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.

scholarly journals The surface impedance of superconductors and normal metals at high frequencies III. The relation between impedance and superconducting penetration depth

1947 ◽  
Vol 191 (1026) ◽  
pp. 399-415 ◽  
Keyword(s):  
Magnetic Field ◽  
Penetration Depth ◽  
Surface Impedance ◽  
Simple Extension ◽  
High Frequencies ◽  
Resistivity Measurements ◽  
Direct Measurements ◽  
Normal Metals ◽  
Velocity Of Propagation ◽  
Theory Of Superconductivity

The theory developed in II is extended to cover the case of a superconductor, and a formula is derived relating the r. f. resistivity to the superconducting penetration depth and other parameters of the metal. It is shown how the penetration depth may be deduced directly from measurements of the skin reactance, and a method of measuring reactance is described, based essentially on the variation of the velocity of propagation along a transmission line due to the reactance of the conductors. For technical reasons it is not convenient to measure the reactance absolutely, but a simple extension of the technique described in I enables the change in reactance to be accurately measured when superconductivity is destroyed by a magnetic field. The method has been applied to mercury and tin. In the former case the results are in agreement with Shoenberg’s direct measurements, and confirm that the penetration depth at 0° K is of the order of 7 x 10 –6 cm. The theory developed at the beginning of the paper is used to deduce the variation of penetration depth with temperature from the resistivity measurements of I, and it is shown that agreement with other determinations and with the reactance measurements is fairly good, but not perfect. Some of the assumptions used in developing the theory are critically discussed, and a qualitative account is given to show how Heisenberg’s theory of superconductivity offers an explanation of some of the salient features of superconductivity and inparticular indicates the relation between superconducting and normal electrons.

Insertion loss of periodic cylindrical shells with helical slit

2021 ◽  
Vol 69 (3) ◽  
pp. 199-208
Author(s):  
Karisma Mohapatra ◽  
Dibya Prakash Jena
Keyword(s):  
Band Structure ◽  
Insertion Loss ◽  
Cylindrical Shells ◽  
Slit Width ◽  
Sharp Peak ◽  
Acoustic Attenuation ◽  
High Frequencies ◽  
Local Resonance ◽  
Resonance Band

We propose periodic shells with helical slit to overcome the lacuna in periodic C scatterers, where the first Bragg band is considerably reduced on increasing width of the slit. The key discovery of this research indicates that, by changing the upright slit of the C scatterers to helical slits, larger insertion loss (IL) is achieved around the first Bragg band without compromising the local resonance band. Comparing the performance of periodic shells without slit or cylindrical scatterers, it is found that IL becomes larger at first Bragg band. The pitch, thickness of the shell and width of helical slit can be altered to adjust the resonance of the proposed shells. On decreasing the pitch or increasing the slit width, the resonance band shifts toward high frequencies without much alteration in acoustic attenuation of bandwidth. Additionally, below threshold pitch, the said peak merges with first Bragg band and broadens with prominent IL. The calculated band structure authenticates the bandwidth of the first Bragg band, and the additional sharp peak in IL can be attributed to local resonance of the periodic scatterers.

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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