Modeling of Physical Systems: HW 6–due 10/25/12 Page 1
Problem 1: Work problem 7-2 from Karnopp, et al [1].
Problem 2: Work problem 7-5 from Karnopp, et al [1].
Problem 3: Work problem 7-9 from Karnopp, et al [1].
Problem 4: A suspension for an extraterrestrial vehicle consists of four wheels and semi-
circular springs, readily folded from the body of the vehicle after landing and then clamped
in the position shown. Study the handout from Chapter 10 of Burr [2] that will be posted
on the course log.
1. Show how you can use a two-port Celement to represent each semi-circular spring
element, especially so you can answer the question from Burr: “Determine in terms of
EI , vehicle load W, and spring radius r: (a) the downward deflection of the supported
body and (b) the the horizontal motion of a wheel due to vehicle load only.”
2. Develop the bond graph for a quarter-vehicle model under static loading conditions.
Consider the translational mass of the vehicle in the longitudinal and vertical directions
only. A quarter-vehicle model does not include rotational dynamics of the vehicle body.
3. Answer (a) and (b) from part 1.
Figure adapted from Burr [2].
References
[1] Karnopp, D., D. Margolis, R. Rosenberg, System Dynamics, Wiley, New York, (any
edition after 2001).
[2] Burr, A.H. Mechanical Analysis and Design, Elsevier, NY, 1981.
R.G. Longoria, Fall 2012 ME 383Q, UT-Austin
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