hw5_solution

# hw5_solution - MEEN 364 Fall 2004 Homework Set 5 Due...

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MEEN 364 Homework Set 4 Fall 2004 October 7, 2004 Homework Set 5 – Due October 7, 2004 @ 5:00 PM 2. First we identify the state variables. There are four independent energy storage elements in the given hydromechanical system are: (1) Fluid compliance, C 1 . (2) Fluid compliance, C 2 . (3) Masses M and m p . (4) Spring k. Accordingly, there are four states, corresponding to the pressure at the left side of the piston, p 1 , the pressure at the right side of the piston, p 2 , and the position and velocity of the piston and mass assembly, x and x ˙ , respectively. The free body diagram of the piston-rod-mass is: x Now we write the dynamic equations of motion and fluid flow: 12 x lr mx F pA p A kx bx = =−− && & ( 1 ) Also, from the definition of fluid compliance, we have the relation dp qC dt = , where, q = Volumetric flow rate p = Pressure in the section C = Fluid Compliance Thus, for the sections 1 and 2, we get 1 11 1 l dp dp A xC dt dt =⇒ = & 1 ( 2 ) 2 22 2 r dp dp A dt dt = & 2 ( 3 ) And from the definition of fluid resistance: 1 ii l p pp RA x q −− = & p R ( 4 ) 2 2 r r 2 p R q & A x R = ( 5 )
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hw5_solution - MEEN 364 Fall 2004 Homework Set 5 Due...

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