Lateral and Longitudinal Vibration of a Rotating Flexible Beam Coupled with Torsional Vibration of a Flexible Shaft
In this study, rotating flexible shaft-disk system
having flexible beams is considered as a dynamic system. After
neglecting nonlinear terms, torsional vibration of the shaft-disk
system and lateral and longitudinal vibration of the flexible beam are
still coupled through the motor speed. The system has three natural
frequencies; the flexible shaft-disk system torsional natural
frequency, the flexible beam lateral and longitudinal natural
frequencies. Eigenvalue calculations show that while the shaft speed
changes, torsional natural frequency of the shaft-disk system and the
beam longitudinal natural frequency are not changing but the beam
lateral natural frequency changes. Beam lateral natural frequency
stays the same as the nonrotating beam lateral natural frequency ωb
until the motor speed ωm is equal to ωb. After then ωb increases and
remains equal to the motor speed ωm until the motor speed is equal to
the shaft-disk system natural frequency ωT. Then the beam lateral
natural frequency ωb becomes equal to the natural frequency ωT and
stays same while the motor speed ωm is increased. Modal amplitudes
and phase angles of the vibrations are also plotted against the motor
speed ωm.
[1] Al Bedoor B. O., Al Sinawi A. and Hamdan M. N. "Nonlinear Dynamic
Model of an Inextensible Rotating Flexible Arm Supported on a Flexible
Base" Journal of Sound and Vibration, 2002, Vol. 251, pp. 767-781.
[2] Al Nassar Y. M., Al Bedoor B. O. and Hamdan M. N. "On the Vibration
of a Rotating Blade on a Torsionally Flexible Shaft" Journal of Sound
and Vibration, 2002, Vol. 259, pp. 1237-1242.
[3] Al Sinawi A. and Hamdan M. N. "Optimal Vibration Estimation of a
Nonlinear Flexible Beam Mounted on a Rotating Compliant Hub"
Journal of Sound and Vibration, 2003, Vol. 259, pp. 857-872.
[4] Alnefaie K. "Effect of Servomotor Control Parameters on the Dynamic
Behavior of a Coupled Elastic Shaft Elastic Beam System" Int. Journal
of Vehicle Noise and Vibration, 2007, Vol. 3, pp. 339-354.
[5] Diken H. and Ankarali A. "Vibration Control of an Elastic Manipulator
Link" Journal of Sound and Vibration, 1997, Vol. 204, pp. 162-170.
[6] Diken H. "Dynamic Behavior of a Coupled Elastic Shaft Elastic Beam
System" Journal Of Sound and Vibration, 2006, Vol. 293, pp. 1-15.
[7] Diken H. "Frequency Response Characteristics of a Single link Flexible
Joint Manipulator and Possible Trajectory Tracking" Journal of Sound
and Vibration, 2000, Vol. 233, pp. 179-194.
[8] Diken H. "Precise Trajectory Tracking Control of Elastic Joint
Manipulator" AIAA Journal of Guidance, 1996, Vol. 19, pp. 715-718.
[9] Diken H. "Servomotor Control of a Coupled Elastic Shaft Elastic Beam
System" Mechanism and Machine Theory, 2007, Vol. 42, pp. 1376-
1387.
[10] Diken H. "Vibration Control of a Rotating Euler Bernoulli Beam"
Journal of Sound and Vibration, 2000, Vol. 232, pp. 541-551.
[11] Kopmaz O. and Anderson K. S. "On the Eigen-Frequencies of a Flexible
Arm Driven by a Flexible Shaft" Journal of Sound and Vibration, 2001,
Vol. 240, pp. 679-704.
[12] Xi F. and Fenton R. G. "Coupling Effect of Flexible Link and Flexible
Joint" Int. Journal of Robotics Research, 1994, Vol. 13, pp. 443-453.
[13] Xi F., Fenton R. G. and Tabarrok B. "Coupling Effects in a Manipulator
with both a Flexible Link and Joint" Journal of Dynamic Systems,
Measurement, and Control, 1994, Vol. 116, pp. 826-831.
[1] Al Bedoor B. O., Al Sinawi A. and Hamdan M. N. "Nonlinear Dynamic
Model of an Inextensible Rotating Flexible Arm Supported on a Flexible
Base" Journal of Sound and Vibration, 2002, Vol. 251, pp. 767-781.
[2] Al Nassar Y. M., Al Bedoor B. O. and Hamdan M. N. "On the Vibration
of a Rotating Blade on a Torsionally Flexible Shaft" Journal of Sound
and Vibration, 2002, Vol. 259, pp. 1237-1242.
[3] Al Sinawi A. and Hamdan M. N. "Optimal Vibration Estimation of a
Nonlinear Flexible Beam Mounted on a Rotating Compliant Hub"
Journal of Sound and Vibration, 2003, Vol. 259, pp. 857-872.
[4] Alnefaie K. "Effect of Servomotor Control Parameters on the Dynamic
Behavior of a Coupled Elastic Shaft Elastic Beam System" Int. Journal
of Vehicle Noise and Vibration, 2007, Vol. 3, pp. 339-354.
[5] Diken H. and Ankarali A. "Vibration Control of an Elastic Manipulator
Link" Journal of Sound and Vibration, 1997, Vol. 204, pp. 162-170.
[6] Diken H. "Dynamic Behavior of a Coupled Elastic Shaft Elastic Beam
System" Journal Of Sound and Vibration, 2006, Vol. 293, pp. 1-15.
[7] Diken H. "Frequency Response Characteristics of a Single link Flexible
Joint Manipulator and Possible Trajectory Tracking" Journal of Sound
and Vibration, 2000, Vol. 233, pp. 179-194.
[8] Diken H. "Precise Trajectory Tracking Control of Elastic Joint
Manipulator" AIAA Journal of Guidance, 1996, Vol. 19, pp. 715-718.
[9] Diken H. "Servomotor Control of a Coupled Elastic Shaft Elastic Beam
System" Mechanism and Machine Theory, 2007, Vol. 42, pp. 1376-
1387.
[10] Diken H. "Vibration Control of a Rotating Euler Bernoulli Beam"
Journal of Sound and Vibration, 2000, Vol. 232, pp. 541-551.
[11] Kopmaz O. and Anderson K. S. "On the Eigen-Frequencies of a Flexible
Arm Driven by a Flexible Shaft" Journal of Sound and Vibration, 2001,
Vol. 240, pp. 679-704.
[12] Xi F. and Fenton R. G. "Coupling Effect of Flexible Link and Flexible
Joint" Int. Journal of Robotics Research, 1994, Vol. 13, pp. 443-453.
[13] Xi F., Fenton R. G. and Tabarrok B. "Coupling Effects in a Manipulator
with both a Flexible Link and Joint" Journal of Dynamic Systems,
Measurement, and Control, 1994, Vol. 116, pp. 826-831.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51707", author = "Khaled Alnefaie", title = "Lateral and Longitudinal Vibration of a Rotating Flexible Beam Coupled with Torsional Vibration of a Flexible Shaft", abstract = "In this study, rotating flexible shaft-disk system
having flexible beams is considered as a dynamic system. After
neglecting nonlinear terms, torsional vibration of the shaft-disk
system and lateral and longitudinal vibration of the flexible beam are
still coupled through the motor speed. The system has three natural
frequencies; the flexible shaft-disk system torsional natural
frequency, the flexible beam lateral and longitudinal natural
frequencies. Eigenvalue calculations show that while the shaft speed
changes, torsional natural frequency of the shaft-disk system and the
beam longitudinal natural frequency are not changing but the beam
lateral natural frequency changes. Beam lateral natural frequency
stays the same as the nonrotating beam lateral natural frequency ωb
until the motor speed ωm is equal to ωb. After then ωb increases and
remains equal to the motor speed ωm until the motor speed is equal to
the shaft-disk system natural frequency ωT. Then the beam lateral
natural frequency ωb becomes equal to the natural frequency ωT and
stays same while the motor speed ωm is increased. Modal amplitudes
and phase angles of the vibrations are also plotted against the motor
speed ωm.", keywords = "Rotor dynamics, beam-shaft coupling, beam
vibration, flexible shaft.", volume = "7", number = "5", pages = "798-8", }