A Boundary Value Problem for equations whose order - download pdf or read online

By Zainulabidova Z.M.

Translated from Differentsial'nye Uravneniya, Vol. forty, No. 10, 2004.

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Unbalance forces are harmonic functions of time, with an amplitude proportional to 2 and a frequency equal to . The gyroscopic matrix contains inertial, and hence conservative, terms that, in the case of rotordynamics, are strictly linked with the gyroscopic moments acting on the rotating parts of the machine. If the equation is written with reference to a noninertial frame, terms linked with Coriolis acceleration also are present in the gyroscopic matrix. The circulatory matrix contains nonconservative terms linked with the internal damping of rotating elements and, when using a linearized model for fluid bearings or seals, with the damping of the fluid film surrounding the rotor.

As the Campbell diagram is symmetrical with respect to both the $ and the axes, all of the information it conveys are contained in any one of its quadrants and it is customary to draw only one of them, usually the first quadrant. 4. 12 1. 4. Standard Campbell diagram (only the first quadrant is represented) and decay rate plot of a flexible rotor. 4 stemming from a single natural frequency at standstill (the rotor is axially symmetrical and the values on the $-axis are double). 4) occurring in the same direction of the spin motion (forward or direct whirling) and one (the lighter) in the opposite direction (backward or reverse whirling).

It is then possible to plot the Campbell diagram in such a way as to dierentiate between forward and backward whirling, using a positive value of $, now interpreted as the speed of the free whirling motion, for the former and a negative value for the latter. 5. , counterclockwise) direction, the second is for reverse whirling when spinning in clockwise direction, the third is for direct whirling in clockwise direction, and the fourth is for reverse whirling in counterclockwise direction. As already said, the direction of the spinning motion is immaterial and two quadrants are enough to convey all of the required information.

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A Boundary Value Problem for equations whose order degenerates along the perpendicular lines of change of type by Zainulabidova Z.M.


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