EG260 Solutions-example_5

# EG260 Solutions-example_5 - [email protected] Slone 2007 1 of 5...

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Unformatted text preview: EG-260 @Avril Slone 2007 1 of 5 EG -260 Dynamics I - Example Sheet5 -AnswersMultiple degree of freedom systems 1.Free Body Diagram First disk ( )1221111θθθθ−+−=ttkkI&&( )2212111=−++θθθtttkkkI&&Second disk ( )12222θθθ−−=tkI&&221222=+−θθθttkkI&&EOM in matrix form ( )( )21222121=⎥⎦⎤⎢⎣⎡+−−++⎥⎦⎤⎢⎣⎡θθttttttkkkkkkII&&Substitute values from question EOM: 22=⎥⎦⎤⎢⎣⎡−−+⎥⎦⎤⎢⎣⎡θθkkkkII&&Natural frequencies det2=−ωMK22det22=−−−−ωωIkkkIkSo that θ1(t)θ2(t)kt1θ1 kt2(θ2- θ1) EG-260 @Avril Slone 2007 2 of 5 ( )( ) ( )( )( )( )( )( )()322222222222222=−−=+−−−=−−=−−−−−ωωωωωωωIkIkkIkkIkkIkkkIkIkThus frequencies are: IkIk3or22==ωωMode shapes, for each frequency: [ ]2=−AωMK2222=⎟⎟⎠⎞⎜⎜⎝⎛−−−−AIkkkIkωωIk=21ωso that 221=⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛−−−−AIkIkkkIkIkSimplifying 211=−=⎟⎟⎠⎞⎜⎜⎝⎛−−AAAkkkkLet A1=1 then A2= -1...
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EG260 Solutions-example_5 - [email protected] Slone 2007 1 of 5...

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