ME 322: Instrumentation Lecture 31 April 8, 2015 Professor Miles Greiner

Announcements/Reminders This week: Lab 9.1 Open-ended Extra-Credit New Due Date: HW 11 due Monday Did you know? – HW solutions are posted on WebCampus

Lab 10 Vibration of Weighted Steel and Aluminum Cantilever Beams This lab can be on the course Final Accelerometer Calibration Data – strumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20 Index.htm strumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20 Index.htm – C = mV/g – Use calibration constant for the issued accelerometer – Inverted Transfer function: a = V*1000/C Measure: E, W, T, L B, L E, L T, M T, M W – Estimate uncertainties of each W L T M T T LBLB LELE Accelerometer Clamp MWMW E (Lab 5)

Figure 2 VI Block Diagram

Figure 1 VI Front Panel

Disturb Beam and Measure a(t)

Time and Frequency Dependent Data

Fig. 5 Peak Acceleration versus Time The exponential decay changed at t = 2.46 sec During the first and second periods the decay rates are – b 1 = /s – b 2 = /s

Effect of Sampling Rate If the sampling rate is too slow, then it is likely that the peak accelerations will be missed for most of the oscillations Can cause a type of aliasing problem

Equivalent Endpoint Mass MEME Beam Mass M B L T M T LBLB LELE Clamp MWMW

Uncertainty

Beam Equivalent Spring Constant, K EQ F  LBLB

Predicted Frequencies

Table 1 Measured and Calculated Beam Properties UnitsValue 3  Uncertainty Elastic Modulus, E [Pa][GPa]633 Beam Width, W[inch] Beam Thickness, T[inch] Beam Total Length, L T [inch] End Length, L E [inch] Beam Length, L B [inch] Beam Mass, M T [g] Intermediate Mass, M I [g] Combined Mass, M w [g]

Table 2 Calculated Values and Uncertainties The equivalent mass is not strongly affected by the intermediate mass The predicted undamped and damped frequencies, f OP and f P, are essentially the same (frequency is unaffected by damping). The confidence interval for the predicted damped frequency f P = 9.0 ± 0.2 Hz does not include the measure value f M = 8.70 ± 0.05 Hz. UnitsValue 3  Uncertainty Equivalent Mass, M EQ [kg] Equivalent Beam Spring Constant, k EQ [N/m] Predicted Undamped Frequency, f oP [Hz] Measured Damped Frequency, f M [Hz] Decay Constant, b 1 [1/sec] Damping Coefficient, M [Ns/m] Damped Frequency, f p [Hz] Percent Difference (f P /f M -1)*100% 3.5%- Decay Constant, b 2 [1/sec] Damping Coefficient, M [Ns/m] Damped Frequency, f p [Hz] Percent Difference (f P /f M -1)*100% 3.5%-

Midterm 2 Average 67

Measurements and Uncertainties Lengths – W, T, w W, w T : Lab 4 – L T, L E, L B : Ruler w = 1/16 inch Masses – M T Total beam mass – M W End components measured together – Uncertainty 0.1 g