TY - GEN
T1 - Equations of Motion for the Vertical Rigid-Body Rotor
T2 - 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021
AU - Laos, Hector
N1 - Publisher Copyright:
© 2022, The Society for Experimental Mechanics, Inc.
PY - 2022
Y1 - 2022
N2 - Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotordynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this chapter is to show examples of how the linear vs. nonlinear formulations differ. This chapter also shows how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.
AB - Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotordynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this chapter is to show examples of how the linear vs. nonlinear formulations differ. This chapter also shows how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.
KW - Equations of motion
KW - Generalized forces
KW - Nonlinear
KW - Rigid body
KW - Rotordynamics
UR - http://www.scopus.com/inward/record.url?scp=85116284281&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-75914-8_5
DO - 10.1007/978-3-030-75914-8_5
M3 - Conference contribution
AN - SCOPUS:85116284281
SN - 9783030759131
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 39
EP - 54
BT - Special Topics in Structural Dynamics and Experimental Techniques, Volume 5 - Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021
A2 - Epp, David S.
PB - Springer
Y2 - 8 February 2021 through 11 February 2021
ER -