APPENDIX 9

Numerical Data for Rotor Lateral/TorsionalFree Vibrations

This Appendix contains the numerical data on the eigenvalues and eigenvectors of a rotorcoupled lateral/torsional vibrations, calculated for two cases.

EXAMPLE 1

This example corresponds to the case of the rotor with a weak lateral/torsional coupling.

Eigenvalue matrix:

1.0eþ002 *

Columns 1 through 2

0.10000003735334þ2.04218466049995i 0

0 �0.10000003735334� 2.04218466049995i

0 0

0 0

0 0

0 0

Columns 3 through 4

0 0

0 0

�0.09999931227747þ 0.05221239056366i 0

0 �0.09999931227747� 0.05221239056366i

0 0

0 0

Columns 5 through 6

0 0

0 0

0 0

0 0

�0.00000185036919þ0.49999892500595i 0

�0.00000185036919�0.49999892500595I

Eigenvector matrix:

Columns 1 through 2

�0.66146838656730þ0.24989510302813i 0.66146838656730� 0.24989510302813i

�0.24989364618721þ0.66146891640559i �0.24989364618721� 0.66146891640559i

0.00015886734973�0.00032269626564i 0.00015886734973þ 0.00032269626564i

1023

© 2005 by Taylor & Francis Group, LLC

The parameters and numerical data are shown in Table 6.7.3 of Chapter 6, value #1.

EXAMPLE 2

This example corresponds to the case of the rotor with a strong lateral/torsional coupling.

Eigenvalue matrix:

1.0eþ002 *

Columns 1 through 2

�0.10034377642665þ2.03409643967616i 0

0 �0.10034377642665� 2.03409643967616i

0

0

0

0

Columns 3 through 4

0 0

0 0

�0.03511664411454�0.46889131709325i 0

0 �0.03511664411454� 0.46889131709325i

0 0

0 0

Columns 5 through 6

0 0

0 0

0 0

0 0

�0.06953337945881�0.10414839071333i 0

0 �0.06953337945881� 0.10414839071333i

Eigenvector matrix:

Columns 1 through 2

�0.65716674854050�0.25968382916350i �0.65716674854050þ 0.25968382916350i

0.22240203223321�0.66922846152294i 0.22240203223321þ 0.66922846152294i

�0.02371903029128þ0.05272640500082i �0.02371903029128� 0.05272640500082i

�0.00111456611551þ0.00328573765144I �0.00111456611551� 0.00328573765144i

0.00106251201896�0.00329105160628i 0.00106251201896þ0.00329105160628i

0.00329105384606þ0.00106250477555i 0.00329105384606�0.00106250477555i

�0.00000161437428�0.00000069887706i 0.00000161437428þ0.00000069887706i

Columns 3 through 4

�0.51519299311146�0.48028123381703i �0.51519299311146þ0.48028123381703i

0.48028958590003�0.51517126760191i 0.48028958590003þ0.51517126760191i

0.00304646301033�0.00454408636647i 0.00304646301033þ0.00454408636647i

0.02077818762307þ0.05887731676808i 0.02077818762307�0.05887731676808i

�0.05887708170732þ0.02077613778886I �0.05887708170732�0.02077613778886i

�0.00042582270981þ0.00023207801634i �0.00042582270981�0.00023207801634i

Columns 5 through 6

�0.00229181962169þ0.00355364782452i �0.00229181962169�0.00355364782452i

0.00030330453314�0.00135611588335i 0.00030330453314þ0.00135611588335i

0.32163152650049�0.94664328418069i 0.32163152650049þ0.94664328418069i

0.00007107327893þ0.00004583622796i 0.00007107327893�0.00004583622796i

�0.00002712239843�0.00000606600333I �0.00002712239843þ0.00000606600333i

�0.01893293019446�0.00643257429415i �0.01893293019446þ0.00643257429415I

Rotational speed: 1000 rpm

1024 ROTORDYNAMICS

© 2005 by Taylor & Francis Group, LLC

The parameters and numerical data are shown in Table 6.7.3 of Chapter 6, value #3.

�0.00333587171671�0.00092880864434i �0.00333587171671þ0.00092880864434i

0.00026432200585þ0.00010356796784i 0.00026432200585�0.00010356796784i

Columns 3 through 4

�0.53391256607864�0.15892201767603i �0.53391256607864þ0.15892201767603i

0.18909540165226�0.04290447488356i 0.18909540165226þ0.04290447488356i

0.80694003140308þ0.02188582863974i 0.80694003140308�0.02188582863974i

�0.00252238319689þ0.01157561058601i �0.00252238319689�0.01157561058601i

�0.00121026097262�0.00394217944602i �0.00121026097262þ0.00394217944602i

�0.00081752984195�0.01714830519653i �0.00081752984195þ0.01714830519653i

Columns 5 through 6

�0.48975701576840�0.37059027789405i �0.48975701576840þ0.37059027789405i

0.46553195222751�0.21532019496695i 0.46553195222751þ0.21532019496695i

0.48757111498782�0.34008250874792i 0.48757111498782þ0.34008250874792i

�0.00289630461164þ0.04895860579650i �0.00289630461164�0.04895860579650i

�0.03494199520245�0.02137032070847i �0.03494199520245þ0.02137032070847i

�0.04420513585706�0.01730203080392i �0.04420513585706þ0.01730203080392I

Rotational speed: 1000 rpm

NUMERICAL DATA FOR ROTOR LATERAL/TORSIONAL FREE VIBRATIONS 1025

© 2005 by Taylor & Francis Group, LLC