第2章図式解法

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1 φ φr ( ct φl ( ct φr ( > φl ( < v t v v,v N, NdN, d A, ρ,e d. v m E E (. ρ. : > : < φ t φ E (. ρ φ v ε E,ρ, N ε N A, E, v t A (. R ( ct ( ct R L L R E E E R L R L ( L R EvR, L EvL φ d φ( ξ dξ (. A,E,ρ A,E,ρ V (,v (,v (..

2 . V Z Z V E (.8 V [MP] Z V E Z E E E Z (. A, Z A v V A A Z Z A A v V, v V A A (.9 Z V Z Z Z v V Z Z E Z, Z ρ (.5 Z Z A ρ (.6 (, v (, v (, v ( <, v > (, v v E v E E E E Z V E E [GP], V [MP] V [m Sc ] 5[m Sc (.7 E E A E A - ] A, E,ρ (,v v V v v v Z Z Z Z v v A A Z A Z Z A A,E,ρ (,v (,v.. β β v v v v Z Z Z Z Z Z Z (. (. v v v v v v v A A Ev Ev Ev

3 E Z β (. : (, v, : (, v [c] t L E A Z V [d] A β (. [] [] A A Z Z, A (. β β, (, v (. 5,. 5V, v A v v t L A, A A β, β (.5. [] A < A []V (.9 (, v : (,v, (, v [] [c] A > A V E A A, v V A A, v V [] A A A A

4 (, vβ (, v β A β A β A A [] t L (, v (, vβ [f] (, v β [g] L ( (-,-v (,-v t t (-,v (,v (,-v (-,-v ( (-,-v (,-v L t t (-,v (,v (,-v (-,-v A A L L ( ( t t - A [ ] A A - A [ ] A < A (,-v (-,-v β ( (,-v β L (-,-v t t A (,-v β (-,v β (-,v L (,v ( t - A [ c] A > A.

5 I πr E G G ρ (.(. A R T, ω d τdτ TdT I,ρ,G τ ω G m G (.8 R ρ Ω.5 τ Ω G R (.9 Ω φ φ E (.6 t ρ τ Z Ω G R Z Z ω R (. Z γ, τ φ R, Rω, γ ω Ω Z Z τ G τ,ω, τ Z Ω T G R Z Z (. γ τ γ Z, G G ω Ω R R R Z Z (.7 I ω, T τ Z ρ I Z ρ I (. t R (.6 φ φr ( t φl( t τ Z Z v ω τ Z Z (. τ R τ R Z I ε τr Z Z I γ R A

6 β β ω ω ω ω Z Z Z Z Z Z Z V E, A, (. (,v (τ,ω ' R,G, A,',I R.5 > (. (,v R.6 ( V (, v ( τ,ω I τ A ω V v R τ ω G R τ G ( κ V E κ v E ω κ V κ V κ v V κ G κ A E (,v gfmm (τ,ω ' ( R.5mm, 9mm,. R mm, 5mm V.msc, mm ' 7msc, 5msc msc (c R,, I, G,.6 A E,, R 5

7 (, v FFT ( τ, ω (,v A ( τi R ω v v v v τ ω E E G R { } L t t t dt (.5 γ i L { } π t d i (.6 γ-i κ κ τ A A ( κ i γ. L{ ( t β ( t }.6(c ( β. L[ t H ( t ] t L[ t]. L t, ( { } >. FFT L ( t ( t ( { } t ( t t ( t τ ( τ dτ 5. Lim ( Lim ( 6

8 6. d t L dt n d t L n dt n n 7. L τ dτ L t t τ L τn τ n dτ n n d dt t t Ldτdτ n 8. ( ωt { } { } L H ( t { t} (, d dt t V [] m( L 6. d d m,, [] dt dt t 6. d t L dt (.7 FFT d t 5 dt t [] m m ω m ( t iπ iπ ω γ i γi γ i ω γi t d t dt [c] 8. [d] L δ (t ( m V n t L ( n n ω V ( [] L{ sin t} ω ω V sin( ωt ω [f] 7

9 N,, L, N π π i γ T T N (.9 N, LN γ iπω (. ω d iπdω ( i N N γ πω γ; ω γ i γ i ω { ( π N } t t γ iπωt ( γt πω i t t γ; ω dω γ N ω γ; ω []FFT FFT FFT [] FFT t T N,,, L, N - [] T N N N T ω T [] γ γ (. t γ T 7 T π (, [] γ i,,, L, N (.8 (. T FFT γt N t [5][] γt N,,, L, N (. T N γ 8

10 v (, ( (. E (, ( (. ( ( (, V E sinh( (, [c] h( t (, ( t, t. t t d d ( ( τ t ( ( v d Ed τ t (, sinh( ( [d] VE h( [].5 [d] 56 V E V H(t.5 A,E,.5 τ τ....7 V V [] ] V M.5. M V A,E,. 5. v( t, V H ( t, ( t, V [] V E sin( βτ β β

11 U d U M A( t,, d t du U, V d t t [] M U V A [] { } (, U (, 7 ( E [c] (, { V } M ( ( AE [d] [] V sinh( β h( V sinh( β h( β Aρ M [g] ( ( (, h VE sinh( βh( [f] [h] τ t (, h( ( [i] V E sinh βh ( ( sin( β τ [j] VE P β H( t ( t, A ( t, [] ( t, ( t, V E β β β. %β. % [] P (A P H( A,E, A,E, τ.9

12 ( t, ( t, [] [c] E ( ( A E P [d], E E E P ( A E P ( A A E [] (, (, P ( A A P ( A A ( { } τ t (, (, P ( A P ( A ( [f] { } [g] [] P A , AE P P H(t τ. (, z Q U [] Q AE U tnh( U sinh( U sinh( [] U AE( Q (, z z Q z U [c]

13 U U U AE Q sinh( sinh( tnh( P Q U [d] U Q U U P U U [] tnh tnh AE AE [f] [] P U P U [g] sinh P P sinh h] sinh sinh P P [i] t τ A P sinh ( h tnh tnh tnh tnh, ( [] FdF F MdM M w d d. w M F. w c t w (.5 I M w EI F w EI M w,, (.6 A EI c ρ (.7 I

14 w (, (, (.8 M (, EI F (, EI [5] M P.5 t [Sc] A,E,I,ρ h P H(t [mm] [mm] h [mm]. w(t, (t, M ( t, F( t, P H (t A [] A ( ( ( ( ( ( ( ( iφ T R c φ < π ( P ( T φ π( EI R i (.9. [],,, f, f E,A,,Ι,ρ.

15 . F f (, f F ( f, [] T T φ M EI f EI φ M EI f A f A f EI AE f ( AE [] f ( F [], [] T T F (. T T AE h( sinh( AE sinh( (, M, f, M T (. D EI (. ( D (. (. M f, f, f E,A,,Ι,ρ M, f (,,,, T,. F f, f, M, f, f, M F ( T,,, ( T

16 ( ij (.5 E,A,,Ι,ρ M f M f, f, f M E,A,,Ι,ρ M, f, f, f, f, f.5.5 [] M f f f f ( M f f M f f [] (.6 5

17 ( ( ij (.7 ] N FFT 8.5 H (t M H (t f (t t df ( τ M ( t f ( M H ( t M H ( t τ dτ (.8 dτ M (t h φd E H L 89 mm h7 mm mm L mm d5 mm H5 mm GP.6 E,, 5(96, 759.,, 8(978, 5. F.Orhttingr,L.dii Ts of Lc Trnsforms,Sringr-Vrg,(97 E.Orn righm,,(979 6

18 5W.rings,H.Wr,:Int.Nm.Mch.Eng., (979, 8. 6, 6, 66(997, 56. 7, 8, 75(98, 8. 8, 5, 5A(988,. 9, 56, 5A(99, 97., 59, 556A(99, 6. S InvLS(Gnm As Do, T As Do, n As Intgr, Y( As Do '****************************************************************** ' Gnm T ny( ' ' FFTDtArr ' cst( '****************************************************************** Dim As Intgr Dim r As Do Dim cst( As Do Dim FFTDtArr As omd ' RDim FFTDtArrn - ' RDim cst(n StInvLDtS Gnm, T, n, FFTDtArr ' r * PAI n ' For To n cst( os( * r Nt FFTInvS n, FFTDtArr, cst( ' r Gnm n '(t For To n - Y( FFTDtArr. * E(r * ' Nt Ers FFTDtArr, cst ' End S S StInvLDtS(Gnm As Do, T As Do, n As Intgr, FFTDtArr As omd '****************************************************************** 'GnmT n FFTDtArr '****************************************************************** Dim As omd, fv As omd Dim Hw As Do, Hw As Do Dim As Intgr, As Intgr. Gnm T For To n n - Hw.5 * (os( * PAI * n #.Y * * PAI T fv Lcfnction( FFTDtArr. n T * Hw * fv. FFTDtArr.Y n T * Hw * fv.y If <> And <> n Thn FFTDtArr. FFTDtArr. FFTDtArr.Y -FFTDtArr.Y End If Nt End S ' ' 7

19 FFT S FFTS(NW As Intgr, ( As omd, cst( As Do '*********************************************** '* (nw- FFT '* st(i(inw*i[inw]: '*********************************************** Dim n As Intgr, n As Intgr, n As Intgr, StgNo As Intgr Dim ttrfno As Intgr, GroNo As Intgr, Stg As Intgr Dim Gro As Intgr, ttrf As Intgr Dim i As Intgr, j As Intgr, j As Intgr, As Intgr Dim DtInd As Intgr, TInd As Intgr, iw As Intgr Dim wc As omd, Wt As omd n NW n n * : n n * StgNo Log(NW Log( ttrfno NW GroNo For Stg To StgNo ttrfno ttrfno DtInd For Gro To GroNo TInd For ttrf To ttrfno i DtInd ttrf j DtInd ttrf ttrfno GoS cttrf TInd TInd GroNo Nt DtInd DtInd * ttrfno Nt GroNo * GroNo Nt ' For i To NW j : i : j NW Do Whi > j j ( Mod * j j j Loo If j > i Thn wc (i: (i (j: (j wc End If Nt Eit S cttrf: If TInd < n Thn Wt. cst(tind Wt. -cst(n - TInd EsIf TInd < n Thn iw TInd - n Wt. -cst(n - iw Wt. -cst(iw EsIf TInd < n Thn iw TInd - n Wt. -cst(iw Wt. -cst(iw Es iw TInd - n Wt. cst(n - iw Wt. cst(iw End If wc oms((i, (j ' (i, (j (i omadd((i, (j ' (i, (j (j omm(wc, Wt Rtrn End S ' wc, Wt 8

20 FFT S FFTInvS(NW As Intgr, ( As omd, cst( As Do '*********************************************** '* (nw- FFT '* '* cst(i(inw*i[inw]: '*********************************************** Dim r As Do Dim wc As omd Dim As Intgr FFTS NW, (, cst( r # NW For To NW (. r * (. (. r * (. Nt For To NW wc ( ( (NW - (NW - wc Nt End S ' Fnction omadd( s omd, s omd s omd omadd... omadd... End Fnction ' Fnction oms( s omd, s omd s omd oms.. -. oms.. -. End Fnction ' Fnction omm( s omd, s omd s omd omm..*.. *. omm.. *.. *. End Fnction ' Fnction omdiv( s omd, s omd s omd On Error Rsm Nt ' dim r As Do ' r. *.. *. omdiv. (.*.. *. r omdiv. (. *. -. *. r End Fnction ' ( Pic Fnction ome( As omd As omd Dim r As Do r E(. ome. r * os(. ome. r * Sin(. End Fnction omd T omd s Do ' s Do ' End T Lcfnction( omd Fnction Lcfnction( As omd As omd Dim s Do. *.. *. Lcfnction.. Lcfnction. -. End Fnction 9

24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x

24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 24 I 1.1.. ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 1 (t), x 2 (t),, x n (t)) ( ) ( ), γ : (i) x 1 (t),

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