机械振动与噪声学部分答案(3)

3－1

fn1?2π4m(1111???)4k14k2k3k42

1???3c???3ka??0, 3－3 ?fn?2mml2π3kaml2

2 C?2ac3l3mk

3－5

x(t)?m22gh(m1?m2)ksinm2gkk t?costm1?m2km1?m2max3－7 4??7.56mm , x??644.5mm/s ,

210.8mm/s, x?1.46mm

3－9 设质量为m和2m的集中质量上下位移x1和x2为广义坐标，向上为正。系统静平衡时位

移为零。

?1?0.81k，?2?2.62k

mm?u????3－10 ? 3－11?212111?? 1.086?0.46??23?97k , 223?97k

?2?8m8m???1L1?

8.42?L??22??u????1.42?2?2k,

?2J?2?2k, 1??1?u????2J?2?2?,

??1??????2???3－12

?u???????

0.855?0.101L??x??y???u??1?x????0.1460.101L????

???? 3－13 ?u???11?,

?u???1?1???1??1?2?2???11.168m1.4241.168mL?1.207cos?1t? ???0.207cos?t2??1?6.908m??8.424??6.908mL??11?,??2m?1?1?11 ?y1??x2)??2(x1? ?

????1??y2???2(x1?x2)?? 3－15 ?2?2T, ??2?9T), ?2?T

R1R3mL2mL14mL ?2R???R2??21??21(Dunkerley)

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4－1 X?cA?(k?m?2)2?(c?)2, ???π?tan?12c?k?m?2

2???c???(k?mgL)??kAcos?t, 4－2 mL?aa2a2kAacos(?t??) ??

(ka2?mgL)(1??2)2?(2??)2 ???,?n??n ??a2ca2kmL2?g L1????ke4－5 m?x x(t)?2Lm(ka2?mgL)i2?i?t, ??arctan2??

2,

x?F0eF0ei(?t??)kcos2?(1??2)2??2?, ????kcos2?m? ??arctan21??2πkg

W4－9 v?L4－10 设质量m的位移x为广义坐标。当x0＝0且系统静平衡时质量m的位置x为零，方向向上为正。

aax??42?1?i?1i?sin(?it??i)(1??i)2?(2??i)2

?i?arctan2??i1??i2?i?2i??mc??2m?2k

n4－11设质量m沿斜面运动的位移为广义坐标x，质量m与弹簧接触时广义位移为零，向下为

正。

??kx?mgsin30? x方程：m?x(t)?t1?2gs?nsin?nt?mg(1?cos?2knt)

?4ksm?arctan(?)???? k?mg?4－12 x?F0(1?cos?nt)/k ?n?km

4－17 x?F0(1?cos?nt)/k ?n?km 4－19 ?1? ?????2?kT?sin?t?2(k?J?2)2?k2?2(k?J?2? ?)T?12

?x1??1?F0?i?t? 4－21 ??????ReZ????e??x0???2???2???k2?ic2? Z??k1?k2?m1??i(c1?c2)?? 2?k2?ic2?k2?k3?m2??i(c2?c3)?????5－2 ??0.1, ?d?19.9rad/s, ??0.63,

xnxn?1?1.88

5－4??0.0202,??0.003215, ?d?44.72rad/s c?1.44Ns/m

5－5 0.58mm, FT?506.4N

5－7 3.166 cm/s

5－9 (a) n < 20.7 rpm；(b) n = 37.6 rpm 5－10 2 . 68 mm

5－12 k2?5?107N/m

?1?35.79rad/s;?2?73.51rad/s

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