MechElem - Equivm’mi mama-.1,- r “Ti-HI M H Equiuafent...

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Unformatted text preview: Equivm’mi mama-.1,- r “Ti-HI M H Equiuafent aprings i—EZZZZZZZE—* 4*£:::::::3“* Mass I: M] attached at end of spring of mass m Cantilever beam ef maaa m carrying an end mass M Simpiyr supported beam of mass m eaiTying a mass M at the middle Ceupled translational and _ rotatiena] masaea Masses en a hinged bar Red under axial load {J a- length, A = erase sectieaal area] Tapered rod under axial load (D, a' 21* end diameters} Helical spring under axial lead {if r: wire diameter, D = mean eeil diameter, a = number of aetive turns) Fixed-fixed beam with lead at the middie Cantilever beam with end lead qufiM+tih mw-M+flflm 55mphr supporiad beam with load 435? m the middIe km a I] Erin inscn' _l__i Ll. 1 P gs ES kw Ii{I + k! I 4—K springs in parallel x kc? = $1 + k2 + H. +k" mallow ahal't under Iorsifln at? 4 i [I -=r length, I) u uulflr dimeter. k"? = 32!“) _ d ) {J - inner diametcr} Relative marina bctween parallt] surfaces fr .. fl _. - [ A '=' area. 0f smaller Flatt) q a L R If!” llushpgt {axial Inc-Lion ol'a c = hall“ 2:: pmlm: m a cyhndcr] w I“ 45!: + r“ W” ? E h ansionaldampcr c” =- W h} + E‘Ef‘ x'L fl = ‘5' 5 f m fix ~ a. , 2‘? fl )1}? 1-: 1N : 15‘5 J inN t “Fl-5" 1, F “+- “"54"; Tar; : €5.63? : liq-{5 5 €5- 3“ E33; 1 Ca“ Dry Friction {Coulflmb damping) . 4p? 4: m -= friction farce, {"9 = WX *1 - Ircqmncy, X : amplitudc nf vibration} ME 3534' - Dynamic fisxem, thrwmm Mass and Stiffness Equivalents This handqu gives the mass audio: stiffiless equivalenees for many eummnnly encountered mechanical systems. These equivalences are sufficient ONLY for the apprflxlmflfifln ef the behavior of the system in the first mede ur for the apprmdmatien of the first natural frequency of the system. - ACTUAL SYSTEM Eeuwseeuce euusnen M Eeuw = MSPHIHG 33 + M em Keeuw=fx1KsHIKr+Kfl Keener = K1 '1" K2 Heme = {3 El } f L3 Mgguw : - MR} Mam + MENU Wham Me = Mess-’{MBHM‘FMEMJ} Kgfluw = l: El} J'r L3 Mguuw '-—' Maw KEeuw :14?! El } f L3 ' MEflUIV = 0.550 Mam, “rue mum = I 3113‘} 1" i 32 L} Jeeuw = “3 in=fgg+MLE R. E. MitcrlinEJr ~ 1991;! 9. Stiffness of common elements: F a Kx T - K3 8 1c - 3—E% E ~ 30 x 106 3? (steel) L in 6 ~ 11 x 106 Eli (steel) in 481312 1 3 _ I K L3 I a 17 bh B3 k ‘ _ bu I a IT!)4 __ 3r 1- . -u D J K _ 12E: L K ‘ 192E: L K _ llgEI L T,B Ka-g—G- ; J-g-g—for circular cross section 10. Equivalent Haas: 1., . .1132. ,4. eq M1 + N2 K “2. _ J1‘12 K9 eq J1 + J2 / 3', J a h 2. was.” ad“ qt. 1.58“ if; 039305 a g:- I]; 2035 it. to tag a; and 3-5 a. .o 5 ND 0 000.5 :d .85 and aim—5? as .332 8.” .333 Illllllllalllllllullll m. . exam d .33.... .— 0. up; .3... 259: a 5580 96 96 IlllllllllnllltlllllllllllrllllllljllJllllllllllll wmmfiu no EEO...“ 932553.!» E V 3.56. . on. Hui-ah 3. R has: 2.:— §~ IA «:30 S. a... in: 9H: 3.1 .3: 82 1..." 55 q «wand 8%. «Eu _ 33 .2 if}; a; .2 x 2.: 553a 31.50» 3334;. 7.: K Fan; Ta. x and T2 x and To. x pm”— .13 x an." n mil—twp; n0 aw—htmlg g .o. 9 TE 33313033. :2 3 .2 53......“ T2 x mm." Egan-a? Ta. x a: .5800 TS x o.— .323 E . a . a E 33.5....- wgfifiwr guflfl HIE mfih n13 mi? mdn Dd" ud— Q: :4... 3— .: 9... um— .....um Han t... E." and... 2—. «an «an 2." on. as 9.3 3' 2.5 S. 1.. l nun 9.... an“ a. was 2.3 S .l. I. 1. 3w 2n «.3 on.“— 3 if “Ex. . 2 T3 a r583 B385. 2. 3 on a... on on 2 o. m. 335.. la gag .=D no autumn—OE g 3..“ 5a 33 83. :.=. S. 3.. a.“ “3.. .3.” =3 8. a." wfin x”... on: 2km 3— 9: 8H t: "a... as a 3.” 3“ «a... 23 3.2 8 z: "3 :H. a? :3 9. a: an an. :3 E... o .2 2d 22 8...“ ST 9? a «S 5.. 23 n2? 8? IIIIIIIirIIIIIIIIIIIIIIIIIIIII _ "EFZTE "5:3.-2 .5??2 33.-.: u. m. ltlltlltlllllllllr minnow—>253 at; 3.35 c283; E 35 §.. OS on 3 a l I has :6 :33 I I I SE in in: 2 l. I. :66 w“ a... : on «no a. 3.85 . 2 E t «3 a. 335.. £90 a 2 3 32. 2 3.- 535.2 a an 2 and 3 is 3 Q. 92 2 a an 3... 5g? a 3 2 26 Iowa?“ on... .35.... as .: a 3. _ in an .3 3.. 33:3 as..." a: 2 a: J 8: 3.. . 8a 3 H. R . 3 n on and 3.. is .33m 3 2 a and a.“ Eu Eu .lllllllzillllllimlllliltrlllillllrl 1.2 5:53.30 w 33 and «:3 8n." 2.: a. and 2.. 38... 2.2 an... a. mad . u; Had an." .2.» 8. n2 3.. 88.9 a: 5.9.. 3 :2 on" "$3 83.. 32 S . 3d . an 83 23” :6 3 3a 2.“ $3 «$5 a H «3.212 tarsal“: .5: 3.37.: o. a. 15533 «EBB: flag 55:83:51? 3553 :6 50 $0 9.4 war; to... «455. «Eu—Kn . Ewan 1.2 1.2 1.2 a; mat—cups... gag-02m LO rho-3E F... . z . 5.2.x: k 32.539200 gum-E. 3W5?“ 0.14.25 to 263mb 024 warn-(.21 Ooh . Etfi. Ha. .‘We‘mamhn— . a 3.63 yo no? _ .2 ova—Ewan: ...
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This note was uploaded on 01/23/2012 for the course ME 3514 taught by Professor J.renno during the Summer '08 term at Virginia Tech.

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MechElem - Equivm’mi mama-.1,- r “Ti-HI M H Equiuafent...

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