Exercises of the course

Pagina 1

Structural dynamics and aeroelasticity exercises • coshx = e× +e- × 2 - - ◦ coshx= 0 ✗ = j T tKIT 2 - _ • ALTERNATIVE FORM: costi✗= COSIj✗)= COSI- jx) costi(Ix)= cosi • Sinhx = e× - e- × 2 - - • sinhx= 0 ✗ = j o +KIT - _ • ALTERNATIVE FORM: sinhx= - jsin /jx)= jsin /- jx) sinhljx)= jsin✗ COSZX= 2<052×-1 cos>✗ = 1 +COSZX 2 • COSZX = COSI- SiriX COSZX = 1 - 251 IX sirt× = 1 - COSZX 2 Slkx)= 1 SI×) K • Dirac ' SDELTA PROPERTIES: 00 fltlsltldt= [7101Sitidi= f-'01 /IoSltldt = fioit. 1 + be- P" + <ejpx• FREE vibrations : f/×)= al × + de' P" = asinhpsx+bcoshpx+ csinpxtdcospx SHAPE FUNCTION S SELECTION TORSION KINEMATIC Bc: ⊖/0)= 0 • 014,ti= NOI4)90ft) POL>NOMIAL | NO= ay+ C 2=1 NO= 4 010)= 0 HARMONIC • no/y)= Accos w 4 t Assin w 4 b b ' natural BC : ②Io)= 0 Ac = ☐ , arbitrari LT As = 1 • Cinematic Bc: GJ@" (b)= O cos tu = o un = IT 2 SUMMINCUP: no(4)= sin IT 4 2 b B.ENDING cinematico BC: Wto)= 0 W'(☐)= 0 • WIll,ti= Nwltw POL>NOMIAL Nw= 242+ C | wioi.co a- un =p w'10)= 0 SWEPT WING • 4= 4-COSI è= eCOSI È= ^ già= 1 gv2COIL= 9cos'1 2 2 • b= ÈCOSI è= ccosnh • BEING L'FT THE SAME IN BOTHREFERENCES: Ld4= [dj • 9CCina× dy= Èc-CÌÀdit 9CClaady= 01COSTICCOSICiaè 4 COSI • (la ✗= CiaÓCOSI (la = ÉLCOSI ✗= ÈCOSI /TOTALCHANCEOFAOA) TORSION y 0cost at = ÒCOSI i 0sind 4EA INCREASE OFAOA 0 ✗ BENDING - 2-141) zlyz) 4I ✗b= - W " sindè 41 - YEA '= dw W' COSI42 dy DECREASE OF AOA 4= Csinnh W' sind ✗ E • ✗= Lt+ db= ÒCOSI- w' /Ù/sind • To t a l l'FT : LT= |l/4)d4= |L/4)d4 THE To t a l l'FT MUST BE THE sane '~ •◦t" riferentesi THE WIND IS THE SAME ' • consideri NGan infinitesimale strip : d4= dyCOSI " " =/"""" " ""= { """"d" """"= """" " SECTIONAL LIFT AND MOMENT STI LL WAT THE Y- AXIS , BUT Written as FUNCTIONS OF LT • Mt =/m'4)COSIdi= m/y)dy nty)= nlylCOSI 4 = MI = m /Ìf)COSI torsionale MOMENT "…