The effect of shear and rotatory inertia

1972 ◽  
pp. 357-382
Author(s):  
Ladislav Frýba
Keyword(s):  
Rotatory Inertia

An Approximate Theory of Lateral Impact on Beams

1955 ◽  
Vol 22 (1) ◽  
pp. 69-76
Author(s):  
B. A. Boley
Keyword(s):  
Sudden Change ◽  
Approximate Theory ◽  
Lateral Impact ◽  
Governing Equations ◽  
Transverse Impact ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Lateral Contraction ◽  
Velocity Of Propagation ◽  
Variation Technique

Abstract The approximate theory derived in this paper describes, by means of a “traveling-wave” approach, the behavior of beams under transverse impact. Lateral impact is considered in detail, namely, one in which a section of the beam undergoes a sudden change in velocity or shear force. The theory considers the effects of shear deformations and of rotatory inertia according to Timoshenko’s model, and that of lateral contraction as suggested by Love. The governing equations and the boundary conditions are developed with the aid of an energy-variation technique. Numerical examples are given in which the behavior of the boundary layer near the point of impact is examined. For one of these the exact solution is available and is in agreement with the present approximate results. Some general considerations concerning the velocity of propagation also are discussed.

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.

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