Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) 0.3 2.72 0.3 2.84 0.3 3.77 0.4 2.07 0.4 2.20 0.4 2.34 0.4 2.61 0.5 1.80 0.5 1.93 0.5 1.53 0.6 0.77 0.6 1.26 0.6 1.66 0.7 0.89 0.7 1.00 0.7 0.66 0.8 1.13 0.8 0.37 Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting frequency from damping ratio. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? C. d. Predict the frequency for modes with damping ratio 0.75. Should the equation be used to predict the frequency for modes that are overdamped (damping ratio > 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?
Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio < 1). Following are the damping ratios and frequencies for those modes. Damping Ratio Frequency (Hz) 0.3 2.72 0.3 2.84 0.3 3.77 0.4 2.07 0.4 2.20 0.4 2.34 0.4 2.61 0.5 1.80 0.5 1.93 0.5 1.53 0.6 0.77 0.6 1.26 0.6 1.66 0.7 0.89 0.7 1.00 0.7 0.66 0.8 1.13 0.8 0.37 Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting frequency from damping ratio. If two modes differ in damping ratio by 0.2, by how much would you predict their frequencies to differ? C. d. Predict the frequency for modes with damping ratio 0.75. Should the equation be used to predict the frequency for modes that are overdamped (damping ratio > 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Structural engineers use wireless sensor networks to monitor the condition of dams and
bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using
Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural
Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed
on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical
modes, the system was underdamped (damping ratio < 1). Following are the damping ratios
and frequencies for those modes.
Damping Ratio
Frequency (Hz)
0.3
2.72
0.3
2.84
0.3
3.77
0.4
2.07
0.4
2.20
0.4
2.34
0.4
2.61
0.5
1.80
0.5
1.93
0.5
1.53
0.6
0.77
0.6
1.26
0.6
1.66
0.7
0.89
0.7
1.00
0.7
0.66
0.8
1.13
0.8
0.37
Construct a scatterplot of frequency ) versus damping ratio (x). Verify that a linear
model is appropriate.
b.
Compute the least-squares line for predicting frequency from damping ratio.
If two modes differ in damping ratio by 0.2, by how much would you predict their
frequencies to differ?
C.
d. Predict the frequency for modes with damping ratio 0.75.
Should the equation be used to predict the frequency for modes that are overdamped
(damping ratio > 1)? Explain why or why not
f.
e.
For what damping ratio would you predict a frequency of 2.0?
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