Out‐of‐Plane Vibration of a Clamped Circular Ring Segment

1963 ◽  
Vol 35 (6) ◽  
pp. 933-934 ◽  
Author(s):  
Frederick C. Nelson
Keyword(s):  
Circular Ring ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Ring Segment

Free Out-of-Plane Vibration of a Ring Elastically Supported at Several Points

1982 ◽  
Vol 49 (4) ◽  
pp. 854-860 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
H. Okada
Keyword(s):  
Differential Equation ◽  
Infinite Series ◽  
Natural Frequencies ◽  
Circular Ring ◽  
Mode Shapes ◽  
Matrix Differential Equation ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Matrix Differential ◽  
Elastically Supported

An analysis is presented for the free out-of-plane vibration of a circular ring elastically supported against deflection, rotation, and torsion at several points located at equal angular intervals. The equations of out-of-plane vibration of the ring is expressed as a matrix differential equation by using the transfer matrix, the solution to which is conveniently given by infinite series. The vibrations arising in the ring are classified into several types, for each of which the natural frequencies and the mode shapes are calculated numerically up to higher modes.

In-Plane Vibration of Simply Supported-Simply Supported Circular Ring Segments

1991 ◽  
Author(s):  
S. Azimi
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Circular Ring ◽  
Mode Shapes ◽  
Simply Supported ◽  
Plane Vibration ◽  
Ring Segment ◽  
Linear Spring ◽  
Circular Rings ◽  
Elastic Constraints

Abstract The general in-plane vibration problem of circular ring segments having linear and torsional elastic constraints at the ends has been studied. One of the interesting cases of concern for which there exists an exact solution is the case where the linear and torsional spring stiffnesses in the circumferential direction become zero (Ku = 0, Kt = 0) and the linear spring stiffness in the radial direction becomes infinity (Kw = ∞). This case is the so-called simply supported-simply supported case. The general form of the equations of motion of circular rings with the proper boundary conditions at the ends have been employed to investigate the vibration of the ring segment. Results for natural frequencies and mode shapes for different angles of the segment have been presented.

Intracorneal circular ring implant with femtosecond laser: Pocket versus tunnel

2021 ◽  
pp. 112067212199472
Author(s):  
Luis Izquierdo ◽  
Ana M Rodríguez ◽  
Ramón A Sarquis ◽  
Diego Altamirano ◽  
Maria A Henriquez
Keyword(s):  
Visual Acuity ◽  
Femtosecond Laser ◽  
Randomized Study ◽  
Circular Ring ◽  
Continuous Ring ◽  
Refractive Outcomes ◽  
Scheimpflug Imaging ◽  
Ring Segment ◽  
Intracorneal Ring Segment ◽  
Student’S T

Purpose: To evaluate and compare visual and refractive outcomes after implantation of the intracorneal continuous ring 360° arc (ICCR) versus the intracorneal ring segment 340° arc (ICRS) using femtosecond laser for central keratoconus. Setting: Research Department, Oftalmosalud, Instituto de Ojos, Lima, Peru. Methods: Randomized study that included 40 eyes of 32 patients diagnosed with central keratoconus between November 2014 and March 2015. Twenty eyes had an implantation of ICCR (MyoRing, Dioptex GmbH, Austria) through an intrastromal pocket and 20 eyes had an implantation of ICRS (Keraring, Mediphacos, Brazil) through an intrastromal tunnel. Both procedures were performed with a femtosecond laser (LDV Z6 model, Ziemer Ophthalmic Systems AG). Visual acuity (VA), refraction, and Scheimpflug imaging analysis were performed pre- and postoperatively at 1 month and 1 year. Comparisons of means were performed using the Student’s t-test. Results: At 1 year, uncorrected VA improved 0.77 LogMAR ( p < 0.001) in the ICCR group and 0.79 LogMAR ( p = 0.01) in the ICRS group; mean sphere improvement was 5.13 Diopters (D) in the ICCR group and 6.27 D in the ICRS group ( p < 0.001 both); mean Steeper Keratometry improvement was 4.24 D in the ICCR group and 5.53 D in the ICRS group ( p < 0.001 both). In the ICCR group, mean decrease in the pachymetry at the thinnest point of the cornea was 32.16 µm ( p = 0.01), and in the ICRS group, mean increase was 4.2 µm at 1 year ( p = 0.61). Conclusion: Intracorneal continuous ring 360° arc (ICCR) and intracorneal ring segment 340° (ICRS) are effective treatments for central keratoconus. No significant differences between rings were found on visual acuity, refraction, and keratometry improvement.

scholarly journals Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
V. Kartik ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Parametric Instability ◽  
Primary Resonance ◽  
Free Edge ◽  
Moving Plate ◽  
Torsional Mode ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Axially Moving ◽  
The Stability

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

Wave localization in a disordered periodic viaduct undergoing out-of-plane vibration

2013 ◽  
Vol 83 (7) ◽  
pp. 1039-1059 ◽  
Author(s):  
Qing-Xu Fu ◽  
Long Zhong ◽  
Jian-Fei Lu
Keyword(s):  
Wave Localization ◽  
Plane Vibration ◽  
Out Of Plane

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

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