The purpose of this lab is to learn about the dynamical behaviour of a vibrating cantilever beam by comparing the observed vibration mode shapes that corresponded to the natural frequencies of steel and aluminium cantilever beams as obtained from an oscilloscope(connected to sensor) versus the theoretical values computed through the natural frequency formula. The cantilever beam was attached to
a mini-shaker that is in turn connected to a function generator. So when a certain frequency is put in, the function generator sent out an amplified signal which in turn caused the cantilever beam to vibrate at that frequency. A piezoelectric sensor is also mounted to the cantilever beam and the output is connected to an oscilloscope from where the observed natural frequencies of the cantilever beams could be obtained. Since the net deflection of the cantilever beam is always higher at one of its natural frequencies, we searched the observable natural frequency by first computing the theoretical natural frequencies using the natural frequency formulas and then searched for the observable natural frequency of the cantilever beam by varying the frequency of the function generator. The first 3 natural frequencies were computed and observed for each the steel and the aluminium cantilever beams with 3 trials for each frequency resulting in a set of total 18 data points.The theoretical natural frequency for the steel beam was 23.44 Hz, 146.85 Hz and 411.20 Hz (1st, 2nd and 3rd order respectively). This was compared to the average observed values for steel of 26.5Hz, 135.8Hz and 375.97 Hz, with errors of 4.38%, 7.50%, and 8.59% respectively . Similarly theoretical natural frequency for the aluminium beam was 30.01 Hz, 188.06 Hz and 526.7 Hz (1st, 2nd and 3rd order respectively). This was compared to the average observed values for steel of 26.3Hz, 190.1Hz and 474.97 Hz, with errors of 12.36%, 1.08%, and 9.82% respectively. More detailed analysis is in the attached report