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55 45 70 75 40 10 Omega rad/s (o) Fig. 2a Data pertaining to X1/F1 can be found in BeachBoard file dB ref 1

55 45 70 75 40 10 Omega rad/s (o) Fig. 2a Data pertaining to X1/F1 can be found in BeachBoard file dB ref 1

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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35 40 45 50 -55 60 65 -70 -75 80 1 10 100 Omega rad/s (eo) Fig. 2a Data pertaining to X1/F1 can be found in BeachBoard file: X1_F1_FRF.txt Frequency Response Function X,/F, -50 55 -60 -70 -75 -80 1.00 omegtPRIys (m) 100.00 Fig. 2B Data pertaining to X2/Fz can be found in BeachBoard file: X2_F2_FRF.txt dB ref 1
Transcribed Image Text:35 40 45 50 -55 60 65 -70 -75 80 1 10 100 Omega rad/s (eo) Fig. 2a Data pertaining to X1/F1 can be found in BeachBoard file: X1_F1_FRF.txt Frequency Response Function X,/F, -50 55 -60 -70 -75 -80 1.00 omegtPRIys (m) 100.00 Fig. 2B Data pertaining to X2/Fz can be found in BeachBoard file: X2_F2_FRF.txt dB ref 1
MAE 376 Fall 2021 Project M,= 5kg M,= 7kg (K2)1=700 N/m case 1 c:=0 F;=F;=0 c,=0 F;=F;=0 (K2)2 = 5000 N/m case 2 wwim wwwm m2 Figure 1. Two-degree of freedom Duffing oscillator. 1) Fig. 2a and Fig. 2b show the Frequency Response Function (FRF) X1/F1 and X2/F2 respectively. The data related to these can be found in BeachBoard. This experimental data pertains to case 1 (k2=700 N/m). Since this is a weak connection, the frequencies pertaining to the peaks in the graphs are good estimates to the natural frequencies (@n) of_ - and . Apply the half- power-bandwidth method to estimate the damping factors ,(use data X1/F1) and 53 (use data X2/F2). 2) Using Simulink, create a block diagram corresponding to Figure 1. Apply an initial displacement of 0.1m on m2. Plot the displacements (with respect to time 0-10s) of m and m2. Solve for case 1 and case 2. 3) Calculate and plot the Frequency Response Function (FRF) for X1/F1 for case 2 (k2=5000 N/m). Compare the FRF with that of case 1. Can good estimates and §, be estimated using case 2 data? ms for 4) Set all of the damping, c's, to zero and derive the equation of motion by applying Lagrange equation.
Transcribed Image Text:MAE 376 Fall 2021 Project M,= 5kg M,= 7kg (K2)1=700 N/m case 1 c:=0 F;=F;=0 c,=0 F;=F;=0 (K2)2 = 5000 N/m case 2 wwim wwwm m2 Figure 1. Two-degree of freedom Duffing oscillator. 1) Fig. 2a and Fig. 2b show the Frequency Response Function (FRF) X1/F1 and X2/F2 respectively. The data related to these can be found in BeachBoard. This experimental data pertains to case 1 (k2=700 N/m). Since this is a weak connection, the frequencies pertaining to the peaks in the graphs are good estimates to the natural frequencies (@n) of_ - and . Apply the half- power-bandwidth method to estimate the damping factors ,(use data X1/F1) and 53 (use data X2/F2). 2) Using Simulink, create a block diagram corresponding to Figure 1. Apply an initial displacement of 0.1m on m2. Plot the displacements (with respect to time 0-10s) of m and m2. Solve for case 1 and case 2. 3) Calculate and plot the Frequency Response Function (FRF) for X1/F1 for case 2 (k2=5000 N/m). Compare the FRF with that of case 1. Can good estimates and §, be estimated using case 2 data? ms for 4) Set all of the damping, c's, to zero and derive the equation of motion by applying Lagrange equation.
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