Flexural Waves in Elastic Beams of Circular Cross Section

1957 ◽  
Vol 29 (1) ◽  
pp. 42-46 ◽  
Author(s):  
H. Norman Abramson
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Flexural Waves ◽  
Elastic Beams

Lateral Vibrations of a Damped Laminated Hollow Circular Cross-Section Beam

1974 ◽  
Vol 96 (3) ◽  
pp. 845-852
Author(s):  
R. A. Ditaranto
Keyword(s):  
Cross Section ◽  
Viscoelastic Material ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Material Loss ◽  
Simply Supported ◽  
Elastic Beams ◽  
Mass Moment ◽  
Elastic Layers ◽  
Loss Factors

The free lateral bending vibrations of an “infinitely” long or simply-supported thin-walled circular cross-section beams having elastic-viscoelastic-elastic layers are investigated to determine the natural frequencies and associated composite loss factors. The analysis considers the inner and outer beams to behave as elastic beams in which the mass and mass-moment of inertia are both considered along with the interaction of the two elastic beams through the viscoelastic material. The results indicate that there are two natural frequencies. The lower one associated with the two elastic beams moving together so that little damping is obtained in this mode of vibration; the higher mode in which the two elastic beams vibrate in opposite directions so that there is an amount of damping comparable to the material loss factor of the viscoelastic material. A simplified model analysis is performed which is used to corroborate the trends obtained in the computer solutions of the more rigorous analysis. A series of curves are obtained for equal thickness elastic layers which can be used to obtain natural frequencies and composite loss-factors for a realistic range of geometrical and physical properties of a laminated circular cross-section simply supported beam.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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