Lab 3 - Measuring Natural Frequencies¶
What are natural frequencies?¶
In free vibration (i.e., no external forcing), structural components oscillate at frequencies (or combinations of frequencies) that are dictated by their geometry and material properties. Since these vibrations occur in the absence of a driving force, the associated frequencies are referred to as natural frequencies. They describe how the system vibrates if left to behave on its own. In contrast, driven linear systems vibrate at the driving frequency. An amplification of the response (called resonance) occurs when the driving frequency coincides with one of the natural frequencies. In short, the system is driven at a frequency at which it likes to vibrate. Large amplitude oscillations are the result. So it is important to know what the natural frequencies are a priori so you can avoid driving the system into resonance.
Determining natural frequencies?¶
In this lab, you will measure the first 3 natural frequencies, \(\omega_n\), of a rectangular beam using strain gauge data. Your goal is to measure the free response time series data using a strain gauge. With this data, you will determine the first natural frequency in two ways:
(i) by peak counting in the time domain (which gives a very rough estimate of \(\omega_n\))
(ii) by a formal frequency domain analysis, using the fast Fourier transform (FFT).
For a rectangular beam, analytic expressions of the natural frequencies exist, and you can confirm that you’re doing everything properly by getting the analytical frequencies to agree with the experimental frequencies.
Deliverables¶
For this assignment, you will have two weeks in the lab. You and your lab partner will submit a joint report as a .pdf to your HuskyCT section within one week of your final lab date. It will only be necessary for one of you to submit the report. Please clearly mark, either in the body as footnotes or in the appendix as a separate section, what each of you contributed to the overall report.
You are limited to 5 pages (not including the title page, references, or appendix) and 4 figures. Additional data, figures, and information can be put in an appendix. The appendix will not be graded, but you may refer to it to explain data, methods, or other relevant information.