Intermittent behaviour of a Cracked Rotor in the resonance region

Vibrations of the Jeffcott rotor are modelled by a three degree of freedom system including coupling between lateral and torsional modes. The crack in a rotating shaft of the rotor is introduced via time dependent stiffness with off diagonal couplings. Applying the external torque to the system allows to observe the effect of crack "breathing" and gain insight into the system. It is manifested in the complex dynamic behaviour of the rotor in the region of internal resonance, showing a quasi--periodic motion or even non-periodic behaviour. In the present paper report, we show the system response to the external torque excitation using nonlinear analysis tools such as bifurcation diagram, phase portraits, Poincare maps and wavelet power spectrum. In the region of resonance we study intermittent motions based on laminar phases interrupted by a series nonlinear beats.Comment: 12 pages, 6 figure

Review of Rotordynamics

Book Review of Rotordynamics, by Agnieszka (Agnes) Muszynska. CRC Press, Taylor & Francis Group, Boca Raton, FL, 2005, 1128 pp., ISBN: 0-8247-2399-

Review of Rotordynamics

Book Review of Rotordynamics, by Agnieszka (Agnes) Muszynska. CRC Press, Taylor & Francis Group, Boca Raton, FL, 2005, 1128 pp., ISBN: 0-8247-2399-

Planning Programming Budgeting Study of the City of Winter Park

The report examines the applicability of Planning, Programming, and Budgeting System to the City of Winter Park. After briefly describing the character of the city, the goals are identified, the means by which they may be achieved and measure of evaluating progress toward them are given. To show how such an effort might be implemented, specific programs, objectives and effectiveness criteria are provided. These are followed by three examples in which the existing system is described and from which problems are revealed. Next, a brief analysis is performed to pinpoint the difficulty and a solution is proposed. The examples are chosen to illustrate a qualitative problem involving the organizational structure of the government, the next problem is more quantitative yet involves qualitative factors to arrive at a final solution, while the third example is entirely quantitative in nature

Quantitative Determination of the Adiabatic Condition Using Force-Detected Nuclear Magnetic Resonance

The adiabatic condition governing cyclic adiabatic inversion of proton spins in a micron-sized ammonium chloride crystal was studied using room temperature nuclear magnetic resonance force microscopy. A systematic degradation of signal-to-noise was observed as the adiabatic condition became violated. A theory of adiabatic following applicable to cyclic adiabatic inversion is reviewed and implemented to quantitatively determine an adiabaticity threshold $(\gamma H_1)^2/(\omega_{osc}\Omega) = 6.0$ from our experimental results.Comment: 5 pages, 3 fig

Multipartite quantum correlations: symplectic and algebraic geometry approach

We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite number of energy levels, classification problems are usually treated in frames of linear algebra. We proposed to shift the attention to a geometric description. Treating consistently quantum states as points of a projective space rather than as vectors in a Hilbert space we were able to apply powerful methods of differential, symplectic and algebraic geometry to attack the problem of equivalence of states with respect to the strength of correlations, or, in other words, to classify them from this point of view. Such classifications are interpreted as identification of states with `the same correlations properties' i.e. ones that can be used for the same information purposes, or, from yet another point of view, states that can be mutually transformed one to another by specific, experimentally accessible operations. It is clear that the latter characterization answers the fundamental question `what can be transformed into what \textit{via} available means?'. Exactly such an interpretations, i.e, in terms of mutual transformability can be clearly formulated in terms of actions of specific groups on the space of states and is the starting point for the proposed methods.Comment: 29 pages, 9 figures, 2 tables, final form submitted to the journa

Using a Fermionic Ensemble of Systems to Determine Excited States

We discuss a new numerical method for the determination of excited states of a quantum system using a generalization of the Feynman-Kac formula. The method relies on introducing an ensemble of non-interacting identical systems with a fermionic statistics imposed on the systems as a whole, and on determining the ground state of this fermionic ensemble by taking the large time limit of the Euclidean kernel. Due to the exclusion principle, the ground state of an $n$-system ensemble is realized by the set of individual systems occupying successively the $n$ lowest states, all of which can therefore be sampled in this way. To demonstrate how the method works, we consider a one-dimensional oscillator and a chain of harmonically coupled particles.Comment: 14 pages, Latex + 4 eps figure

Nonlinear Vibrations of Fractionally Damped Systems

This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing\u27s equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior

Modal Uncoupling of Damped Gyroscopic Systems

A new approach for uncoupling the equations of motion typical for rotordynamical systems is presented. The method does not neglect the speed-dependent e!ects, such as gyroscopic e!ects, and can be particularly valuable in the controller design of actively controlled rotors. In the presence of hysteretic type of damping, the resulting uncoupled gyroscopic systems come with an equivalent viscous damping, equivalent in a sense of yielding the same natural frequency and decay rate. The approach is illustrated through three examples of technical interest: a Je!cott rotor with hysteretic damping, a Stodola}Green rotor, and a rotor of a small gas turbine. The generated results demonstrate that the developed approach is correct and straightforward

Comparison of Mobility Method and Mass Conservation Method in a Study of Dynamically Loaded Journal Bearings

The inverse problem of dynamically loaded journal bearings was solved using generalized Reynolds equation coupled with a complete mass conservative cavitation boundary conditions, as outlined by the Jacobsson-Floberg and Olsson (JFO) cavitation theory. In the course of solution, the modified Thomas algorithms was employed, instead of standard Gauss±Jordan reduction method, which fully utilizes the sparse character of the system matrix, and thus greatly reduces computational time. The developed model was tested against the well-known mobility method for the case of journal bearings in a commercial reciprocating air compressor. It was found that the mobility method overestimates minimum film thickness and underestimates such parameters as lubricant flow rate and bearing power loss. In general, the level of error is acceptable for most industrial applications. However, for the journal bearing where the feed pressure is time dependent and starvation effects are predominant, the mobility method may produce large not acceptable errors