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

2. 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

3. Lab 10 Vibration of Weighted Steel and Aluminum Cantilever Beams This lab can be on the course Final Accelerometer Calibration Data – http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322In strumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20 Index.htm http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322In strumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20 Index.htm – C = 616.7 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)

4. Figure 2 VI Block Diagram

5. Figure 1 VI Front Panel

6. Disturb Beam and Measure a(t)

7. Time and Frequency Dependent Data

8. 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 = -0.292 1/s – b 2 = -0.196 1/s

9. 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

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

13. Uncertainty

14. Beam Equivalent Spring Constant, K EQ F  LBLB

15. Predicted Frequencies

16. Table 1 Measured and Calculated Beam Properties UnitsValue 3  Uncertainty Elastic Modulus, E [Pa][GPa]633 Beam Width, W[inch]0.990.01 Beam Thickness, T[inch]0.18320.0008 Beam Total Length, L T [inch]24.000.06 End Length, L E [inch]0.380.06 Beam Length, L B [inch]10.000.06 Beam Mass, M T [g]196.80.1 Intermediate Mass, M I [g]21.91.5 Combined Mass, M w [g]741.20.1

17. 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]0.76310.0005 Equivalent Beam Spring Constant, k EQ [N/m]2445124 Predicted Undamped Frequency, f oP [Hz]9.00.2 Measured Damped Frequency, f M [Hz]8.700.05 Decay Constant, b 1 [1/sec]-0.292- Damping Coefficient, M [Ns/m]0.450.00 Damped Frequency, f p [Hz]9.00.2 Percent Difference (f P /f M -1)*100% 3.5%- Decay Constant, b 2 [1/sec]-0.196- Damping Coefficient, M [Ns/m]0.300.00 Damped Frequency, f p [Hz]9.00.2 Percent Difference (f P /f M -1)*100% 3.5%-

18. Midterm 2 Average 67

20. 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