ECP's systems are unique in their ability to demonstrate high order flexible system dynamics. The three DOF experiments cover many important properties of such systems including:
- Mode shapes and frequencies
- Orthogonality and linear independence of the modes
- Modal analysis and modal coordinates
- The effect of changes in inertia and stiffness parameters
- Free and forced system responses
- Superposition of the modes in the output response
- Frequency domain phase and magnitude properties
- Poles and zeros
These experiments expand on the topics described in more detail for the 2 DOF tests, to include additional dynamic complexity and provide an introduction to general high order systems.
As an example of the 3 DOF tests, Figure 1 gives the frequency response of one of the several possible configurations using ECP's input forcing function and data plotting options (plots displaced by 20 Db for viewing clarity). Several key principles are demonstrated. At low frequency the positive definite configuration shown yields a common constant amplitude at all outputs. At high frequency the encoder data at outputs 1, 2, and 3, shows attenuation of -40, -80, and -120 Db/dec respectively. The first inertia has two zeros (antiresonances) interspersed in frequency between the poles (resonances), the second inertia has one zero, and the third has none. Phase measurements show the -180 degree shift with the poles and +180 degree with the zeros. From this, the mode shapes and frequencies shown in Figure 2, are inferred directly from the amplitude data alone.
By witnessing the actual system motion, examining the various dynamic states available through the plotted data, and working related theoretical exercises, students are given a practical interpretation of dynamic system behavior.
