机械振动与噪声学赵玫课后答案15章.pdf

1 11 (a) (b) (c) 120.20 cm0.15 s 1382 Hz 50 g 1410 Hz4.57 m/s 15 Acos nt + Bcos ( nt + ) = Ccos (nt + ) 0/2 16 17x1= X1cos tx2= X2cos (+) t m 1 ) 26 27 28 2929 210LL 3 211211x 212mLOn L 2 12O 29 211 212 213213LEI 214214mO J0 215215 216216m1m2( m1= 2 m2) T 213 214 215 216 217217k1= k2= k3= km1= m2= mr1= r2= rJ1= J2= J 211 11 L L 11 11 EIEI 3 218218m1k m2L 217 218 31 3131ak1k2k3ab k3k4mbab m 3232 3333mO (a) (b) (c) 3434(a) (b) (c) 3535m1k m2hm1 32 33 34 35 36m = 10 kgs2/mk = 1000 kg/mx0= 0.01 m, x0= 000.21.0 3737m = 9 kg k = 7 kN/m= 0.15 xx 00 250mm,(a) (b) (c) (d) m 38 37 1 O (a) (a) k 3 = 0.01 m, = 0.01 m, 4 4F/k( F) 3939() 310310C 39 310 3113- 11k1= k2= kJ1= 2 J2= 2 J(a) (b) )0( 1 = 1 rad)0( 2 = 2 rad0)0()0( 21 3123- 10uu 313313uu 3143- 14J = mR 2/4 R = L/4 311 313 314 315Rayleigh Dunkerley 216 4141mkc y = A sin t 4242 4343F 0sin t 41 42 43 44k = 3 kN/m 1 s 11 11 3 313 13 Dunkerley 13 13 21616 k k t t 5 0.2F = 20 cos 3t (N) 45k = k0e i 2 46 Q 47 Q 48 Q 4949 v 410410m = 20 kgk = 3.5 kN/m c = 0.2 kN s /m60 rpm0.01 m x (t) 41141130 49 410 411 412t = 0F 0 Duhamel 412 413t = 0F 0 t0(413) tt0tt0tt0t0/ t0? 414414Duhamel t t1 415415 412 413 414 415 416t = 0f (t) = a t ( a = const ) 4 410 10 10 10 F 0 0 41212 F t1 4 41515 6 Duhamel 417412 418413 419419 420JJd 420 T sin t(a)(b)J d (c)Jd/ J1.2 421421 419 420 421 51 5 52m = 17 5 kgk = 70.0 N/cm c = 0.70 N s/cm(a) (b) (c) (d) 53m = 1 kg, k = 5 kN/m,5 25c 54m = 5 kgk = 10 kN/m 10.98 abc c(d) 55453.4 kg5.08 mm 0.2308 kg m(a) 1200 rpm (b) () 56551136 kg 5.08 mm 57113 kg20 Hz 15.24 cm/s2k = 2802 N/cm= 0.10 5858180 N900 rpm 0.01 m0.01 kg m (2) (a) (b) (c) 1200 rpm 59592500 kNk = 800 kN/m= 0.1 (a) (b) (b) = 1 kg, = 1 kg, k k = 5 kN/m m m = 5 kg= 5 kg a a = 70.0 N/cm= 70.0 N/cm (c) = 5 kN/m, , = 5 kg 1200 rpm 1200 rpm 1136 kg1136 kg 5.08 mm 7 (b)20 5101600 rpm 2200 rpm 85 5115110.5 Hz0.5 m 512600 rpm 500 kN400 rpm125 kNk2 (5- 12) 58 59 511 512 513232 rpm 232 rpm 2kg198 rpm 272 rpm 160320 rpm 61Lf = ( n + 1/2 )C / 2L,CEg /n = 012 62L 63J 64 65 50 50 300 mm 0.224 L1690 Hz 1530 kg / m 7120 1000 Hz0 dB 120 dB 722074 dB 73 74120 dB 110 dB 20 dB 752510100 320 rpm320 rpm = 012 2 0.224 0.224 1000 Hz1000 Hz 8 13610dB 76 20 415 6 10481. , 7740,70 dB70 dB 78nL jdB ,n 79 n dB, )101 (lg10 10 n L (dB) n = 0,LL 1dBn L 0 . 1dB n 710L 2 L 22 LLL, 1 LL )101 (lg10 10 1 2 L L (dB) 810.01m1000Hz 0.05m/s50m? 820.01 m 1000 Hz 1 m 74 dB 83 m W10- 3 e p 0.1 840.005 m f = 100 Hz 0.008 m/sl = 15 cm 85 3 m4710 zyx lll0.2 d R 60 T 86100 dB200 2 m , 2m , 87V T60 pe Wp V T e 10 42 60 ) ) 1010 2 m m WWm m 2 L 1000Hz1000Hz 1000 Hz 1000 Hz 10- 3 f 3 3 mm4 47 d d 9 88 T60 T60 L T T p 10 60 60 lg() 89 lll xyz 30 157 3 m 2 s 1 280dB 3400 S j =0.5m2, 4 53m10m 81050 m2 10251 1 m 60 dB 1 2 30.1m 91250Hz0.45 20 kg m/ 3 91p. 170 920.04 0.30.5 9320 cm 2000 2 kg/ m 100 Hz 1000 Hz 100Hz 941000Hz TL1 40 dB TL2 25 dB 10T L 950.4 mm 0.2 1000 Hz 7500 3 kg/ m 0.1m1m 0.04 20 cm20 cm 10 () 14 m07270 max .x , 2 max sm14287.x, t = 0.1 s 15 0 0 BAc A B tanarc 22 BAc )(0BA BAc )(BA ABc 18 (a) 3 i e2f) 4561i e10, h) 640i e5 22 0 2 3 2 3 l g m k 24 0)( 2 2 3 2 2 xaR R k xm 25 0) 2 (xkx M m, 26 cLLLmLmLm 2 3 2 433 2 22 2 11 )( 0)( 22 2 43 gLmkLL 27 x 0)/()( 2 22 222 21 2 11 2 2 xrkbarkxrmrmI 210 )4(243 3 LIE 211 2 2 22 1e cosbkakk 212 mm n n )1 ( 1 3 1 e 2 214 0 0 )(0 0 21 2 1 11 0 x kkRkR kRk x J m 215 2 1 11 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 216 0 0 21 12 10 02 2 1 2 2 1 x x Lm T x x 217 12 0 0 2 2 0 0 2 1 22 22 2 1 2 1 rkrk rkrk J J 218 0 0 0 02 2 2 22 221 x glm kx lmlm lmmm x x 0 0 0 0 2 x 1 4 43 3 x x x k kk k 1 1x 11 31 ) 11 4 1 4 1 ( 4 2 1 4321 n kkkk m f 33 0 33 2 2 ml ka m c , 2 2 n 3 2 1 lm ak f km l a C3 3 2 c 35 t mm k k gm t mm k kmm hgm tx 21 2 21 21 2 cossin )( 2 )( 37 mm5674. , s/mm5644 max .x , s/mm8210., mm461.x 39 2 12 m k 81. 0 1 m k 62. 2 2 46. 0086. 1 11 u 310 m k 8 9723 2 1 , m k 8 9723 2 2 LL u 42.842.1 11 311 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 11 312 LmLm mm u 908. 6 424. 8 168. 1 424. 1 908. 6 1 168. 1 1 x L L xuy 101. 0146. 0 101. 0855. 0 1 313 11 11 u , 11 11 2 1 m u , )( )( 21 2 1 21 2 1 2 1 xx xx y y 315 Lm T 3 2 2 R , ) 14 9 2 R Lm T , Lm T 2 2 1 )(Dunkerley 2 1 2 1 2 R 2 R 22 1 11 1 u t t 1 1 cos coscos207 Lm L L L 101101. 0 0146 101101. . 0 0 1 1 1 12 41 222 )()(cmk cA X , 2 1 tan 2 mk c 42 ts a kA a mgL kc a mL co)( 22 2 , 222 2 )2()1 ( )(cos )( t mgLka aAk n , L g mL ka 2 2 n )(2 2 2 mgLkamL ca , 2 1 2 arctan 45 t Fxkxm i 0 2i ee, 222 )(i 0 )1 (2cos e )( k F tx t 2 1 arctan , mk2cos 49 W kgL v 2 410 00 22 1)2()1( )(sin 1 24 ii ii i t i aa x 2 i 1 2 arctan i i k mi i 2 2 n 2 m c 411 30singmxkxm )cos1( 2 sin)( nn n t k gm t sg tx ) 4 (arctan2 1 gm sk k m t 412 ktFx)/cos1 ( n0 mk n 417 ktFx)/cos1 ( n0 mk n 419 TJk Tk kJk t )(2)(2 sin 2222 2 1 2 2 ) ) i i k k m m 2 2 n n 2 m c coscos1 1( ( 2 k ) 4 4s sk k 13 421 t F Z x x i01 2 1 e 0 Re )i(i