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- Vibration_of_rotating_structures abstract "Rotating structures - or more general - structures with constant but otherwise arbitrary velocity are important elements of machinery as rotor shafts and blades of propellers, helicopters or wind turbines.Vibrations in such structures require special attention.Gyroscopic matrices are to be added to classical matrices of mass, damping and stiffness.The equation of vibration read: where:M,D,K classical matrices: mass matrix, damping matrix and stiffness matrixG gyroscopic matrix of vibration velocity (includes e.g. coriolis elements)N gyroscopic matrix of elastic deflection (includes e.g. centrifugal elements)B gyroscopic matrix of small footpoint excitationA gyroscopic matrix of the structure if it is not vibratingV transposition matrix (consists of distances between grid- and foot- point)rE small grid point deflection, components measured relative to moving structure (non inertial)sE small foot- or reference- point excitation movement, components measured relative to an inertial point (important for connection of non rotating structures) (large)constant velocity of structure foot pointpE variable external loadspU constant load on grid points due to , required for stiffness corrections due to constant initial deformationsall gyroscopic matrices depend on .Further they contain inertia terms and distances of the structure. Details are given in the references.These equations are directly comparable with classical equations of non rotating structures and therefore directly applicable to available solution routines. No other physics is required, all specialities of rotating masses are included in the gyroscopic matrices. Straight forward coupling with non rotating structures is possible.For the most simple case (one grid point, D=K=0) it results a gyro (spinning wheel) with the eigenvalues:0 for the deflection in direction of - and for rotation around of - the rotating axis.the rotation speed for the other translatory deflections.the inverse of the Euler period for one rotatory deflection. The last eigenvalue depends on the studied degree of freedom. For sE=0, one gets from the left side of the equation of movement. For rE=0, one gets the inverse Euler period from the right side. sE=0 means fixed foot point. rE=0 allows a movement of the foot- (reference-) point. Eigenvectors describe circles, coupling two translatory or two rotatory deflections.".
- Vibration_of_rotating_structures wikiPageID "20916450".
- Vibration_of_rotating_structures wikiPageRevisionID "535467048".
- Vibration_of_rotating_structures hasPhotoCollection Vibration_of_rotating_structures.
- Vibration_of_rotating_structures subject Category:Structural_analysis.
- Vibration_of_rotating_structures subject Category:Structural_dynamics.
- Vibration_of_rotating_structures comment "Rotating structures - or more general - structures with constant but otherwise arbitrary velocity are important elements of machinery as rotor shafts and blades of propellers, helicopters or wind turbines.Vibrations in such structures require special attention.Gyroscopic matrices are to be added to classical matrices of mass, damping and stiffness.The equation of vibration read: where:M,D,K classical matrices: mass matrix, damping matrix and stiffness matrixG gyroscopic matrix of vibration velocity (includes e.g. ".
- Vibration_of_rotating_structures label "Vibration of rotating structures".
- Vibration_of_rotating_structures sameAs m.0hr63k3.
- Vibration_of_rotating_structures sameAs Q7924653.
- Vibration_of_rotating_structures sameAs Q7924653.
- Vibration_of_rotating_structures wasDerivedFrom Vibration_of_rotating_structures?oldid=535467048.
- Vibration_of_rotating_structures isPrimaryTopicOf Vibration_of_rotating_structures.