Effect of Boundary Conditions and Damping on Critical Speeds of a Flexible Mono Rotor

An analytical investigation was made on the effect of axial torque on the critical speeds of a continuous rotor whose motion was described by a set of partial differential equations including the effects of transverse shear, rotatory inertia, and gyroscopic moments. The equations of motion and associated boundary conditions for long and short bearings were cast in nondimensional form to facilitate the study of the influence of the aforementioned effects on a torque-transmitting rotor’s critical speeds. The results of this study were compared to classical results of Bernoulli-Enter and Timoshenko to determine the relative importance of the rotor’s “secondary phenomena” in a critical speed calculation.

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The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 2: Transient Response

Journal of Vibration and Acoustics ◽

10.1115/1.2888179 ◽

1996 ◽

Vol 118 (3) ◽

pp. 285-291 ◽

Cited By ~ 21

Author(s):

S. F. Felszeghy

Keyword(s):

Steady State ◽

Boundary Conditions ◽

Elastic Foundation ◽

Transient Response ◽

Timoshenko Beam ◽

Equations Of Motion ◽

Steady State Solution ◽

State Solution ◽

Critical Speeds ◽

Particular Solution

The transient response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions were developed in Part 1 of this article for all load speeds greater than zero. The solution to the homogeneous equations of motion is developed here in Part 2. It is shown that the latter solution can be obtained by numerical integration using the method of characteristics. Particular attention is given to the cases when the load travels at the critical speeds consisting of the minimum phase velocity of propagating harmonic waves and the sonic speeds. It is shown that the solution to the homogeneous equations combines with the steady-state solution in such a manner that the beam displacements are continuous and bounded for all finite times at all load speeds including the critical speeds. Numerical results are presented for the critical load speed cases.

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Effects of Boundary Conditions on the Natural Frequencies and Critical Speeds of Rotating Cylindrical Shells

International Journal of Aerospace and Lightweight Structures (IJALS) - ◽

10.3850/s2010428611000080 ◽

2011 ◽

Vol 01 (01) ◽

pp. 143 ◽

Cited By ~ 4

Author(s):

T. Y. Ng ◽

R. E. S. Koh

Keyword(s):

Boundary Conditions ◽

Natural Frequencies ◽

Cylindrical Shells ◽

Critical Speeds

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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