MECH 322 Instrumentation Lab 10 Damped Vibration of a Weighted Cantilever Beam Performed: 4/1/15 Group 0 Miles Greiner Lab Instructors: Marissa Tsugawa

ABSTRACT The goal of this experiment was to measure the dependence of oscillatory frequency of a weighted cantilever beam on the beam length, and compare it with predictions based on measured beam dimensions, elastic modulus and masses. The oscillations were measured using an accelerometer and computer data acquisition system. The frequency decreases as the beam length increased. The predicted frequencies were roughly 15% larger than the measured values, and their confidence intervals did not overlap. The damping rate was not constant during the experiment, and had little effect on the beam frequency.

Figure 1 VI Front Panel

Figure 2 VI Block Diagram

Table 1 Measured Steel Beam Properties The value and uncertainty in E were determined in Lab 5 W and T were measured using micrometers whose uncertainty were determined in Lab 5. L T, and L E were measured using a tape measure –readability = 1/16 in M T and M W were measured using a analytical scale –readability = 0.1 g

Acceleration versus time measurements were acquired at a sampling rate of 600 Hz for two beam lengths, L B = 7 and 13 inches. The sampling rate was sufficiently high so the peaks decreased monotonically The longer beam clearly had fewer peaks and a lower oscillatory frequency. Figure 3 Acceleration versus Time

Figure 4 Oscillatory Amplitude Versus Frequency The sampling time and frequency were T 1 = 10 sec and f S = 600 Hz, so the system is capable of detecting frequencies between 0.1 and 300 Hz, with a resolution of 0.1 Hz. For beam lengths of L B = 13 and 7 inches, the peak frequencies are, respectively, f M = 7.50 ± 0.1 and ± 0.1 Hz. –These frequencies are easily detected from this plot.

Fig. 5 Peak Acceleration versus Time The average exponential decay constants for the beam lengths of L B = 13 and 7 inches, are b = and , respectively The magnitude of these constants (slope of the curves) decreased slightly with time.

Table 2 Calculated Values and Uncertainties The intermediate mass is small compared to the equivalent mass. For both beam lengths, the damping is sufficiently low so that the predicted undamped and damped frequencies, f OP and f P, are nearly the same The predicted damped frequencies are roughly 15% higher than the measured values, and their confidence intervals do not overlap.

Extra (not part of report)

Warning: Be careful to check your data before processing For example, see oscillations between 2 and 4 seconds

Very repeatable frequency for same beam length (7 and 15 inch) 7 inch

Class Summary 2006 Measure versus Predicted Frequency

Damping Coefficient