Complete course materials for Mechanical Systems Dynamics in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: TRASIWERSTO AMBITI DARI STReC Tae DS TRINE rd . = TCH KU © 7 is f [aM Nor ne ne Bo DOUNDARY Wd. PI È YL S CyNYiT IGN — FP i | | RAMSUENSE Hp (alx; e)v TASPLATNGAT QE IHS serva) , \ ii IX | AT PIMS [tl 4) suear AND ML NCGLETED 2) tomo GENIUS MATERIAL ANO CONSTANT CROSS =~ ICOCTIO
Complete course materials for Mechanical Systems Dynamics in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: TRASIWERSTO AMBITI DARI STReC Tae DS TRINE rd . = TCH KU © 7 is f [aM Nor ne ne Bo DOUNDARY Wd. PI È YL S CyNYiT IGN — FP i | | RAMSUENSE Hp (alx; e)v TASPLATNGAT QE IHS serva) , \ ii IX | AT PIMS [tl 4) suear AND ML NCGLETED 2) tomo GENIUS MATERIAL ANO CONSTANT CROSS =~ ICOCTIO
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0 l A = 0 linear algebraic homogeneous system sin(yL) cos(yL) 0 of 2 equations in the 2 unknowns A and B det)=o la wii > sim@be6 LL GET Wyrattc = | COUMABLE INFINITY Lwa=de=ur|t AJ=T,2... JORTURAL, FREQUIANCY IL ; L(t ex j j b, Di -siu( >) FA IL CACHI ONG LS) Al SEJFIE MOVE sharexnro) TH W oh. - a = ik KW u TAI = he 1-2 ARTETA ITH A": 2, = wavelength z: LL sama Hel He! | WAR Mu DES PCK Ek = MORA x) [Ca sim(wut)+Gu Cod. 4) ‘ WE) Se Wax) CSEMPIO Ls wl X, = sal LL sima. x) set PE (ZĘ > ee WICK) = or x sind)
NS (Ari URAL uopes) © BOUNDATII GONOPITIGN* 1) u(0,4)=0 > ©(0)=0 > B=0 2) u(L,t)=0 > ©D(L)=0 > Asin(yL) + B cos(7L) = 0 0 1 A _ 0 this is a linear algebraic homogeneous system sin(yL) cos(yL) 0 of 2 equations in the 2 unknowns A and B deo Enia sE ulu: Se = = L- US ETRE ldotwrAtce| SO } => fir Eri S NATO TURĄC ENEQ, p Eta bs |P "fu È n ae simnGt9 comestevp Ay CiGAJFWET(CA (More SUArE) EG! ape MOTUIALISATTO NI Ag= fl 1 LS MAX AT ANTI NODO? of PLC SMAK AT WODE oF # -(x) Ex + BOTH MODUATED WITH TIME By HARMOVIC Function GE Wa
AJ i 5 No external loads, except for ów trated (constraint mdx - concentrated (constraint or T(x,0) ot active) forces/moments at the boundary, are supposed to OM . M(x,1) M(x,t)+§ dx act on the beam Ox In any case, boundary conditions are not specified L_| 8T , de TO Sani NOSEOrTEO @erorce BALANCE Ca. TO RotATION me: OM __ Ów E) © TP ae op O. LN NEC CAL VIZELNON | BENDIUY VIBRATION QUVATTOIN E DO Db => (EL LION POP) —— > SAME CONT TODA 97 Sas PDG STANDINĄ WAVE 5" U w(x,t) =[Asin(7x) + B cos(7x)+ C sinh(7x) + D cosh(7x)]:cos(ot + vy) 17? BEAMS UNDVAMPED VIBRATIONS LP INDIPeENDeN FROM BC. > BOTH Free AnD Fotce RESPONITE 4 cz
—> de4B))=25sim(f)simb (er) =o with Sto LO =>sinh(fL)*Fo =a Mose ee eh or L = _ 9 |EJ (it ° [EJ COUNT ARIE DS =, m (LIN m NATURA. FASE Ls Oi THAT of FOUND IW 3) G) =) FO CIGGN RUMAIJUS Fn _ _ | it b, (x) = sin(y,x) = sin ra Vitt B=ECEDSO A At Bi TRARY e MODE SHANE DI WLAN | COMES Tan nA Cin A 2L a) A, == À; = wavelength YU INCRE ASES KTH THE SOULE MEE O ——> GUADORA TIE-SGGUENCE Pa ACH .-SAME|cCUNdEPI oF |BEFOEE | PPTI TP | Jade MODE TAKES PATUT| TO THE Free ViBRATION w(x, t) = x w (x,1)= Ysin (= „| -[C,, sin(@,t) + C,, cos(@t)] i=l AND You COMVUTE C41 © Cod KIK IN Cond.
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