!"#$%& '$%'( )*+,-./, 2012 03 (1& 531/534:[57+61] .!. "#$%&'())#*&, +.+. ,)-*#*./ !"#$%&' ()*&+(),-(.' &$$,!/+0)1!,-$%&' 2+,&1!3(&4!$%&' 5(&0!"$&1!1, !"#-, 6+$$&7 01 2!3""43 5+ 2024 6789+"2+2+ 2:373"6 80:;"3!0<0 268+ 8,53 70,7!1$7 +/(&# &9 450$10, $ 2+#+:-; %+1+".3 #. 2+9()<# +%"5=);:&' #&". >)"5?!(&! $,53) 0$,!/$10&! 1")0# &,& 2)1+,+@&& +1"&*)1!,-(+ $%)9.0)!1$7 () %)4!$10! =&9(&, 2+$%+,-%5 4!,+0!% (! #+=!1 0.2+,(71- %+##5(&%)1&0(.! A5(%*&&. B1+$%,!"+9 – +/(+ &9 4)$1.3 9)C+,!0)(&'. D&"5"@&4!$%+! ,!4!(&! – $1)2!/+2,)$1&%). E)((.' 0&/ +2!")*&& +1(+$&1$7 % #&%"+3&"5"@&4!$%&# +2!")*&7#. F!1+/&%) /)((+' +2!")*&& &90!$1() $ 1958 @+/). "& $1)2!/+2,)$1&%! +/(&# &9 $)#.3 5790&#.3 905%+2"+0+/7:&3 90!(-!0 $&$1!#. $,53+0.3 %+$1+4!% 70,7!1$7 $1"!#7, %+1+"+! 9)#!(7!1$7 $1!"=(!0.# 2"+1!9+# 2+"?(!0+@+ 1&2). 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E,7 +2"!/!,!(&7 $+C$10!((.3 4)$1+1 2"+&90!/!(+ $")0(!(&! )(),&1&4!$%+@+ "!?!(&7 & 2"&C,&=!((+@+, 2+,54!((+@+ 2"& 2+#+:& #!1+/) %+(!4(.3 G,!#!(1+0 (FJK). 6!95,-1)1. $")0(!(&7 2+%)9),& 2")0&,-(+$1- #!1+/) "!),&9)*&& "!?!(&7 0 2"+@")##! & 0+9#+=(+$1- 5$,+=(!(&7 ")$4!1+0. =)>?,/@, A)./&: $1)2!/+2,)$1&%), A+"#) $1!"=(!0+@+ 2"+1!9), $0!"30.$+%&! $+C$10!((.! 4)$1+1., 1!A,+(. S.V. Nigmatullina, +.+. Selyaninov Perm National Research Polytechnic University, Perm, Russian Federation THE EIGENFREQUENCIES THE IMPLANT STAPES PISTON TYPE Hearing is one of the senses, through which we learn about the world. Hearing impairment due to injury or disease affects the quality of life. The patient is unable to perform communicative functions. Otosclerosis – one of the most common diseases. Treatment is surgery to stapedioplasty. Technique of the operation has been known since 1958. When stapedioplasty one of the most vulnerable sections of conductive auditory ossicles is the stirrup, which is replaced by the prosthesis piston type rod. This type 135 .!. "#$%&'())#*&, +.+. ,)-*#*./ of operation is to microsurgery. To determine the natural frequencies of the method of finite elements. The differential equation of longitudinal vibrations of the rod. The natural frequencies of the prosthesis is much higher sound range and fall into the super-high-MHz range. In order to reduce the effect of radiation of mobile phones and car alarms in the auditory system of the person introduced the criterion of first natural frequencies of the output of the graft-MHz range, so the material and shape of the prosthesis are determined by minimizing the first natural frequency. The prosthesis is modeled in engineering software package. Form is selected, the corresponding longitudinal vibrations that provide conductivity ear from the middle ear to the inner ear. Considered the natural frequencies of a homogeneous rod of different materials. According to the results of the best materials are teflon and gold. To determine the natural frequencies of a comparison of analytical and approximate solutions obtained using the finite element method. Keywords: stapedioplasty, shape of the rod prosthesis, ultra-high eigenfrequencies, teflon. !"#"$%" 2*3 453657-589. 8:;<,9= >*:54*/ 9*?@*9 453657-589= /566A-./,B.. . 458C?.@9.@ 5/?A7,DE*F5 6.?,. ":A+ – G95 8C585H-589= 458C?.-.6,9= 34A/54;* /5:*H,-.@ >,89595I .3 5C?*J*:*--5F5 J.,C,35-,. K*:54*>*8/5* A+5 458C?.-.6,*9 34A/54;* /5:*H,-.@ >,89595I 59 5 J5 20 /LB. M8-54-AD ?5:= C?. C*?*J,>* 34A/, 59 4-*<-*I A<-5I ?,/54.-; / 4-A9?*--*6A A+A .F?,D9 /5895>/. 8?*J-*F5 A+, (65:595>*/, -,/54,:=-@, 89?*6*>/5) (?.8. 1) [7]. 5 4?*6@ 4.H?,B.. 8:A+54;* /5895>/. 59?,H,9;4,D9 8:57-AD /.-*6,9./A J4.7*-.@. 3,4.8.6589. 59 4*:.>.-; 34A/545F5 J,4:*-.@ 89?*6@ J4.F,*98@ 4C*?*J . -,3,J, 4?,E,*98@ 59-58.9*:=-5 C?5J5:=-5I 58. . 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C*?*6*--5F5 8*>*-.@ 8 F5:54/5I J:@ /?*C:*-.@ / -,/54,:=-*. 141 .!. "#$%&'())#*&, +.+. ,)-*#*./ 2. 0-$"*$--1("2"$)$'3 ."'(%4'5%3 4'#'*% 9*5?*9.>*8/5I 6*+,-./* 6*+,-.>*8/,@ 8.89*6, 8 n 89*C*-@6. 845H5J; .6**9 n 85H894*--;+ >,8959, 85594*9894ADE.+ n 4.J,6 -5?6,:=-;+ /5:*H,-.I, 9,/ >95 C*?*6*E*-.* /,7J5I 95>/. 8.89*6; C?. 845H5J-;+ /5:*H,-.@+ C?*J89,4:@*98@ 4 4.J* F*56*9?.>*8/5I 8A66; C*?*6*E*-.I, /595?;* C5:A>.:, H; 95>/, C?. /,7J56 .3 -5?6,:=-;+ /5:*H,-.I. '?. 5J-56 95:=/5 -5?6,:=-56 /5:*H,-.. /,7J,@ 95>/, 8.89*6; 854*?<,*9 F,?65-.>*8/5* /5:*H,-.*. #,/.6 5H?,356, -5?6,:=-;6 /5:*H,-.*6 6,9*?.,:=-;+ 95>*/ -,3;4,*98@ 9,/5* 845H5J-5* J4.7*-.*, C?. /595?56 /,7J,@ 95>/, 854*?<,*9 C?5895* F,?65-.>*8/5* /5:*H,-.*, C?.>*6 >,8959; /5:*H,-.I 48*+ 95>*/ 5J.-,/54; . 48* 95>/. /5:*H:D98@ 4 5J-5I Q,3*. %8C5:=3A@ 6*95J /5-*>-;+ G:*6*-954, J.8/?*9-;* A?,4-*-.@ J4.7*-.@ 9*:, 657-5 C?*J89,4.9= 4 4.J* 6,9?.>-5F5 A?,4-*-.@ [8] [ M ]{2} % [C ]{2} % [ K ]{2} " {P}, (9) 4 /595?56 {2} – 4*/95? A3:54;+ C*?*6*E*-.I J:@ 48*F5 9*:,; {2} , {2} – 4*/95?; A8/5?*-.I . 8/5?589*I J:@ 95>*/ 9*:,; [ K ] , [C ] , [ M ] – «F:5H,:=-;*» 6,9?.B; 7*89/589., J*6CQ.?54,-.@ . 6,88 J:@ 48*F5 9*:,; {P} – 4*/95? G/4.4,:*-9-;+ A3:54;+ 8.: J:@ 9*:,. '?. 598A9894.. 4-*<-.+ 8.: A?,4-*-.* (9) 657-5 3,C.8,9= 4 4.J* [ K ]{2} " $ [ M ]{2}. (10) (?,4-*-.* (10) 9.C.>-5 J:@ 48*+ 3,J,> /5:*H,-.I 8 /5-*>-;6 >.8:56 89*C*-*I 845H5J;. '?. 85H894*--;+ /5:*H,-.@+ 48* 95>/. J4.7A98@ 4 Q,3*, C5G956A 6; 657*6 3,C.8,9= {2} " {20 }sin 3t , 59/AJ, {2} " $32 {20 }sin 3t. '5J89,4:@@ ?*3A:=9,9 4 (10), C5:A>,*6 8:*JADE** A?,4-*-.*: ([ K ] $ 32 [ M ]{2 0 }) " 0. (11) N95 A?,4-*-.* @4:@*98@ 9.C.>-;6 J:@ 3,J,> -, 85H894*--;* 3-,>*-.@. !8:. 6,9?.B; [;] . [<] .6*D9 ?,36*? n×n, 95 6; HAJ*6 .6*9= n ?,3:.>-;+ 3-,>*-.I AF:545I >,8959; Y, /595?;6 HAJ*9 AJ54:*945?@9= A?,4-*-.* (11), . 5-. ?,886,9?.4,D98@ /,/ 85H894*--;* >,8959; 9*:,. 142 .01'/,**2, 3&1'.'2 #%4)&*'&'& 1'5,%,*# 4.56*,/.$. '#4& &,7J,@ .3 G9.+ >,8959 HAJ*9 84@3,-, 8 /5-/?*9-5I Q5?65I .:. «65J5I» {2 0 } , 4 /595?5I A89,-54:*-; 59-5<*-.@ ?,3:.>-;+ A3:54;+ 86*E*-.I, -5 -*.34*89-; .+ 4*:.>.-; [1]. " B*:=D 8?,4-*-.@ ?*<*-.@ )&N 8 ,-,:.9.>*8/.6 C?5.34*J*>,8959-;I 9?*+6*?-;I ,-,:.3 89*?7-@, @4:@DE*F58@ C?59*356 89?*6*-. .3 9*Q:5-,. P,8>*9 C?5.345J.:8@ 4 .-7*-*?-5-?,8>*9-5I C?5F?,66* SolidWorks. /,>*894* 6,9*?.,:, .8C5:=354,:8@ C5:.9*9?,Q95?G9.:*- (9*Q:5-). P,36*?; 65J*:. 89*?7-@ C?*J89,4:*-; 4 9,H:. 3, 845I894, 9*Q:5-, – 4 9,H:. 4 [2]. #,H:.B, 3 W,?,/9*?.89./, 89*?7-@ ',?,6*9?; 1:.-, P,J.A8 K.8:*--;* J,--;* (66) 3,5 0,39 #,H:.B, 4 W,?,/9*?.89./, 6,9*?.,:, "45I894, )5JA:= Z-F,, 8, 109 ', &5GQQ.B.*-9 'A,885-,, = ':59-589=, T, /F/63 K.8:*--;* J,--;* 5,5 0,46 920 '5:A>*-; 85H894*--;* >,8959; 89*?7-@ /,/ AC?AF5F5 6,9*?.,:,. %3 H5:=<5F5 8C*/9?, Q5?6 . 85594*9894ADE.+ .6 >,8959 -,8 .-9*?*8AD9 .6*--5 C?5J5:=-;* /5:*H,-.@. '5 Q5?6,6 /5:*H,-.I AJ,:58= 4;H?,9= 9*, /595?;* 85594*9894AD9 C?5J5:=-;6. $, ?.8. 3 C?.4*J*-; >*9;?* C*?4;+ 65J;, >,8959; /595?;+ 85594*9894AD9 C*?4;6 >*9;?*6 85H894*--;6 >,8959,6 C?5J5:=-;+ /5:*H,-.I. $, ?.8. 4 C?.4*J*-5 8?,4-*-.* ,-,:.9.>*8/5F5 . >.8:*--5F5 ?*<*-.I J:@ C*?4;+ >*9;?*+ 85H894*--;+ >,8959 C?5J5:=-;+ /5:*H,-.I 89*?7-*45F5 .6C:,-9,9, C5?<-*45F5 9.C,. "?,4-*-.* ?*3A:=9,954 ,-,:.9.>*8/5F5 . >.8:*--5F5 ?*<*-.I C5/,3,:5 -*3-,>.9*:=-5* ?,8+57J*-.* 3-,>*-.I 85H894*--;+ >,8959, C5G956A 5H, C5J+5J, 657-5 .8C5:=354,9= J:@ >,8959-5F5 ,-,:.3, 89*?7-*45F5 .6C:,-9,9,. '*?4;* >,8959; J:@ .6C:,-9,9, C5?<-*45F5 143 .!. "#$%&'())#*&, +.+. ,)-*#*./ 9.C, C?*4;<,D9 170 /LB, 9.*. J,:*/5 4;+5J@9 3, C?*J*:; 34A/545F5 J.,C,35-,. MJ-, .3 -.3<.+ >,8959, 85594*9894ADE,@ 4-I 65J*, A7* 4+5J.9 4 )LB-J.,C,35-. & 0 / $ P.8. 3. "5H894*--;* Q5?6; 89*?7-@ .3 9*Q:5-, 4 ?*3A:=9,9* C?5J5:=-;+ /5:*H,-.I P.8. 4. L?,Q./ 8?,4-*-.@ J,--;+ J:@ 9*Q:5-,: ,-,:.9.>*8/5* ?*<*-.* (/LB); >.8:*--5* ?*<*-.* (/LB) 144 .01'/,**2, 3&1'.'2 #%4)&*'&'& 1'5,%,*# 4.56*,/.$. '#4& 2;954,@ !"#$%&''() $"*'+#( (,&$&-." $"!"/&'., ,+0'(!+1(2+) (-$&3&4+!) + $.5.) %(4&$("$ - $&3 6+(5(1&'" 7(,$&$, 5& $&38 5%"6,$(-!)"$ +'$"%", 6(!9'":;+: ('(!+1 5& -.-&68 ,&4,$-"''.* 7(,$&$ +35!('$($( +1 <=2-6+(5(1&'(. >,*&6) +1 5%&-"6"''&0& 7(,$&$'&0& ('(!+1( - #(7",$-" #%+$"%+) #(7",$-( +35!('$($( 5&%;'"-&0& $+5( 3&?'& 5%+')$9 3+'+383 5"%-&: ,&4,$-"''&: 7(,$&$.. @(# #(# - <=26+(5(1&'" &,$("$,) 2"!.: %)6 ,&4,$-"''.* 7(,$&$ +35!('$($(, '(, +'$"%",8"$ 6(!9'":;+: ('(!+1 %"1&'(','.* )-!"'+: - +35!('$($" 5%+ +,5&!91&-('++ ,&$&-.* $"!"/&'&-. !"#$! 1. A%&+1-"6"' ('(!+1 ,&4,$-"''.* 7(,$&$ +35!('$($( 5&%;'"-&0& $+5(, 5%+3"')"3&0& - ,$(5"6&5!(,$+#" '( &,'&-" ('(!+$+7",#&0& + 7+,!"''&0& %";"'+:. B.4%('. +'$"%",8CD+" '(, 5%&6&!9'." #&!"4('+). E+1;+" 7(,$&$. !"?($ - 6+(5(1&'" ,-.;" 170 #=2 + 8?" , 4-: 7(,$&$. 8*&6)$ - <=2-6+(5(1&'. 2. B-"6"' #%+$"%+: 83"'9;"'+) '"0($+-'&0& -!+)'+) -'";'+* +1!87"'+: '( 5&-"6"'+" +35!('$($( - <=2-6+(5(1&'". >,*&6) +1 7(,$&$'&0& ('(!+1( 3&?'& -.4%($9 6!) #%+$"%+) #(7",$-( +35!('$($( 8,!&-+" 3+'+383( 5"%-&: ,&4,$-"''&: 7(,$&$.. %&'(&#)*+,&-./0&1 /2&/#0 1. F"08' A.>., G8#":!& H.I. F+&3"*('+#(. – JA4.: A&!+$"*'+#(, 2000. – 463 ,. 2. F&%&68!+'( @.J., J"!)'+'&- I.I., A&60("2 K.<. B.4&% 5(%(3"$%&- 5%&$"1( ,$%"3"'+ 5%+ ,$(5"6&5!(,$+#" '( &,'&-" ,&4,$-"''.* 7(,$&$ //K&,,+:,#+: ?8%'(! 4+&3"*('+#+. – 2009. – @. 13, L 4 (46). – J. 42–53 3. F+&/+1+#( / H.I. B!(6+3+%&-, M.>. K&D85#+', I.N. A&$(5"'#&, I.>. M""-. – <.: <"6+2+'(, 1983. – 272 ,. 4. B8!9;$":' O. J!8*&8!87;(CD+" &5"%(2++. – <.: <"6+2+'(, 1972. – 426 ,. 5. K"3+1&- I.E. P%($#+: #8%, 3"6+2+',#&: + 4+&!&0+7",#&: /+1+#+: !"#2++ + ,"3+'(%. / 5&6 %"6. 5%&/. I.E. K"3+1&-(; K&,. 0&,. 3"6. 8'-$. – <., 2001. – 383 ,. 6. K86') A.=. I$!(, &5"%($+-'&: &$&%+'&!(%+'0&!&0++. – <.: <"6+2+'(, 1983. 145 .!. "#$%&'())#*&, +.+. ,)-*#*./ 7. Rosowski J.J. Mechanism of sound conduction in normal and diseased ears // The Function and Mechanics of Normal, Diseased and Reconstructed Middle Ear. – Hague: Kugler Publications, 2000. – P. 137–145. 8. P&!"4('+) !+'":'.* ,+,$"3 / 5&6 %"6. B.B. F&!&$+'(. – @. 1. – <.: <(;+'&,$%&"'+", 1978. – 352 ,. References 1. Begun P.I., Shukeylo Y.A. Biomechanika [Biomechanics]. St. Petersburg: Politechnics, 2000, 463 p. 2. Borodulina T.S., Selyaninov A.A., Podgaets R.M. Vibor parametrov proteza stremeni pri stapedoplastike na osnove sobstvennich chastot [Choice of parameters of prosthesis appliance of stirrup at the stapedioplasty arts on the basis of the natural frequencies]. Russian journal of biomechanics, 2009, no 4 (46), pp. 42–53. 3. Vladimirov Y.A., Rotchupkin D.I., Potapenko A.Y., Deev A.I. Biofisika [Biophysics]. Mocsow: Medicine, 1983, 272 p. 4. Vulshtein H. Sluhouluchshayutchie operazii [To the operations on the improvement of hearing]. Mocsow: Medicine, 1972, 426 p. 5. Remizov, A.N. Kratkiy kurs medicinskoi i biologicheskoy fisiki. Lektsii i seminary [Short course of medical and biological physics. Lectures and seminars]. Russian State Medical University, 2001. 383 p. 6. Rudnya P.G. Atlas operativnoi otorinolaringologii [Atlas of operative otorhinolaryngology]. Mocsow: Medicine, 1983. 7. Rosowski J.J. Mechanism of sound conduction in normal and diseased ears The Function and Mechanics of Normal, Diseased and Reconstructed Middle Ear. Hague: Kugler Publications, 2000, pp. 137–145. 8. Kolebaniya lineynyh sistem [Vibrations of the linear systems]. Ed. V.V. Bolotin, vol. 1. Moscow: Mashinostroenie, 1978, 352 p. 3' +"4#*+5 6&)7+48((&9+ :+9&; +$&7#"9+ (A"%39, K&,,+)) – 3(0+,$%('$ #(/"6%. $"&%"$+7",#&: 3"*('+#+ A"%3,#&0& '(2+&'(!9'&0& +,,!"6&-($"!9,#&0& 5&!+$"*'+7",#&0& 8'+-"%,+$"$( (614990, 0. A"%39, P&3,&3&!9,#+: 5%., 29, e-mail: sonya.nigmatullina@mail.ru). :.(;9&9#" <(.0/+9$* <9+4#(=."&- (A"%39, K&,,+)) – 6&#$&% $"*'+7",#+* '(8#, 5%&/",,&% A"%3,#&0& '(2+&'(!9'&0& +,,!"6&-(- 146 .01'/,**2, 3&1'.'2 #%4)&*'&'& 1'5,%,*# 4.56*,/.$. '#4& $"!9,#&0& 5&!+$"*'+7",#&0& 8'+-"%,+$"$( (614990, 0. A"%39, P&3,&3&!9,#+: 5%., 29, e-mail: luba@theormech.pstu.ac.ru). About the authors Nigmatullina Saniya Vadimovna (Perm, Russian Federation) – graduate student, department of Theoretical Mechanics Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: sonya.nigmatullina@mail.ru). Selyaninov Aleksandr Anatolyevich (Perm, Russian Federation) – Doctor of Technical Sciences, Professor of Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: luba@theormech.pstu.ac.ru). A&!87"'& 25.08.2012 147