机械振动与噪声学答案

1、 cLLLmLmLm 2 3 2 433 2 22 2 11 )(0)( 22 2 43 gLmkLL 1113 1212 2221 rmgmf r b a k b a f rkf 1121122 grmrk b a k 2222113 rrmJrffrf 0 2 21 2 2 22 2 2 2 11 rk b a rkmrrmJ f2f1 f3 2 1cos k 22 2 a kb2 2 22 1e cosbkakk 22 3 232 11 ()() 33 11 (1)() 33 mm JLnLLnLnLnL LL JmnLmnL 2222 1 3 JmLmnLmn L 3 23 1 ( 1

2、) 3 JmLnn or e 2 11 (1) 3 mm nn 2222 22222 2222 2222 1 3 111 222 1 3 ee e JmLmnLmn L nLx Jm xm n L mLmnLmn L J m n Ln L f1 f2 12 fk R 21 fk xR 12 fk R 21 k R Rk xRRJ 21 fk xR 2 121 0Jk Rxkk R 21 fk xR 1 k xRmx 11 0mxk xk R 0 0 )(0 0 21 2 1 11 0 x kkRkR kRk x J m 11 0mxk xk R 2 121 0Jk Rxkk R 2 1 11

3、11 2 1 2 1 0 0 x x cc cc x x m m 0 0 2 1 433 3321 x x kkk kkkk 0 0 21 12 10 02 2 1 2 2 1 x x Lm T x x 21 12 T L 11 2 22 21200 120103 xx m L xx T 21 123 L T 0 0 0 0 2 1 2 32 2 2 2 2 2 21 2 1 2 1 rkkrk rkrkk J J 1 2 , , k r 2 J 1 ,-1 1 , , 3 k r 2 J 1 , 1 1 0 0 0 0 2 1 2 32 2 2 2 2 2 21 2 1 2 1 rkkrk

4、rkrkk J J 1 2 , , k r 2 J 1 , 1 1 , , 3 k r 2 J 1 ,-1 1 ) 11 4 1 4 1 ( 4 2 1 4321 n kkkk m f 详细推导详细推导 1 1 2 2 12 3 3 4 4 1 4 1 4 1 22 1 2 x k x k xx x k x k 1 1 2 2 12 3 3 4 4 1 4 1 4 1 22 1 2 x k x k xx x k x k 1234 1111 161644 e x kkkk t mm k k gm t mm k kmm hgm tx 21 2 21 21 2 cossin )( 2 )( tctc

5、tx n2n1 sincos)( n02 /xc 01 xc 0.15 99.8 1.89 mm 7000 f F Nmg kkk xx 00 250mm, mm5674. . xx 00 250mm, 0 0nn n 0 () cossin 0 xx xxtt x 0 0nnnn n 0 ()sincos 0 xx xxtt x 0 22 0nnnn n 0 0nn n 0 ()cossin 0 00()cossin xx xxtt x x xxxtt xx 00 250mm, max0n 7000 ()250.189 9 xx s/mm5644 max . . x 0 0nnnn n 0

6、()sincos 0 xx xxtt x 4210.8 mm/s n mm461. .x xx 00 250mm, mm5674. . 0n () cosxxt 0nn ()sinxxt n 0,xt 0 ()xx xx 00 250mm, )0( 1 )0( 2 0)0()0( 21 J k 2 22 2 1 J k 2 22 2 2 22 11 u t t 2 1 2 1 cos207. 0 cos207. 1 22 11 11 11 u 11 11 2 1 m u )( )( 21 2 1 21 2 1 2 1 xx xx y y := M m0 0m := K 2 k k k 2 k

7、k m 3. k m := 1 := -1 0 xxMH EI L EI L EI L EI L H 2 23 2 23 4 0 0 2 mR m M 1.702053777 EI L3m 16.28198431 EI L3m := K 12 EI L3 6 EI L2 6 EI L2 4 EI L 详细推导详细推导 0 0 21 12 10 02 2 1 2 1 x x mL T x x , 3 2 3 2 T L m 3 2 3 2 T L m 2 1 2.366025404 T m L 0.6339745960 T m L Rayleigh := X1, 1 1 2 T 3 m L 9

8、T 14 m L Rayleigh := X1, 1 1 2 T 3 m L 9 T 14 m L 4 m L 3 T m L 3 T 2 m L 3 T 2 m L 3 T Dunkerly T 2 m L 0.6339745960T m L Rayleigh 2 T 3 m L 9 T 14 m L Dunkerly T 2 m L 1.051566847 1 1 R 1 2 R 1 D 1.014010888 0.7886751350 0kxyxcxm 2 1 tan 2 mk c 222 )()( cmk cA X tAckxxcxmcos x ts a kA a mgL kc a m

9、L co)( 22 2 0 cos () F t k n L g mL ka 2 2 n )(2 2 2 mgLkamL ca 2 1 2 arctan 2 222 cos () () (1)(2) k A at kamgL i2 0 eei tmxkxF i() 0 ( )e t x tX 2i2i 000 eemXkXF 2i 00 cos 2sin 2ekmikXF 0 0 22 2 cos 2sin 2 F X kmk 2 sin 2 arctan cos 2 k km t L v kYkxx g W2 sin 0 W xk xy g 2 sin v yYt L 0 n n ( )si

10、nsin F x ttt k W kgL v 2 k g L 2 4 2 v 2 W0 ( )x t 2 sin kg t W k Yg L vW k g L 2 4 2 v 2 W k Y g L 2 sin 2 v t L k g L 2 4 2 v 2 W t L v kYkxx g W2 sin W kgL v 2 ktFx)/cos1 ( n0 mk n plot(subs(F0=1,m=1,omegan=2,X1),t=0.20) 1 m n d ( ) F ()sin n()t t t m F tx 0 n n 0 dsin t k Ft t k F n 0 n 0 cos1 0

11、 cos 0 0 n 0 n sind t F x tt m 0 00 nn0n coscoscos 0 tFF tttt kk 2 F 0 sin 1 2 n t0 k F0t0()sin nt m n k tF n 00 2 1211222 2 2223223 i()i ii() kkmcckc Z kckkmcc 12212211110 2232232222 0cos 00 ccckkkmxxxFt ccckkkmxxx 10 2 cos Re 0 xFt H x 1 2 11211222 2 2223223 i()i ii() kkmcckc HZ kckkmcc k2k32m2 c

12、2 I c 3 Ik2 c 3 I3c1m2I c 1 k2I c 2 k3Ik1 c 3 I()( 3m1c2I3c2m2I2c1c22c1c33m1c3I c 1 k3I2c2c3k12m2k1k2 k1k3k2k3k1 c 2 Ik22m22m1k22m1k34m1m2) 1,1H 121212 ,mmmccckkk 1110 222 022cos 0220 xxxmcckkFt xxxmcckk 10 2 cos Re 0 xFt H x 0.1 2 c cc cmk 22 d 1119.9 rad/s n k m 2 2 0.628 1 n2 d 2 2 1 1 ee1.88 n n

13、 x x 02020. . 0032150. . rad/s7244 d . . Ns/m441. .c 3 9.81 43.94/ 5.08 10 n g rad s 1200 /30 2.86,0 43.94 2 sinMxkxmet 该系统振动微分方程为该系统振动微分方程为 2 2 22 0.23082.86 0.579() 453.4 1 2.86 1 me Xmm M 223 453.4 43.940.579 10507N Tn FkXMX 2 2 2 2 0 12 12 T F S F 或或 2 1 1 2 2 0 22 1121200 0.2308507N 11 2.8660 T

14、 FSFme 2 2 22 0.23082.86 0.579() 453.4 1 2.86 1 me Xmm M (a) n 23.9 rpm 2 n 2 2 2 2 12 12 0.2 S (b) n = 43.45 rpm 2 1 0.15 1 S 2.77 1600 2 60.51/ 2.7760 2.77 n rad s 22 981 2.667() 60.51 st n g mm 11221 2222 0sin 00 xkkkxMt xkkxm 2 1 122 2 2 22 sin 0 xtkkMk xkkm 2 22 2 212 1 22 122 2 2 222 1222 sin 0() () () sin () () kmk tkkkM X kkMkm kmt kkMkmk 22A