ASE 365 - Lecture 28 - Modal expansion (decomposition) [ ]...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Modal expansion (decomposition) [ ] [ ] x e e e x e I x x x x x x x x x x n i n n n i n i i n n n i = = = = + + + = = = = 1 1 1 1 2 1 1 1 1 1 1 1 1 , , 1 : basis a form , vectors unit the D,- In = = = = = = = j i j i x x x x ij i n j n j j ij j j T i T i i i if , if : ity orthogonal use we formally, of t coefficien the find To 1 1 1 e e x e e could x u u u x u x u M m m m M M U T r n s n s r r r r s rs r s s T r T r r r = = = = = = 1 1 1 so : ity orthogonal- mass of property s ' use can we , in of t coefficien the find To ) i.e., , and , " normalized- mass " is (If or , : orthogonal- mass are of Columns . 1 . = = = = = = r rs s T r T rs r s T r T m M I MU U U m M diagonal M MU U U u u u u ) so becomes this , normalized- mass is (If x u u u x u M M M U T r n s n s r r s rs s s T r T r = = = = = = 1 1 . 1 = = = n r r r U U u x x as d represente be can vector any so D,- n in basis a form columns its so r, nonsingula is matrix modal the system, DOF- n an For [ ] [ ] x x M U M M MU U M U n r T T T r 1 , , 1- = = = = : once at , ts coefficien modal the of all find To [ ] ) : simpler this makes ion normalizat (Mass x x M U I MU U M U T T T = = = [ ] [ ] ) if ( so , : Velocities I M M U M U M M MU U M U t U t T T T T = = = = = =- x x x x 1 ) ( ) ( x u x u x x M m M m U U U U T r r r T r r r r = =- = =-- 1 , 1 1 1 : s ' want you which for columns the just of all know to have even t don' invert to have t don' : , over Advantages Modal response to ICs (revisited) + = + = = = = sin cos ) ( ) ( ) ( ) ( 1 r r r r r r r r r n r r r t b t a t b a t t t U t if if where response, free In u x = = = = = = = = = =...
View Full Document

This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas at Austin.

Page1 / 22

ASE 365 - Lecture 28 - Modal expansion (decomposition) [ ]...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online