第2章 摩 擦 振 動 - Oita University

1 16 2 1 1 1 (Frictional vibration) 2 4 (1) (1) (Viscous damping) (2) (Dry friction) (3) (Coulomb friction) (4) (Traction) (1) 17 (Dry friction) (1) (1) (Directional character) (2) (3) 1 (4)

2 (5) (6) (7) (6) 1 v m k x vxkm()VfxvV =0v()Vf ()fV vVvx= ()fV vxk m 18 Vvx= ()fV xv<< (0)V> 1 ()mx kxf v x+= ( ) ()()()fvx fv fvx = v ()/xfv k = ()0mfv k ++= ( ) v () 0fv < ( ) ()fv (2,2) ()fv k c ()fvx ()av x b= + a, b ()/xbavk = ( ) ()0mcak + + = ( ) ca< (c) (a) b 0 Vvx= = c (7)

3 V m k x 1 vx ()fvx dm dc dk dx Mx + Cx + Kx =0 ( ) 0'(),,,0ddd dddddddxmfvcckkkxmcckk+ + == == xMCK dfd / fn v k mdcd kd xd x m 19x dx ,,MCK '( )dfvc+ dc '( )0dfv c+> ( ) ( ) 1 = yAy ( ) 11[, , , ],Tddxx xx == IyAMK MC 0 0 2 2 I 2 2 T ( ) A 1 2 (Hz) ()fv dc d '( )2fvmk = 2ddddcmk = ( ) = //2nfkm = 1kHz= == df //2ddkm = d /dnff d (1)

4 (2) (0d =) (3) (a) (Wine glass) (a) (b) (Video2-1) 20 (Top view) (b) (1) (2) (b) 45D 4 2 2 (3)

5 2 21 ( )/( ) 2 Tea Time 3 3 2, 3, 4 Tea Time 100m 30 (Violin)

6 22 (Video2-2) Video2-3 2 mm (Stick-slip) 2 0 (2,0) (Chladni s figures) 2, 3, 4 0 2 (2) 2 (0rr=) (Nrr R==) 23 N 1(,R ) 2(,R ) 2 1P 2P 1P 2P Mindlin j j (3) 322112jjjjjjjrrrrrhMMMMQ rrrt ++ = ( ) 3222112jjjjjjrrhMMMQ rrrt ++ = ( ) 21221(,)(, )jjjjrrjQQQwP PhRRrrrt rr ++= ( )

7 221,211,,(1)1 21 2jjjjjjjjrrrrrjjjjjjjjj jj jrrrjrjjMMDrrDrrMwwGGQhQhDrrrr =+ += + + = + = + = + ( ) ,r ,,jjjrrMMM ,jjrQQ jw ,jjr (a) jh t E (G) 32/12(1)jjDEh = () Dirac (, )R ()( )rR = ( ) a 30 mm 30N i(1,2)= iV ()iifv 12VV= m/s,= ()iifv iv (3123()ii iiiiifveveve= +) 331150 s /m ,ie= ,ie= = (Internal resonance) Mindlin m, s (m, s) (1,0) (0,0)(2,0)(3,0)(4,0) (0,1) (1,1) (2,1) 327 407 633 1 5602 7332 892 3 175 4 266 (Hz) 355 429 643 1 5492 8612 892 3 302 4 361 24 2 (5) 30N (1,0) (2,0) (3,0)

8 5 2 2 NPP== 0 =D msa msb 2 090 DD 0 =D 1 12PP= 2 S AS msa msb S 0,0msmsab = AS 0,0msmsab= 0,0msmsab S AS #1 #1 1 ( ) #1 #1 (1,0) (2,0) S AS (3,0) (0,0) (4,0) (1,0), (2,0), (3,0) 25 2 (2,0) (1,0) S 45 =D (1,0) S AS (2,0) AS 90 =D (1,0) AS (2,0) S b (Circular plate) 2 (Point 1, 2) 2 (Friction rod) 3 (Spring) (Load adjuster)

9 SK4 20mm 400mm S45C m/sVV== #800 12,VV (1) NPP== (a) =D (b) =D (2,0) A, C (b) (a) S (b) AS NPP== =D (1,0) S (2) (2,0) S AS NPP== (a) NPP== (b) 0 =D S 45 =D AS = 30D S AS (a) (b) S AS D S D AS =D S AS 26 50 100 (2,0) S AS 12PP= (2,0) (Video2-4, Video2-5) OHP BB 2 (6)(7)(8) 27 (12) (9) (10)(Shooting m)