Download Analytical Methods in Rotor Dynamics: Second Edition by Andrew D. Dimarogonas PDF

By Andrew D. Dimarogonas

The layout and building of rotating equipment working at supercritical speeds was once, within the Twenties, an occasion of innovative significance for the then new department of dynamics referred to as rotor dynamics. within the Nineteen Sixties, one other revolution happened: In under a decade, imposed by means of operational and financial wishes, a rise within the strength of turbomachinery through one order of value came about. Dynamic research of advanced rotor types grew to become a need, whereas the significance of approximate tools for dynamic research was once under pressure. eventually, the emergence of fracture mechanics, as a brand new department of utilized mechanics, supplied analytical instruments to enquire crack impression at the dynamic habit of rotors.

The scope of this e-book is predicated on these types of advancements. No subject matters concerning the well known classical difficulties are integrated, relatively the publication offers solely with sleek high-power turbomachinery.

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Extra info for Analytical Methods in Rotor Dynamics: Second Edition

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Mech. Des. Trans. ASME 123(4), 562–568 (2007) 31. : Nonlinear modeling and dynamic analysis of the rotor-bearing system. Nonlinear Dyn. 57(4), 559–577 (2009) 32. Avramov, K. , Borysiuk, O. : Nonlinear dynamics of one disk asymmetrical rotor supported by two. journal bearings. Nonlinear Dyn. 67(2), 1201–1219, (2012) 33. Lu Y. , Ji, L. , Zhang, Y. , Liu, Y. : Dynamic behaviours of the rotor non-linear system with fixed-tilting-pad journal bearings support. In: Proceedings of the Institution of Mechanical Engineers, Part J: J.

1 x_ 2 ðtÞ Àx2 ðtÞ x1 ðtÞ x2 ðtÞ ð2:20Þ ¼ x_ 1 ðtÞ x_ 2 ðtÞ W À_x1 ðtÞ x1 ðtÞ If the initial conditions are given: " # x ðt Þ x_ ðtÞ " ¼ t¼0 From Eq. 18b) we derive " # " x0 x 1 ð 0Þ ¼ x_ 1 ð0Þ x_ 0 x0 x_ 0 # ð2:21Þ x 2 ð 0Þ x_ 2 ð0Þ #" A1 A2 # ð2:22Þ or " A1 A2 # " ¼ x 1 ð 0Þ x_ 1 ð0Þ x2 ð0Þ x_ 2 ð0Þ #À1 " x0 x_ 0 # ð2:23Þ which determines the column of arbitrary constants, and, consequently, the final solution assumes the form 36 2 Variable Elasticity Effects in Rotating Machinery ! 1 x1 ðtÞ x2 ðtÞ x ðt Þ x_ 2 ð0Þ ¼ x_ ðtÞ W x_ 1 ðtÞ x_ 2 ðtÞ À_x1 ð0Þ Àx2 ð0Þ x 1 ð 0Þ !

Most times, both analyses are necessary. The complexity of the model is determined from the individual features of the particular rotor in conjunction with the experience of the analyst and the scope of the analysis. For example, if the rigid body motion of a rotor has frequencies close to the rotating speed and far from the frequencies at the bending modes, a single disc description will suffice. If the rotating speed is in the vicinity of a higher bending mode, the model devised should at least be able to include that mode.

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