BMM3553 Mechanical Vibrations

Transcription

1 BMM3553 Mhaial Vibraio Chapr 3: Damp Vibraio of Sigl Dgr of From Sym (Par ) by Ch Ku Ey Nizwa Bi Ch Ku Hui Fauly of Mhaial Egirig mail: y@ump.u.my

2 Chapr Dripio Ep Ouom Su will b abl o: Drmi h aural frquy for amp fr vibraio Solv h problm rla o amp fr vibraio Rfr Sigiru S. Rao. Mhaial Vibraio. 5 h E Abul Ghaffar Abul Rahma. BMM3553 Mhaial Vibraio No. UMP. M Muafizur Rahma. BMM3553 Mhaial Vibraio Lur No. UMP

3 SDOF Damp Fr Vibraio Giv a iiial oiio, rmi h rulig moio. Iiial oiio: : Iiial poiio ሶ Iiial vloiy

4 Viou Dampig Elm (Dahpo) Dampig for i liar a proporioal o vloiy For, F Δሶ F F F ΔF ሶ Vloiy, ሶ i h viou ampig offii Ui: N-/m

5 Maiai Dyami Equival Fr Boy Diagram A r, X = (Sai quival) mg = k

6 Maiai Dyami Equival Apply Nwo Law F m mg F X m k k m Equaio of Moio: m k

7 Equaio of Moio: m k orr iffrial quaio Homogou Liar Coa offii Form of oluio: Ai or A

8 Equaio of Moio: m k Aum, A h A a A ma A ka m k A for a o - rivial oluio m k

9 Equaio of Moio: m k m k 4mk, m m A A if a ar o qual

10 Thu h gral oluio i: ( ) A A A m m k m A m m k m whr A a A ar arbirary oa o b rmi from h iiial oiio of h ym.

11 Dampig Paramr Criial Dampig Coa a Dampig Raio: m m k m k m km Th ampig raio, ζ i fi a: m /

12 Damp Soluio Dfi: C k m Naural Dampig, Frquy Raio

13 Thu h gral oluio i: ( ) A A Aumig ha ζ, oir h followig 3 a: Ca. Uramp ym ( or or / m k / m) For hi oiio, (ζ -) i gaiv a h roo ar: i i

14 whr (C,D) a (A,Φ) ar arbirary oa o b rmi from iiial oiio. A D C A A A A i i i i i i o ) ( a h oluio a b wri i iffr form: Frquy, Damp D C i o ) (

15 For h iiial oiio a = C a D a h h oluio bom ( ) o i Thi quaio rib a amp harmoi moio. I ampliu ra poially wih im. Damp Frquy,

16 Th frquy of amp vibraio i: Frquy, Damp A i o ) ( Imag our: hp://ommo.wikimia.org/wiki/fil:uramp_oillaio_.pg

17 Ca : < Ur amp (plo of () v. im) C o Di

18 Ca : = Criially amp (Ral qual roo), A A A A or A a A ar oa o b fou from iiial oiio

19 Ca. Criially amp ym ( or or / m k / m) h wo roo ar: Du o rpa roo, A m ( ) ( A A ) Appliaio of iiial oiio giv: a Thu h oluio bom: A ( )

20 Ca : = Criially amp (Ral qual roo) A A

21 Th roo ar ral A A ) ( A A For h iiial oiio a =, Ca3. Ovramp ym ) / or or ( m k m /

22 Damp Vibraio Rpo I a b ha h moio i aprioi (i.., oprioi). Si, h moio will vually imiih o zro. a Compario of moio wih iffr yp of ampig

23 Fr Vibraio wih Viou Dampig X X ) o( ) o( m l Logarihmi Drm: Th logarihmi rm a b obai

24 Logarihmi Drm Logarihmi rm : h ra of rm for fr amp vibraio ampliu. I i fi a h raio of ay wo uiv ampliu.

25 For mall ampig, H, or if (.86) (.87) (.88) Thu, m l m (.9) whr m i a igr.

26 Logarihmi Drm l

27 Logarihmi Drm

28 Logarihmi Drm

29 Problm.98 (S.S. Rao 5 h E) Th raio of uiv ampliu of a viouly amp igl-gr-of-from ym i fou o b 8:. Drmi h raio of uiv ampliu if h amou of ampig i (a) oubl (b) halv Eri

30 oluio l 8 l (a) If ampig i oubl l w.8358 w w (a) If ampig i halv l.9 w.9 w 3.896

31 Eri Problm.3 (S.S. Rao 5 h E) For a prig-ma-ampr ym, m = 5 kg a k=5n/m. Fi h followig: Criial ampig oa C Damp aural frquy wh = C/ Logarihmi rm.

32 Soluio m 5 kg, k 5 N/m C k m m km 5 5 m N -/m C / / 5 N -/m k m C ra/ m

33 ) ( ) ( i o ) ( For Ca For Ca For Ca REVIEW

34 Eri Problm.4 (S.S. Rao 5 h E.) A railroa ar of ma kg ravllig a a vloiy v=m/ i opp a h of h rak by a prig ampr ym a how i h figur. If h iff of h prig i k=4n/mm a h ampig oa i = 5 N-/mm, rmi (a) h maimum iplam of h ar afr gagig h prig a ampr a (b) h im ak o rah h maimum iplam.

35 Soluio m kg, v m/, k 4 N/mm 5 N-/mm 5N -/m m k ra/ 4 N/m C C N -/m m (Ur amp) ra/

36 ( ) For, a m/ o i ( ) i A ma, a i - ma.8387 m

37 Thak You Ch Ku Ey Nizwa Bi Ch Ku Hui Fauly of Mhaial Egirig Uivrii Malayia Pahag Tl: Fou Group Wbi: