Resonance Search and Dwell Test
In structural fatigue testing, sometimes it is desirable to shake a structure at its resonant frequencies for an extended period of time. The Sine test suite in EDM has functions that find and track these resonances. This section describes how such a test is implemented.
The peak displacement, velocity, and acceleration response of a system undergoing forced, steady-state vibration occur at slightly different forcing frequencies. A resonance frequency is defined as a frequency for which the response reaches a local maximum. These resonances are given as:
Displacement resonance frequency:
Velocity resonance frequency:
Acceleration resonance frequency:
For physical systems with small damping ratios, say <0.1, the difference among the three resonance frequencies is negligible.
A direct method to find resonances is to measure the transfer function between the force excitation signal and the response signal of the structure (acceleration, velocity or displacement). Resonances will be seen as peaks on the transfer function curve. Unfortunately, this approach is unpractical in many shaker tests because the force measurement is not easy to obtain. Instead, transmissibility measurements are commonly used to find the resonances.
Acceleration transmissibility measurements are calculated from the response of two accelerometers, one on the shaker table and the other on the structure under test. Transmissibility is defined as the ratio of the response between two points.
There may be more than one response accelerometer, and transmissibility functions are calculated for each one. It is critical to select the right mount locations for these reference and response accelerometers. The wrong location may make it impossible to find some resonances. Also, if the response and reference channels are reversed, anti-resonances will appear as resonances.
The accelerometer for the reference channel should be mounted on the shaker table in a location that will accurately record the base movement. Each accelerometer for the response channels should be mounted on the structure in a location that has the greatest resonant vibration. This is based on the mode shapes of each of the resonances; accelerometers will not detect any response from resonant frequencies corresponding to modes that have a node at their location.
The resonance search works best with transmissibility signals that have clean, high-amplitude peaks. In the CI control system, the transmissibility function is represented as:
Transmissibility y,x (f) = channel y / channel x
where y is the response channel and x is the reference channel.