To study the effect of damping due to branching in trees and fractal structures, a harmonic analysis was performed on a finite element model using commercially available software. The model represented a three-dimensional (3D) fractal treelike structure, with properties based on oak wood and with several branch configurations. As branches were added to the model using a recursive algorithm, the effects of damping due to branching became apparent: the first natural frequency amplitude decreased, the first peak widened, and the natural frequency decreased, whereas higher frequency oscillations remained mostly unaltered. To explain this nonlinear effect observable in the spectra of branched structures, an analytical interpretation of the damping was proposed. The analytical model pointed out the dependency of Cartesian damping from the Coriolis forces and their derivative with respect to the angular velocity of each branch. The results provide some insight on the control of chaotic systems. Adding branches can be an effective way to dampen slender structures but is most effective for large deformation of the structure.
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August 2015
Technical Briefs
Vibrations of Fractal Structures: On the Nonlinearities of Damping by Branching
Peter Torab,
Peter Torab
Department of Mechanical Engineering,
Gannon University,
109 University Square, PMB 3824,
Erie, PA 16541-0001
e-mail: pctorab@gmail.com
Gannon University,
109 University Square, PMB 3824,
Erie, PA 16541-0001
e-mail: pctorab@gmail.com
Search for other works by this author on:
Davide Piovesan
Davide Piovesan
Biomedical Engineering Program,
Department of Mechanical Engineering,
Gannon University,
109 University Square, PMB 3251,
Erie, PA 16541-0001
e-mail: piovesan001@gannon.edu
Department of Mechanical Engineering,
Gannon University,
109 University Square, PMB 3251,
Erie, PA 16541-0001
e-mail: piovesan001@gannon.edu
Search for other works by this author on:
Peter Torab
Department of Mechanical Engineering,
Gannon University,
109 University Square, PMB 3824,
Erie, PA 16541-0001
e-mail: pctorab@gmail.com
Gannon University,
109 University Square, PMB 3824,
Erie, PA 16541-0001
e-mail: pctorab@gmail.com
Davide Piovesan
Biomedical Engineering Program,
Department of Mechanical Engineering,
Gannon University,
109 University Square, PMB 3251,
Erie, PA 16541-0001
e-mail: piovesan001@gannon.edu
Department of Mechanical Engineering,
Gannon University,
109 University Square, PMB 3251,
Erie, PA 16541-0001
e-mail: piovesan001@gannon.edu
1Corresponding author.
Manuscript received August 1, 2015; final manuscript received December 1, 2015; published online March 17, 2016. Assoc. Editor: Charalabos Doumanidis.
J. Nanotechnol. Eng. Med. Aug 2015, 6(3): 034502 (7 pages)
Published Online: March 17, 2016
Article history
Received:
August 1, 2015
Revised:
December 1, 2015
Citation
Torab, P., and Piovesan, D. (March 17, 2016). "Vibrations of Fractal Structures: On the Nonlinearities of Damping by Branching." ASME. J. Nanotechnol. Eng. Med. August 2015; 6(3): 034502. https://doi.org/10.1115/1.4032224
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