ADS Homework 3 - -= = l t q t p l t q t p l x Cos l t q dx...

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Homework 3: m 0 : constant; EI 0 : constant; q 0 (t) : uniform distributed load Assumption for the specific vibration shape: = l x Sin x π ψ ) ( Find the equation of motion for the given distributed parameter system. Solution: The boundary conditions are: 0 ) 0 ( 0 ) 0 ( = = = x and 0 ) ( 0 ) ( = = = l l x 0 0 ) 0 ( 0 ) 0 ( = = = = l Sin x and 0 ) ( 0 ) ( = = = = l l Sin l l x The assumption for the specific vibration shape satisfies the boundary conditions. The equation of motion for any given distributed parameter system is; ) ( ) ( ) ( ) ( * * * * t p t p t Y k t Y m eff + = + = l dx x x m m 0 2 * ) ( ) ( ; [ ] = l dx x x EI k 0 2 ' ' * ) ( ) ( ; = l dx x t x p t p 0 * ) ( ) , ( ) ( [ ] = - = = = l x Sin l x l x Sin l x l x Cos l x l x Sin x 2 4 4 2 ' ' 2 2 ' ' ' ) ( ) ( ) ( ) ( = = l x Sin x l x Sin x 2 2 ) ( ) ( l m m l m m l x Sin l x m dx l x Sin m m l l 0 * 0 * 0 0 0 2 0 * 50 . 0 2 1 2 4 1 2 1 = = - = = 1
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3 0 * 3 0 4 * 0 4 4 0 0 2 4 4 0 * 705 . 48 2 2 4 1 2 1 l EI k l EI k l x Sin l x l EI dx l x Sin l EI k l l = =
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Unformatted text preview: -= = l t q t p l t q t p l x Cos l t q dx l x Sin t q t p l l ) ( 637 . ) ( ) ( 2 ) ( 1 ) ( ) ( ) ( * * * = = -= = The equation of motion for the given system is; l t q t Y l EI t Y l m t p t p t Y k t Y m eff ) ( 637 . ) ( 705 . 48 ) ( 50 . ) ( ) ( ) ( ) ( 3 * * * * = + + = + 2...
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ADS Homework 3 - -= = l t q t p l t q t p l x Cos l t q dx...

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