mode ◽  
Velocity Of Propagation

Abstract An analysis is presented of the problem of the propagation of axisymmetric waves in an elastic circular tube. The theory includes the effects of rotatory inertia and transverse shear in the same manner as does Timoshenko’s theory of the vibrations of bars. These effects are of importance for waves at high frequencies; they tend to decrease the velocity of propagation and introduce an additional mode due to shear.

Elastic Crack Propagation Along a Pressurized Pipe

1976 ◽  
Vol 98 (1) ◽  
pp. 2-7 ◽  
Author(s):  
A. F. Emery ◽  
W. J. Love ◽  
A. S. Kobayashi
Keyword(s):  
Finite Difference ◽  
Transverse Shear ◽  
Critical Stress ◽  
Maximum Stress ◽  
Terminal Velocity ◽  
Rotatory Inertia ◽  
Stress Criterion ◽  
Short Cracks ◽  
Elastic Crack ◽  
Pressurized Cylinder

A finite difference shell code which considers transverse shear and rotatory inertia is used to calculate the dynamic behavior of axially running cracks. Short cracks were instantaneously introduced into a static pressurized cylinder and their tips advanced according to a maximum stress criterion. Calculations were made for a range of the critical stress and the terminal velocity of the crack tip was found to be linearly related to the value of the critical stress. Calculations were also made for rapid and slow depressurization of the cylinder to observe the nature of the arrest. In all cases where arrest occurred it did so abruptly.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

1979 ◽  
Vol 46 (2) ◽  
pp. 303-310 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Shear Force ◽  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Theoretical Procedure

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

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