Study and Analysis of the Electrical and Mechanical Parts in a Wind Turbine
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(22) " * ,.#)(,#( #*& . . " ,).), & -1#&&.% ." ( ,!3)/.) ." 1#( < " 31)/& ? . "@." 1#( ( ." (.,(- ),'#.-').#0 ( ,!3#(.) ." "/ ,)..#)(91"# "." *,) #& #-+/#. -#'#&,.)." #,*&( 1#(!-< ).), & -1)/& **&3." -' ?&# .@*,#( #*& ; G<" #,-., '*,) / -)0 ,*, --/, &)1." 1#(!< H< )0 ." 1#(!#-#(0 //'-../-< )." - .1),/& -1)/& & .." ,).),)* ,. ( ,).. <. . #!/, GG &)1-")1-."..3*# &1#( ./, #( & -< #!/, GG3*# &3* #( /, #( & -C , ( ND . " . ,#& . #(&3 ." ,).), & - )(-#-. ) ." -3(." .# - , #( ), #( &/ #(! ." # ,!&--( ." , )( # ,-< " &3 ,-1)/& -.# %.)! ." ,1#."." *)23, -#(( ." 1)) ( ." 1)) *)23 ( ." 1)) = # ,= *)23 )'*)/( - .". 1)/& & -- 1# &3/- )'*,#(!1#."." )'*)( (.- ), < (1"#& ." 1)) (,).), & - )/& , 3 & < &/'#(/' ( -. & &&)3- , '/ " " 0# , .". 1)/& & - .) ." '. ,#& .#!/ 9 ." , ), ." - '. ,#&- , )(&3 /- ), .#(3 1#( ./, #( -*,) / .#)(<. . . GN.
(23) L<H / . " "/ #- ." (. , ) ." ,).), '%#(! ." .. "' (. 1#." ." ,).), & -< (." )." ,-# 9." -.#,)(),." -.-. &1)/& /- < " "/ 1#." ,1- ." ( ,!3 ,)' ." ,).), & - #, .&3 .) ." ! ( ,.),<. ./, #( "- #, . ,#0 9 ." ( ." "/ .,(-'#.- ." ( ,!3 )( .) ." ,#(!! ( ,.),< " , , - 0 ,&13-) ." ,).), & -.". ( .. " .)." "/ &#% '%#(!#( #2 *)-#.#)(),1#.",.# /&.#)(),-* ( /&/'< " &.. ,)( #-/(#+/ 0 ,-#)()(." .1)= & ,).),.".." -1#(!-- * ( /&/'1)/& ( "), .)." "/ < /,, (.&3 ')-. '(/ ./, ,- 1)/& &#% .) /- #2 "/ ), .". #. )/& -./, 3.), / '(3')0 & )'*)( (.-.".'#!". #&< &-)#.#-, &.#0 &3 -3.) )(-.,/ . < #!/, GH &)1-")1-."..3*# &.3* ) 1#( ./, #( "/ <. . #!/, GH3*# &3* #( /, #( / C , ( ND . . . GO.
(24) L<I)1 ,)(.,)& . " *)1 ,) ." 1#( ./, #( -), -")/& )(.,)&& ),." , -)( .".--/' &3." 1#( #-.))-.,)(!-)." *)1 ,#-, / .)*, 0 (. ." '! .)." -3-. '< -# &&3." , , .1) )( *.- )/.." *)1 ,, !/&.#)(< ( #-." -.&& )(.,)&.".#-, !/&. 3." &)1- *,.#)(< . ( ."#- , !/&.#)(9 ." ,).), & - 1#." ."#- .3* ) )(.,)& 1#&& )(( . .)." "/ . #2 (!& < " ,).), & *,) #& #- -#!( .)& #(." ./, /& ( .*,.# /&, -* "#( ." ,).), & -< (1"#& 9 ." 1#( #- -) -.,)(! .". ." -3( ",)()/- ! ( ,.), 1)/& &-), -.,# .." *)1 ,! ( ,.#)(' "(# &&3< . .1#&&&-) )(.,)&." -3-. '-* .)." *)1 ,!,# 1),%#(! , +/ ( 3< ( ." ,).), )/& (). )* ,. -. , 1"#& ." 1#( &)1- '/ " -.,)(! ,< . ( ."#- )( *.9 ." ,).), & - ( .) -#!( .) '% ." &)1 - *,.#)( . ,.#( 1#( -* ( ." *)1 , #(*/. #- , / &.")/!"." & -."., ().*#. " 3." '- &0 -< . (." .#0 -.&& )(.,)&.".." ,).), & -*#. " )/& 0 ,# # 9( ."#- .3* ) )(.,)& -3-. ' #- &')-. /- #( ." &,! .3* ) ." 1#( ./, #( -'), ."(G< . ." 1#( 1 , .))-.,)(!." (." ,).), & -1)/& ./,( #(.)." 1#( 91"# "1)/& #( , - ." ./, /& ( < " .#0 -.&& , !/&.#)( & . ." *)1 , , !/&. #( '), /,. 13."(." ' -/, ' (.) ." *--#0 -.&&, !/&.#)(< ()." ,*)1 ,, !/&.#)(#-." *#. " )(.,)&.".1- 0 &)* ,)'." 3 ,) GOOF/*.)HFFF< "-#(!& ,).), & ( ./,( /(&#'#. &3#(.)9),)/.) ." 1#( < " ,#0 ),." *#. " $/-.' (.#- #." ,' "(# & ),." -3-. '-#( ( )/.*/. &)1 GFF % ), "3 ,/&# .". -.,.#(! . IFF% ), & .,# .".#-." ')-.)( -* #&&3 ),." &,! ./, #( -)0 ,KFF%< " , ), )(.,)&& ,/-/&&3')(#.),-)/.*/. ),." ./, #( *)1 ,< . ." 1#( 1 , .))-.,)(!9." (." ,).), & -1)/& ./,( )/.) ." 1#( &)(!." 2#- 3 , .#)() ." !, 9( #.1)/& &-), / ." &# .#(!9 " ( ." ,).), 1)/& % * ! ( ,.#(! ." *)1 , . ,. * #.3.")/!"#("#!"1#( 0 &) #.3< . HF.
(25) ( ." )." , "( 9 ." -1 *. , ) ." 1#( ./, #( )/& & /&. 3/-#(!." +/.#)( ),." , ) ." #, & #--")1(;. C , ( ND ,)'." & (!.") ." ./, #( & -1" , ." , #/-) ." #, & +/&- ." & (!.") ." & -")1(-#(." #!/, &)1< ." #!/, H #!/, GI" 3*# &/, #( & -C , ( ND . . . . HG.
(26) "*. ,M #( /, #( ).), . ( ), , .) /( ,-.( ")1 ! ( ,.),- 1),% #. #- '/ " -# , .) %()1 ")1 ').),- )* ,. " ), ." . .". ( & .,# ').), ( ( & .,# ! ( ,.),, /( ' (.&&3." -' /.." ').), )(0 ,.- & .,# & ( ,!3 .)' "(# & ( ,!3( ." ! ( ,.), ) -." , 0 ,- < )-. ) ." ').),- 1),% - )( ), (.4 ), < " ,#!".="( -# ) ." #!/, #&&/-.,. - .". 1" ( & .,# /,, (. &)1- .",)/!" 1#( #(! .". #- 1,** ,)/( ,,)/-'. ,#&91"# "' (-) ),, &. .)." #,)( '#&3 ) ' .&-9'!( .# # & #- , . 9( '!( .# # & #-." , ,)/( '!( ..".3)/ )/& - ), &'!( .#-'9( 1" , '!( .1),%- ,." , ,)' ." '!( . ." ( #. ) - (). .., . ' .& *,.# & - " ( #. -")/& )/.-# ." '!( .# # & < #!/, GJ &)1-")1-.".." ,#!".="( ,/& -.) . ,'#( ." '!( .# # & #, .#)(( ." ), #, .#)()(1#, #('!( .# # & < #!/, GJ" #!".= ( /& -) . ,'#( " !( .# # & #, .#)(( " ), #, .#)((#, (!( .# # & C , ( GD. . (').),." , , &).) 1#, -.". ,,3 & .,# /,, (.( . "#(-.(. , *)-#.#)( #(-# ." # & ) '!( .< &&-/ $ ..) ), -.".1" ( .)! ." , , . .),+/ #(." ').),-" . ( '% #../,(< )' ').),- )/& 1),% - )( # , (. *,#( #*& 9 ( , !, & -- ) ), (.4 ), 1 &-) "0 , &/ .( ), 9 ( #. -")1- .". # ." , #- '!( .# # & ." ( ), 1#&& 2 ,. )((3 ,,)/-'. ,#&.".&# -#(." '!( .# # & 9 1"# " )/& .". ) * ,'( (. '!( .9 ), #. )/& ! ( ,. 3 1#( #(! .". ,,# - ( & .,# /,, (.< ( ." )(.,,3 '!( ..".#-! ( ,. 3( & .,# /,, (..",)/!"1#, 1#( #(!&)- -#.- '!( .#-' 1" ( ." , #- () /,, (. #( ." 1#, ( .". #- && ( & .,)'!( .< #!/, GK &)1 -")1- ." ! ( ,& )* ,.#)( *,) /, ) ').), #( 1#( ./, #( < . HH.
(27) #!/, GK " ( ,& * ,.#)( ,) /, ).), ( #( /, #( C , ( GD . . . #!/, GL &)1 -")1- .". ." ,)--=- .#)( ) -1#. " , &/ .( ' "#( 1#." L -..), ( J ,).), *)& - ( ().# ." )( (.,. 1#( #(!- )( ." -..),< #!/, GL " #!,' ")1- ". ,)--=- .#)( 1#. " &/ .( "#( #." L ..), ( J ).), )& - ( ).# " )( (.,. #( #(!-(" ..),)& - C , ( GD . . HI.
(28) "*. ,N #( /, #( ( ,.), N<G#, ./,, (. ( ,.),-. . " , #-()*& ), #, . /,, (.! ( ,.),.." & 0 &) #( /-.,#&*)1 , ! ( ,.#)(9 ")1 0 , -'&& #-)&. ./, #( ( )(( . .) ! ( ,.),< " )/.*/.) ! ( ,.),#-!)) ), ",!#(! .. ,# -9( -/ "- (,#) )/& "** ()(&3#(-'&&=- & **&# .#)(-<),#(-.( *)1 ,#(!")/- #( , '). , .".- .) .. ,# - )/& ",! 3-'&&1#( ./, #( < -/ " ")/- #- -#'#&, .) (),'& ")/- ( /-#(! ." +/#*' (. &#% , ,#! ,.),91-"#(!' "#( ( 91"# ", ,/( 3 & .,# #.3." ( ." & .,# #.3-.), #(." .. ,3-")/& )(0 ,. .) #, /#.1#."." , +/#, 0)&.! ( , +/ ( 3 .",)/!" ( #(0 ,. ,9 1"# " #- ( & .,)(# 0# .". )(0 ,.- & .,# #.3 .) & .,# #.3 ( ." +/&#.3 ) ." )(0 ,. -#!(& * ( -)(." #(0 ,. ,< #, . /,, (. ! ( ,.), #- -#'#&, .) ').),9 ( &. ,(.#0 &3 ! ( ,.), )/& -'&& .", =*"- &. ,(.), ." 0)&.! ) 1"# " #- )(0 ,. .).",)/!", .# # ,91"# "#-( & .,)(# 0# .". )(0 ,.- & .,# #.3.) & .,# #.3< " , -)( ),/-#(!(&. ,(.),( , .# # ,#- /- ) -'&& ,-#4 ( & --1 #!". )'*, .) 3(')C #, . /,, (.! ( ,.),D9( ." 0)&.! ) ." & .,# #.3! ( ,. #( 3(') * ( -)(." -.,/ ./, ) ." ' "#( ( ." ,)..#)(-* )(#.< #!/, GM &)1-")1-." 13-) #-)&. **&# .#)() 1#( ./, #( -<. . #!/, GM " #!,' ")1- ". " 3- -)&. **&# .#)( #( /, #( -C , ( GD . . . . HJ.
(29) N<H3( ",)()/- ( ,.),- . " -.( , .3* ) ! ( ,.#)( ),&&*)1 ,! ( ,.#)(.." )'' , #&& 0 & .". 2 *.#(1#( ./, #( -#-.", =*"- -3( ",)()/-! ( ,.),< * ( #(!)(." ') ) )* ,.#)(." 3 )/& &-) /- #(1#( ./, #( -< " -* # # # , ( .1 (-3( ",)()/-! ( ,.),( (-3( ",)()/- ! ( ,.),#-.".-3( ",)()/-! ( ,.),'/-. ,).. . )(-.(.,*'#( ), , .) )(( . .) !,# 9 )." ,1#- ." , +/ ( 3 ) ." ! ( ,. & .,# #.391"# " * ( -)(." ,*'9#-().!)#(!.) )(-.(.( #2 . , +/#, 0&/ 9" ( #.#-#'*)--# & .)"0 '), .".)( , +/ ( 3#(!,# < . (-3( ",)()/-! ( ,.),." , +/ ( 3 * ( -)(." (/' ,) '!( .# *)& -* ,*"- <" (/' ,) *)& -* ,*"- )/& -'&&-HC'#(#'/'D9 1"# " ,)'(),.".)-)/."*#,9.)"#!" ,(/' ,-< (), ,.)"0 ,.#( , +/ ( 39." -* .1"# "." ! ( ,.),'/-. ,).. C#(,*'D )/& )/( ,)'." ),'/&; . Ns =. 60 f p. C , ( GD. " , #- ." , +/#, , +/ ( 39 ( * #- ." (/' , ) *#,- ) *)& - * , *"- < "#- +/.#)( )/& +/&&3, *, - (. 3; . 120 Ns = P / 3 C , ( GD " , #-." .).&(/' ,) *)& -#(." -..),CQL*D< --#'#&,.)&&! ( ,.),-9-3( ",)()/-' "#( )/& - ,0 -').),),- ! ( ,.),9( # #.#-,).. ." (#.! ( ,. - & .,# #.39( # #.#- )(( . .) & .,# #.3#. "0 --').),< && ." .", =*"- ' "#( - 1),% - )( ." ,)..#(! '!( .# # & 9 1"# " #- '!( .# # & .". ,).. - )/. ( 2#-9 ( ."#- 2#-.- #(-# ." -..),) ').),-( )(-.#./. -." -#-) ." #,)* ,.#)(< #(!& =*"- ' "#( -"0 ." -' -.,/ ./, -." .", =*"- ' "#( - 2 *..".." 3"0 )(&3)( *"- 1#( #(!( #. )/& )(( . )(&3.) -#(!& =*"- & .,# #.3< . (-3( ",)()/-! ( ,.),." '!( .# # & ,).. -#(-# ." -..),1#( #(!-< " ! ( ,. & .,# #.3#-.% ( ,)'." -..),1#( #(!-91"# ", -..#)(,3< & M &)1#&&/-.,. -." -3( ",)()/--* #(,*' ),0,#)/-(/' ,-) *)& -1#."." # , (. , +/ ( # -< . HK.
(30) & M ),'-")1-." -3( ",)()/--* #(,*' ),0,#)/-(/' ,-) *)& - 1#."." # , (. , +/ ( # -C , ( GD /' , )& - G H I J K L N O GF #, ,"- 3( ",)()/- ILFF GNFF GHFF OFF MHF LFF JKF JFF ILF ,*' ),LF 3( ",)()/- IFFF GKFF GFFF MKF LFF KFF IMK III IFF ,*' ),KF . . N<I-3( ",)()/-), ( / .#)( ( ,.),-. . " , , .1) .3* - ) #( / .#)( ' "#( -9 ( ." 3 , (' - )( ." -.,/ ./, ) ." ,).),< ( #- && -+/#,, &= ! ' "#( ( ." )." , #- && 1)/( =,).), #( / .#)( ' "#( C D9 1"# " #- .3* ) #( / .#)( ').),),! ( ,.),1")- ,).), )(.#(-1#( #(!-9-)**)- .)-+/#,, &= ! ' "#( ."."-()1#( #(!-#(." ,).),<" ,,(! ' (. ),1#( #(!-)(." ,).),.".,).. -.) )(( . .))/.-# -)/, -."., -..#)(,3#- )( .",)/!" -&#*=,#(!-9 1"# " #- ' .&&# ,#(! )( ." ,).), ) ,.#( .3* - ) & .,# ' "#( - 1" , ,/-" - -&#* )( ." -&#*=,#(!- .) .,(- , & .,# /,, (.< " ", . ,#-.# "0#),) (#( / .#)(' "#( #-.".# #.-,).),#-./,( -&)1 , ."( #.- -3( ",)()/- -* ." ( #. #- ').),9 ( # #. #- ./,( -. , ."(." -3( ",)()/--* ." (#.#-! ( ,.),< " -3( ",)()/--* #-!)0 ,( 3." !,# .)91"# "." -..),#- )(( . ( #.#-." )(-.(.-* ) -3( ",)()/-' "#( 9( ."#--* * ( - )(." , +/ ( 3) ." -/**&3 & .,# #.3< #!/, GN &)1 -")1- ." ", . ,#-.# /,0 ) ( #( / .#)( ' "#( 9 #( # .#(!." , &.#)(-"#* .1 (-* ( .),+/ <. . #!/, GN " ", . ,#-.# /,0 ( ( / .#)( "#( 9 #( # .#(! ." , &.#)(-"#* .1 (-* ( .),+/ C , ( OD . . . . HL. GL HHK GNM.
(31) ." 1#( -* !, /&&3 ,)*-9 . )( *)#(. ." ! ( ,.), -* )' - &)1 ,."(." -3( ",)()/--* <" ! ( ,.),./,(-#(.)').),( #(-. ) !#0#(! ( ,!3 ,)'." !,# 9#. )' -&) < . ."#- .#' 9 ." ./, #( )(.,)&& , '/-. *, 0 (. ."#- ,)' "** (#(! 3 #- )(( .#(!." ! ( ,.), ,)'." !,# < (."#- )( #.#)(9/(.#&." 1#( -* . " - /*9 ." ./, #( ,).. - , &3 ( "- , 1" & -../-9 1"# " #- -.( 3 -.. ) 1#( ./, #( 1" ( #(-/ # # (. 1#( #- 0#& & .) ./,( ." ./, #( < (." )." ,-# 9." 0#.#)( ,)'." -3( ",)()/--* #- && -&#*91"# " #- ." . ) (). ,)..#(! . -3( ",)()/- -* #( #( / .#)( ').),- ( ! ( ,.),-< . N<J* ,.#)() -) #( /, #( - . ) - ) )* ,.#)( && #(.) .1) . !),# - #( ." #,-. *& ; .")- .". , -* .#0 /- #(-3( ",)()/-! ( ,.),-( -3( ",)()/-! ( ,.),-< (." #,-. . !),3." ') -, ; #, . ,#0 ') 9 #2 -* ') ( 0,# & -* ') < ( ." - )( . !),39 ." , , &-) .", # , (. ') - ( ." 3, ;-+/#,, &= ! ! ( ,.),') 90,# & -&#*') C13) )* ,.#)( )(.,)&) 1#( ./, #( - 1#." ( #( / .#)( ! ( ,.), ), )(( .#(! .) !,# <D ( 0,# & -&#*1#." )/ &3 #( / .#)(! ( ,.),') <. #<. #, .,#0 ) . . ( ." #, . ,#0 ') ) )* ,.#)( ." ./, #( ( ! ( ,.), , #, .&3 )(( . .) ")." ,9( ." , #-()! , )2 .1 (." '< .", =*"- .,(- ),' , -.( - .1 ( ." ! ( ,.), ( ." !,# .) #( , - ." 0)&.! ,)' ." ! ( ,.), .) ." !,# 0)&.! ( # # /&. )( #.#)(.) -.#- # " , #(-/ "') #-." ( --#.3 ),." ./, #( ( ." ! ( ,.),-* .) ." -' < '*&)3#(! * ,'( (. '!( .- &#'#(. - ." ( ), "#!" , -* - ) ! ( ,.),#(), ,.)*,)0# ." ,).),'!( .# # & < )1 0 ,9." , +/ ( 3 ) ." ! ( ,. & .,# #.3 #- &)1 " ( , +/ ( 3 )(0 ,. , '/-. '*&)3 .),#- ." , +/ ( 3.).".) ." !,# <)-., (.&3* ,'( (. '!( .! ( ,.)," (#(.,) / ),1#( ./, #( -/- #(0,# & -* ') 9 /. )(( . #, .&3.)." ./, #( ,).),91#.")." , -#!( ./, -&#% *& #(!." * ,'( (.'!( .-)(." )/.-# ) ." -..),1#( #(!< #!/, GO &)1-")1-." ') &) #, .1#( ./, #( <. . #!/, GO #, .,#0 #( /, #( C , ( GD. . HM.
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
(33) #!/, HG3( ",)()/- ( ,.),-#.", +/ ( 3)(0 ,. ,C , ( GD . . N<K,# & &#*) . ." -&#* ) ' "#( #- &. , 3 #(.,) / #(! 2. ,(& , -#-.( #( - ,# - 1#."." ,).),1#( #(!." (#.#-*)--# & .) .. , *.." )* ,.#(!*)#(.) (#( / .#)(! ( ,.),.)." '2#'/'*)#(.) ." ./, #( ", . ,#-.# /,0 < "#- ' .") "- ( #'*& ' (. #( -)' ./, #( - #( ), , .) "0 ." ./, #( )* ,. '), # # (.&3 ( ( , ." '2#'/' *)#(. ) #.- ", . ,#-.# /,0 < . (." #!/, 91"# "#--")1( &)19." -.,#!".0 ,.# &&#( , *, - (.-." - # -3( ",)()/- ! ( ,.), 1- '*&)3 < " -&(. &#( - , *, - (. ." ", . ,#-.# /,0 - ) ( #( / .#)( ! ( ,.), 1#." #0 # , (. , -#-.),- #( ." ,).), 1#( #(!< " )/. ,')-. /,0 .) ." ,#!".9 1#." ." -'&& -. -&)* 9 ),, -*)( - .) ." "#!" -. , -#-.( #( ." ,).), #, /#.9 ), ." & -. ,).), /,, (.< 0#)/-&3 ), "#!" , 1#( -* -9 ."#- /,0 #(. ,- .- ." ./, #( ", . ,#-.# /,0 -( ,.)." '2#'/'0&/ -- )'*, 1#."." /,0 - 1#.""#!" ,-&)* < ( ." ./, #( "- .. , # # ( 3<. . #!/, HH &)1-")1-." 0,# & -&#*') ) ./, #( )* ,.#)(1#."1)/( ,).),#( / .#)(! ( ,.),<. . #!/, HH,# & &#*) /, #( * ,.#)(#.")/( ).), ( / .#)( ( ,.),C , ( OD. . HO.
(34) ,# & &#*#.")/ &3 ( / .#)( ( ,.),. . ( ." - " '.# ), ." - ./* ) ." )/ &3 #( / .#)( ! ( ,.),9 ." & .,# #.3 ,)' ." -..), #- )(( . #, .&3 .) ." !,# 9 ( ." & .,# #.3 ,)' ." ,).), '/-. *-- .",)/!" ." %=.)= % )(0 ,. ,- ,)' =.)==.)= )(0 ,-#)(<" %=.)= % )(0 ,. ,1),%- )."13-9( #. )(-#-.-) .1)*,)!,'' & )(0 ,. ,-.". ( )(0 ,..)),.)9 1"# "#- - )(." , +/#, ' (.) ." 1#( -* < " )(0 ,. ,-, )(( . .)! ." , 3 * #.),9* , ),'#(!--)/, < " 0)&.! ) ."#- * #.),#-% *.. )(-.(.0&/ 3)( ) ." )(0 ,. ,- .".* , ),'--)/, 1"#& ." )." , )(0 ,. ,- .--&) < " 0(.! ) ."#-') )0 ,." 0,# & -* ') &# -#(." ..".." )-. ) ." & .,)(# )'*)( (.- #( -/ " ') #- &)1 , ."( #( ." 0,# & -* ') 9 ( ."#- #- ." , ',% & 0(.! ) )/ &3 #( / .#)( ! ( ,.),- /- #( 1#( ./, #( - )'*, .) 0,# & -* ') /-#(! -3( ",)()/-! ( ,.),-< )/ &3 #( / .#)( ! ( ,.), "- -&#* ,#(!- ), )(( .#)( .) ." ,).), 1#( #(!< ( )/ &3 #( / .#)(! ( ,.),( -'), '#(. (( ."( -+/#,, &= ! ! ( ,.),< #!/, HI &)1-")1-." )/ &3 #( / .#)(! ( ,.),- " '.# < #!/, HI)/ &3 ( / .#)( ( ,.), " '.# C , ( GD . . . IF.
(35) N<L)(.,)& " ' -) #( /, #( -. . #( 1#( ./, #( #-( & .,)' "(# &-3-. '9 )(.,)&-")/& #(0)&0 && ." *,' . ,-< " 0,# & - #( 1#( ./, #( ( ." )'')( -3' )&- .) (). ." ' , ./, #( ,).),-* C ω t D:./, #( ,).),.),+/ C τ t 9 )(.,)&-3-. ''#!"./- ." ').), .),+/ D: ' "(# & *)1 , C Ρt 9 *,) / . ) ω t ( τ t D: & *#. " (!& C θ D: !,# , +/ ( 3 #( " ,.4 C f D: -..), , +/ ( 3 #( ,*' C ω s 9 ),, -*)( #(!.)./, #( ,).),-* ω t D:-..),0)&.! C Vs 9'/-. ." -' -!,# 0)&.! D:( -..), /,, (.C Is D< #.#)(&&39)." ,*,' . ,-&#% ." ! , )2,.#)9." & .1#-.(!& 9( -))(, *,.) ." -#!(( ." 3" ( #2 < ." )0 0,# & -9." -..),0)&.! ( , +/ ( 3'/-. +/&-.).")- ) ." !,# 9( f C( ."/-9 ω s D( Vs '/-. % *. )(-.(.< && ." ! ( ,.), )/.*/. & .,# & 0,# & - '/-. )(.,)&& - )( ." 0#& & *)1 , ,)' 1#( 9 ( (3 , +/#, ' (. ), *"- (!& ϕ - 1 &&< " - , , -* .#0 &3 P 9 Q ( Is < . ." , #-(**,)*,#. /,, (.#(." ,).),1#( #(!." (#. )/& )(.,)&." , .#0 *)1 , ), #(! .) ." &. ,#(! ." '!( .# # & ) ." ,).),< #. #- (). * ,'( (. '!( . #( ." - ) -3( ",)()/- ! ( ,.), ." ( () )(.,)& .#)()(." , .#0 *)1 , )/& ' < . . . IG.
(36) "*. ,O ,# )(( .#)() #( /, #( . 2 *. ),-'&&./, #( -.". (*)1 ,(#-)&. ), )''/(#.39." ./, #( - #( 1#( ,'9 1"# " , *,. ) ." ! ( ,.#(! ), #( ( .1),% ), *)1 , *,) / .#)( #&#.39'/-. )(( . .)!,# < ./, #( #-' ' ,) ." !,)/*) & .,# #.3-)/, -.".1),%.)! ." ,( '/-. #( . "(# & ), 1#." " )." ,< " ,)& ) " ./, #( 1" ( )(( . .) 1")& #- .) #($ . *)1 , #(.) ." !,# 1#.")/. #-./, #(! ." -3-. ') )'#(!&) #(-. ) )(.,# /.#)(--)/, < ./, #( .".#-&, 3 )(( . '3 )' #- )(( . 9),./, #( '3 -.,.1),%#(! ,)', -.< . ( , )(( . .)." !,# )(&3# #.#-, 39 3 -.#- 3#(!-)' . "(# &, +/#, ' (.< . ( )(( .#(!1#( ./, #( .)!,# #.#-( --,3.".; G< " 0)&.! ) ." ./, #( )/.*/.#-." -' -." !,# 0)&.! < H< " , +/ ( 3) ." ! ( ,. /,, (.#-." -' -." !,# , +/ ( 3< I< " ./, #( )/.*/.#--3( ",)(#4 1#."." !,# < J< " .", =*"- ), ,-C- +/ ( D) ." ./, #( ( ." !,# , ." -' < K< ( #.#)(.)." - *,#',3, +/#, ' (.-.".#.#-( --,3.".." *)1 , .),) ." !,# '#(.#( 1#."#( ,.#(0&/ -<" , ), -)' .#' - #.#-( --,3.".9# *)--# & 9." *)1 , .), #'*,)0 9),.& -.(). , - 3." #(.,) / .#)() ./, #( .)." !,# < " 0)&.! ) ./, #( ! ( ,.), #- (),'&&3 -. ** 3 .,(- ),' , .) "#!" ,0)&.! ),, -*)( #(!.)-/ -..#)(C( & .,# #.3/.#&#.3 )(-#-.#(!) (/' , ) .,(- ),' , ( )." , +/#*' (. .) #( , - ), , - ( , !/&. ." 0)&.! ) #( )'#(!.", =*"- & .,# #.3D ), #.#-,#- !#( .).".) !,# < &&." 1#( ./, #( -#(1#( ,', )(( . .)-/ -..#)(91"# "#(."#- - #- && ." )&& .),C*)#(.1" , &&." ./, #( )/.*/.#(1#( ,' , )(( . .) /,." , )(( . .)!,# 3.,(- ),' ,D" , '3 # , (../, #( -9"0#(!! ( ,.),-. # , (.0)&.! -9 /.." #,.,(- ),' , '/-. ), #(!&3 ,#(!/*." #,0)&.! .)." 0)&.! ) ." )&& .),-/ -..#)(< " , +/ ( 3 ) ! ( ,. /,, (. #- /( .#)( ) ." )* ,.#(! -* ) ./, #( ! ( ,.),91"# "#-'.. ,.".'/-. )(-# , /,#(!." -#!( *,) --< " , +/ ( 3 ) ." & .,# #.3 ,)' ./, #( '/-. 1#."#( ,.#( ,(! C**,)2#'. GPD ) ."#- (/' ,9 ' (1"#& ." '2#'/' ,,), C 0#.#)(D ."../, #( )/& "0 #-&#'#. 3&) &/."),#.3 ), & .,# )* ,.#)(-( -.( , -< . .#-&-)+/#. #'*),.(..".." /*( )1(C-#(/-)# &D0,#.#)() 0)&.! ),, -*)( 2 .&3.).")- ) ." !,# 9)." ,1#- ." ./, #( )' -&) .) ." !,# 9 )(-/'#(! ( ,!3 ,)' #. #(-. ) )(.,# /.#(! C#($ .#(! ( ,!3D #(.)#.< ()." , #'*),.(. #. ' ) "0#(! ." ),, . - +/ ( ), ." .", *"- - #- .% ( , ) /,#(!#(-.&&.#)() ./, #( ( '%#(! & )(( .#)(-<" #, .#)(- ) ./, #( ,)..#)( ( #.- ! ( ,.), , . ,'#( #( ." -#!( -.! ) 1#( ./, #( < )1 0 , /,#(! #(-.&&.#)( #. #- +/#. #'*),.(. .". . IH.
(37) ." & -, )(( . ),, .&3 ), #(!.)." '(/ ./, ,>-- " '.# -< &) - , (),'&&3 #( / .#0 ,." , ."( * #.#0 9 ." &) - #( !,# )(-#-.- ) &#!".#(!9 " .#(!9 ( ." ').),< )' ! ( ,.),- &-) )(-/' , .#0 *)1 ,-." 31),%", 9."/-9 )(.,# /. .)&)1 ,#(!." *)1 , .), ) !,# 91"# "#-(). -#, & <* #.),- ( &." /,, (.) #( / .#0 &) - ( 9."/-9 )/& '*&)3 .) ),, .." *)1 , .),.)-)' !, <(." )." , "( 1"#& #( )* ,.#)( .". -)' .3* - ) ! ( ,.),- )/& * , ),' #( -/ " 13 .". ." 3 #($ . * #.#0 , .#0 *)1 , #(.) ." !,# 9 ."/- #'*,)0#(!." *)1 , .),< . . II.
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
(39) #!/, HJ )1 , /.*/. )(.,)& #." " #( * ( KHAKJ=KFF% #( /, #( C , ( GFD . . IK.
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
(41) & O & ( . ), " /.*/. ) " #( )1 , ( # , (. #( * C , ( GGD #( * C'A- D /.*/.C%D H F I<K F J I<G K JI<N L OL<G M GLI N HJH O IHK GF JFF GG JKH GH JNG GI JOJ GJ JON GK KFF GL KFF GM KFF GN KFF GO KFF HF KFF HG KFF HH KFF HI KFF HJ KFF HK KFF. . #!/, HK &)1-")1-." *)1 , /,0 ), ( ,!3KFF1#( ./, #( < . IM.
(42) #!/, HK " )1 ,/,0 ),( ,!3KFF#( /, #( C , ( GHD. . IN.
(43) "*. ,GG )( &/-#)( . ,."9 &.")/,!" &,! .) /-9 #- &#'. #( -#4 ( ()( ) #.- )(. (.- ( /(&#'). < 1 )()..% , .)/- ." ,.">-, -)/, 1#- &3( '#(.#( ." &( 9 ." 3 1#&& 0 (./&&3 ,/( )/.< /,#(! ." *-. IF 3 ,- '(3 , - , " ( 0 &)*' (. 1),% "- ( ,,# )/. )( , ( 1 & ( -/-.#( & ( ,!3< #( ( ,!3 #- )( ) ." #'*),(. , ( 1 & ( ,!# - #( ." 1),& ( "/'( #(!-"- ( 2*&),#(!." 1#( ( ,!3-#( ( # (. 3-< , &&3**, #. /(#+/ )**),./(#.3) ."#-." -#-*,)$ ..)*,)0# /-1#." 2*&),#(!." #(. , .#(!.)*# B1#( ( ,!3( 1#( ./, #( < . ( )/, ." -#- *,)$ . 1 ( )(&3 ) /- )( -)' % 3 #. '- #( 1#( ./, #( 9 '#(&3 ." ./, - ( )* ,.#)( *,#( #*& - ) .")- ,#.# & )'*)( (.- ) ' "(# & ( & .,# & *,.-< )1 0 , ." ,#0#(! ), ) )')'# - ) 1#( .,/ #( #( ." 1#( ,'- ( ." )." , )( ,(- , !, #(! ." . ) 1#( .,/ #( - )( ." (0#,)(' (.9 -/ " - ()#- 9 -.,),#(! ." (./, 0# 19 -.,/ .#)( ) ." &( - * 9 %#&&#(! #, -9 ( #-.),.#)( ) ), - ( )''/('# .#)( -#!(& - . < , "). .)*# - 1"#& 1 .&% )/. 1#( ( ,!3 ( 1#( ,'< -. /.().." & -..".." - .3( )'*&#( .)- .3,/& -) 1#( ,' ( 1),%#(! #( 1#( .,/ #( , ) *,')/(. #'*,).( 1" ( 1 1(. .) -/ -- /&&3 -#!( ( )* ,. ." 1#( ./, #( ( 1#( ,'9 1"# " ." .#& #- /--#)() ." - )( ,(-, 2 &/ #(."#-." -#-*,)$ .< . . IO.
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