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.

References

References
1.
Moller
,
A. R.
,
1961
, “
Network Model of the Middle Ear
,”
J. Acoust. Soc. Am.
,
33
(
2
), pp.
168
176
.
2.
Zwislocki
,
J.
,
1962
, “
Analysis of the Middle-Ear Function—Part I: Input Impedance
,”
J. Acoust. Soc. Am.
,
34
(
8
), pp.
1514
1523
.
3.
Bornitz
,
M.
,
Zahnert
,
T.
,
Hardtke
,
H. J.
, and
Huttenbrink
,
K. B.
,
1999
, “
Identification of Parameters for the Middle Ear Model
,”
Audiol. Neuro-Otol.
,
4
, pp.
163
169
.
4.
Dai
,
C.
,
Cheng
,
T.
,
Wood
,
M. W.
, and
Gan
,
R. Z.
,
2007
, “
Fixation and Detachment of Superior and Anterior Malleolar Ligaments in Human Middle Ear: Experiment and Modeling
,”
Hear. Res.
,
230
(
1–2
), pp.
24
33
.
5.
Eiber
,
A.
,
1999
, “
Mechanical Modeling and Dynamical Behavior of the Human Middle Ear
,”
Audiol. Neuro-Otol.
,
4
, pp.
170
177
.
6.
Gan
,
R. Z.
, and
Sun
,
Q.
,
2002
, “
Finite Element Modeling of Human Ear With External Ear Canal and Middle Ear Cavity
,”
Second Joint EMBS-BMES Conference
, Houston, TX, Oct. 23–26, Vol.
1–3
, pp.
264
265
.
7.
Taschke
,
H.
,
Weistenhofer
,
C.
, and
Hudde
,
H.
,
2000
, “
A Full-Size Physical Model of the Human Middle Ear
,”
Acustica
,
86
(
1
), pp.
103
116
.http://www.ingentaconnect.com/contentone/dav/aaua/2000/00000086/00000001/art00015
8.
Ravicz
,
M. E.
,
Peake
,
W. T.
,
Nakajima
,
H. H.
,
Merchant
,
S. N.
, and
Rosowski
,
J. J.
,
2004
,
Modeling Flexibility in the Human Ossicular Chain: Comparison to Ossicular Fixation Data
,
Word Scientific
,
Singapore
.
9.
Nakajima
,
H. H.
,
Ravicz
,
M. E.
,
Merchant
,
S. N.
,
Peake
,
W. T.
, and
Rosowski
,
J. J.
,
2005
, “
Experimental Ossicular Fixations and the Middle Ear's Response to Sound: Evidence for a Flexible Ossicular Chain
,”
Hear. Res.
,
204
(1–2), pp.
60
77
.
10.
Feng
,
B.
, and
Gan
,
R. Z.
,
2002
, “
A Lumped-Parameter Mechanical Model of Human Ear for Sound Transmission
,”
Second Joint EMBS-BMES Conference
, Houston, TX, Oct. 23–26, Vol.
1–3
, pp.
267
268
.
11.
Rusinek
,
R.
,
Warminski
,
J.
,
Szymanski
,
M.
,
Kecik
,
K.
, and
Kozik
,
K.
,
2016
, “
Dynamics of the Middle Ear Ossicles With an SMA Prosthesis
,”
Int. J. Mech. Sci.
, epub.
12.
Savi
,
M. A.
, and
Pacheco
,
P. M. C. L.
,
2002
, “
Chaos and Hyperchaos in Shape Memory Systems
,”
Int. J. Bifurcation Chaos
,
12
(
3
), pp.
645
657
.
13.
Tanaka
,
K. O.
, and
Nagaki
,
S. O.
,
1982
, “
A Thermomechanical Description of Materials With Internal Variables in the Process of Phase Transitions
,”
Ing. Arch.
,
51
(
5
), pp.
287
299
.
14.
Liang
,
C.
, and
Rogers
,
C. A.
,
1990
, “
One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials
,”
J. Intell. Mater. Syst. Struct.
,
1
(
2
), pp.
207
234
.
15.
Brinson
,
L. C.
,
1993
, “
One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation With Non-Constant Material Functions and Redefined Martensite Internal Variable
,”
J. Intell. Mater. Syst. Struct.
,
4
(
2
), pp.
229
242
.
16.
Paiva
,
A.
, and
Savi
,
M. A.
,
2006
, “
An Overview of Constitutive Models for Shape Memory Alloys
,”
Math. Probl. Eng.
,
2006
, pp.
1
31
.
17.
Frémond
,
M.
, and
Miyazaki
,
S.
,
1996
,
Shape Memory Alloys
(CISM Courses and Lectures), Vol.
351
,
Springer
,
New York
.
18.
Paiva
,
A.
,
Savi
,
M. A.
,
Braga
,
A. M. B.
, and
Pacheco
,
P. M. C. L.
,
2005
, “
A Constitutive Model for Shape Memory Alloys Considering Tensile-Compressive Asymmetry and Plasticity
,”
Int. J. Solids Struct.
,
42
(
11–12
), pp.
3439
3457
.
19.
Savi
,
M. A.
, and
Braga
,
A. M. B.
,
1993
, “
Chaotic Vibration of an Oscillator With Shape Memory
,”
J. Braz. Soc. Mech. Sci. Eng.
,
15
(1), pp.
1
20
.
20.
Savi
,
M. A.
, and
Braga
,
A. M. B.
,
1993
, “
Chaotic Response of a Shape Memory Oscillator with Internal Constraints
,” COBEM 93 - XII Congresso Brasileiro de Engenharia Mecânica, Brasília, Brazil, Dec. 7–10, p. 33–36.
21.
Savi
,
M. A.
,
Pacheco
,
P. M.
, and
Braga
,
A. M.
,
2002
, “
Chaos in a Shape Memory Two-Bar Truss
,”
Int. J. Non-Linear Mech.
,
37
(
8
), pp.
1387
1395
.
22.
Savi
,
M. A.
,
,
M. A.
,
Paiva
,
A.
, and
Pacheco
,
P. M.
,
2008
, “
Tensile-Compressive Asymmetry Influence on Shape Memory Alloy System Dynamics
,”
Chaos, Solitons Fractals
,
36
(
4
), pp.
828
842
.
23.
Latalski
,
J.
, and
Rusinek
,
R.
,
2017
, “
Static Analysis of C-Shape SMA Middle Ear Prosthesis
,”
Eur. Phys. J. Plus.
(submitted).
24.
Brzeski
,
P.
,
Pavlovskaia
,
E.
,
Kapitaniak
,
T.
, and
Perlikowski
,
P.
,
2016
, “
Controlling Multistability in Coupled Systems With Soft Impacts
,”
Int. J. Mech. Sci.
, epub.
25.
Chávez
,
J. P.
,
Brzeski
,
P.
, and
Perlikowski
,
P.
,
2017
, “
Bifurcation Analysis of Non-Linear Oscillators Interacting Via Soft Impacts
,”
Int. J. Non-Linear Mech.
,
92
, pp.
76
83
.
26.
Gilardi
,
G.
, and
Sharf
,
I.
,
2002
, “
Literature Survey of Contact Dynamics Modelling
,”
Mech. Mach. Theory
,
37
(
10
), pp.
1213
1239
.
27.
Hutzler
,
S.
,
Delaney
,
G.
,
Weaire
,
D.
, and
MacLeod
,
F.
,
2004
, “
Rocking Newton's Cradle
,”
Am. J. Phys.
,
72
(
12
), p.
1508
.
28.
Blazejczyk-Okolewska
,
B.
,
Czolczynski
,
K.
, and
Kapitaniak
,
T.
,
2010
, “
Hard Versus Soft Impacts in Oscillatory Systems Modeling
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
5
), pp.
1358
1367
.
29.
Kundu
,
S.
,
Banerjee
,
S.
, and
Giaouris
,
D.
,
2011
, “
Vanishing Singularity in Hard Impacting Systems
,”
Discrete Contin. Dyn. Syst. Ser. B
,
16
(
1
), pp.
319
332
.
30.
Witelski
,
T.
,
Virgin
,
L. N.
, and
George
,
C.
,
2014
, “
A Driven System of Impacting Pendulums: Experiments and Simulations
,”
J. Sound Vib.
,
333
(
6
), pp.
1734
1753
.
31.
Shaw
,
S. W.
, and
Holmes
,
P. J.
,
1983
, “
A Periodically Forced Piecewise Linear Oscillator
,”
J. Sound Vib.
,
90
(
1
), pp.
129
155
.
32.
Andreaus
,
U.
,
Placidi
,
L.
, and
Rega
,
G.
,
2010
, “
Numerical Simulation of the Soft Contact Dynamics of an Impacting Bilinear Oscillator
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
9
), pp.
2603
2616
.
33.
Serweta
,
W.
,
Okolewski
,
A.
,
Blazejczyk-Okolewska
,
B.
,
Czolczynski
,
K.
, and
Kapitaniak
,
T.
,
2014
, “
Lyapunov Exponents of Impact Oscillators With Hertz's and Newton's Contact Models
,”
Int. J. Mech. Sci.
,
89
, pp.
194
206
.
34.
Falk
,
F.
,
1980
, “
Model Free Energy, Mechanics, and Thermodynamics of Shape Memory Alloys
,”
Acta Metall.
,
28
(
12
), pp.
1773
1780
.
35.
Falk
,
F.
, and
Konopka
,
P.
,
1990
, “
Three-Dimensional Landau Theory Describing the Martensitic Phase Transformation of Shape-Memory Alloys
,”
J. Phys. Condens. Matter
,
2
(
1
), pp.
61
77
.
36.
Rusinek
,
R.
,
Warminski
,
J.
,
Zadrozniak
,
M.
, and
Szymanski
,
M.
,
2013
, “
Nonlinear Approach to Modelling of Otosclerosis in a Human Middle Ear
,”
Differ. Equations Dyn. Syst.
,
21
(
1–2
), pp.
45
57
.
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