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Spring
Length = 1 m Loading
Case 1: A step force input, f(t) = 4π2 on the mass M in the +x direction.
Case 2: A ramp force input, f(t) = (4π2 )t, on the mass M in the +x direction. ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. 3–6 VME3 Analysis Assumptions and Modeling Notes
The magnitude of the step force input for Case 1 was chosen to equal the spring stiffness constant to produce
a steadystate static deflection of unity. The ramp input for Case 2 was defined such that the input for Case 1 is
the time derivative of the input for Case 2. The value of the stiffness constant was chosen so that the system
undamped natural frequency equals 2 Hz. The damping constant was chosen to produce a damping ratio that
results in a theoretical 50% overshoot of the steadystate deflection for the step input.
As outlined in G. F. Franklin, J. D. Powell, A. EmamiNaeini, Feedback Control of Dynamic Systems, for a single DOF
system subjected to a step input, the relationship between overshoot, Mp, and damping ratio, ζ, is given by: Mp = exp (π ζ / 1  ζ 2 )
For the system in Figure 3.1: “Support Structure Problem Sketch”:
Mp = (Xmax  Xsteadystate)/Xsteadystate The expression for peak time, tp which is the time to reach xmax is given by: tp = π / ( ω n 1  ζ 2 )
where ωnis the system undamped natural frequency in units of radians per second. Results Comparison
Table E3.1 Case 1: Step Input
Target ANSYS Ratio Maximum Ux of Mass 1.5000 1.5...
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This note was uploaded on 12/09/2010 for the course DEPARTMENT E301 taught by Professor Kulasinghe during the Spring '09 term at University of Peradeniya.
 Spring '09
 kulasinghe
 The Land

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