PRE-LAB 4 You are doing a dynamic strain experiment on a vibrating beam. The bea

Question

PRE-LAB 4 You are doing a dynamic strain experiment on a vibrating beam. The beam is fixed at one end (cantilever) and has a strain gage attached in the longitudinal direction that is hooked up to a strain box and the signal is fed into a DSO At a certain time, you drop a weight onto the end of the beam as shown The following is what you see on the DSo: 200 100 100 200 300 400 500 500 -700 0 02 04 0.6 08 112 14 16 18 2 Time (Seconds 1. What is the natural frequency of the beam? 2. What is the maximum strain felt by the beam (assuming initially 0 strain equals a constant 0-voltage) if 200 mV-500 ? 3. What is the static strain due to the weight of the magnet only (not the force of dropping it)?

Explanation / Answer

From the given graph, certain amount information can be extracted such as the frequency and nature of oscillation, amplitude of oscillation etc.

Question (1):

The natural frequency of the beam is given by:

1/ time period of oscillation = 1 / (0.1) = 10 Hz approximately.

Question (2):

The maximum amplitude of oscillation is 600 mV. This corresponds to maximum strain felt by beam.

200mV corresponds to 500ue of strain then 600mV corresponds to 250m * 500/200 = 1500 ue of strain.

Question (3)

The time response settles at a voltage of 200mV approximately. This corresponds static strain due to weight of the magnet. So the static strain felt by the beam is given by 500 u e of strain.

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