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Research Papers

Soft Impact in a Biomechanical System With Shape Memory Element

[+] Author and Article Information
R. Rusinek

Department of Applied Mechanics,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: r.rusinek@polub.pl

M. Szymanski

Department of Otolaryngology
Head and Neck Surgery,
Medical University of Lublin,
Jaczewskiego 8,
Lublin 20-090, Poland
e-mail: marcinszym@poczta.onet.pl

J. Warminski

Professor
Department of Applied Mechanics,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: j.warminski@polub.pl

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 30, 2016; final manuscript received April 13, 2017; published online September 7, 2017. Assoc. Editor: Tomasz Kapitaniak.

J. Comput. Nonlinear Dynam 12(6), 061013 (Sep 07, 2017) (9 pages) Paper No: CND-16-1593; doi: 10.1115/1.4036614 History: Received November 30, 2016; Revised April 13, 2017

The analysis of the shape memory prosthesis (SMP) of the middle ear is presented in this paper. The shape memory prosthesis permits the adjustment of its length to individual patient needs, but sometimes the prosthesis cannot be properly fixed to the stapes. In this case, the impact between the prosthesis and stapes is important. Therefore, the reconstructed middle ear is modeled as a two degree-of-freedom system with a nonlinear shape memory element and soft impact to represent its behavior when the prosthesis is not properly placed or fixed. The properties of the shape memory prosthesis, in the form of a helical spring, are represented by a polynomial function. The system exhibits advisable periodic and undesirable aperiodic and irregular behavior depending on the excitation amplitude, the frequency, and the prosthesis length. The prosthesis length can change, resulting in a modification of the distance between the prosthesis and the stapes. The results of this study provide an answer in terms of how the prosthesis length, which produces the ossicular chain tension, influences the system dynamics and its implication in medical practice.

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Figures

Grahic Jump Location
Fig. 1

Three degrees-of-freedom model of intact middle ear

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Fig. 2

Two degrees-of-freedom model of reconstructed middle ear with SMA helical spring

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Fig. 3

Two degrees-of-freedom model of reconstructed middle ear with SMA helical spring and soft impact

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Fig. 4

Regions of periodic solution (1T) near the first resonance Ω = 0.2981 (f = 1020 Hz)

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Fig. 5

Influence of external excitation frequency Ω on (a) the malleus and (b) the stapes vibrations presented as a Poincaré section for Q = 0.0079 (connected model)

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Fig. 6

Influence of external excitation frequency Ω on (a) the malleus and (b) the stapes vibrations presented as maxima diagram for Q = 0.0079 (connected model)

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Fig. 7

Influence of external excitation frequency Ω on (a) the malleus and (b) the stapes vibrations presented as Poincaré section for Q = 0.02 (connected model)

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Fig. 8

Influence of external excitation frequency Ω on (a) the malleus and (b) the stapes vibrations presented as a maxima diagram for Q = 0.02 (connected model)

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Fig. 9

Phase diagram and Poincaré section (red) of the malleus (black) and the stapes (blue) for Q = 0.02 and Ω = 0.3: (a) connected model, (b) disconnected model s = 0 and Ω = 0.3, and (c) disconnected model s = −0.1 and Ω = 0.2981 (see figure online for color)

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Fig. 10

Influence of external frequency Ω on (a) the malleus and (b) the stapes vibrations presented as Poincaré section for Q = 0.0079 and s = 0 (disconnected model)

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Fig. 11

Influence of external frequency Ω on (a) the malleus and (b) the stapes vibrations presented as maxima diagram for Q = 0.0079 and s = 0 (disconnected model)

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Fig. 12

Influence of external frequency Ω on (a) the malleus and (b) the stapes vibrations presented as Poincaré section for Q = 0.02 and s = 0 (disconnected model)

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Fig. 13

Influence of external frequency Ω on (a) the malleus and (b) the stapes vibrations presented as maxima diagram for Q = 0.02 and s = 0 (disconnected model)

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Fig. 14

Influence of distance s (prosthesis tension) on (a) the malleus and (b) the stapes vibrations presented as Poincaré section for Q = 0.0079 and Ω = 0.2981 (disconnected model)

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Fig. 15

Influence of distance s (prosthesis tension) on (a) the malleus and (b) the stapes vibrations presented as maxima diagram for Q = 0.0079 and Ω = 0.2981 (disconnected model)

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Fig. 16

Influence of distance s (prosthesis tension) on (a) the malleus and (b) the stapes vibrations presented as Poincaré section for Q = 0.02 and Ω = 0.2981 (disconnected model)

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Fig. 17

Influence of distance s (prosthesis tension) on (a) the malleus and (b) the stapes vibrations presented as maxima diagram for Q = 0.02 and Ω = 0.2981 (disconnected model)

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