Nonlinear Dynamics of a Rotating Flexible Link

This paper deals with the study of the nonlinear dynamics of a rotating flexible link modeled as a one dimensional beam, undergoing large deformation and with geometric nonlinearities. The partial differential equation of motion is discretized using a finite element approach to yield four nonlinear, nonautonomous and coupled ordinary differential equations (ODEs). The equations are nondimensionalized using two characteristic velocities-the speed of sound in the material and a velocity associated with the transverse bending vibration of the beam. The method of multiple scales is used to perform a detailed study of the system. A set of four autonomous equations of the first-order are derived considering primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. Numerical simulations show that for certain ranges of values of these characteristic velocities, the slow flow equations can exhibit chaotic motions. The numerical simulations and the results are related to a rotating wind turbine blade and the approach can be used for the study of the nonlinear dynamics of a single link flexible manipulator.

Solution of a class of vibration problems by flowgraph methods

A 4-degree-of-freedom single-input system and a 3-degree-of-freedom multi-input system are solved by the Coates', modified Coates' and Chan-Mai flowgraph methods. It is concluded that the Chan-Mai flowgraph method is superior to other flowgraph methods in such cases.

A rational synthesis of vibration isolators

The paper deals with a rational approach to the development of general design criteria for non-dissipative vibration isolation systems. The study covers straight-through springmass systems as well as branched ones with dynamic absorbers. Various design options, such as the addition of another spring-mass pair, replacement of an existing system by one with more spring-mass pairs for the same space and material requirements, provision of one or more dynamic absorbers for the desired frequency range, etc., are investigated quantitatively by means of an algebraic algorithm which enables one to write down straightaway the velocity ratio and hence transmissibility of a linear dynamical system in terms of the constituent parameters.

Effect of vibration on heat transfer from a horizontal cylinder to a normal air stream

The effect of vibration on heat transfer from a horizontal copper cylinder, 0.344 in. in diameter and 6 in. long, was investigated. The cylinder was placed normal to an air stream and was sinusoidally vibrated in a direction perpendicular to the direction of the air stream. The flow velocity varied from 19 ft/s to 92 ft/s; the double amplitude of vibration from 0.75 cm to 3.2 cm, and the frequency of vibration from 200 to 2800 cycles/min. A transient technique was used to determine the heat transfer coefficients. The experimental data in the absence of vibration is expressed by NNu = 0.226 NRe0.6 in the range 2500 < NRe < 15 000. By imposing vibrational velocities as high as 20 per cent of the flow velocity, no appreciable change in the heat transfer coefficient was observed. An analysis using the resultant of the vibration and the flow velocity explains the observed phenomenon.

On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Estimating Frequencies of Minority Nevirapine-Resistant Strains in Chronically HIV-1-Infected Individuals Naive to Nevirapine by Using Stochastic Simulations and a Mathematical Model

Nevirapine forms the mainstay of our efforts to curtail the pediatric AIDS epidemic through prevention of mother-to-child transmission of HIV-1. A key limitation, however, is the rapid selection of HIV-1 strains resistant to nevirapine following the administration of a single dose. This rapid selection of resistance suggests that nevirapine-resistant strains preexist in HIV-1 patients and may adversely affect outcomes of treatment. The frequencies of nevirapine-resistant strains in vivo, however, remain poorly estimated, possibly because they exist as a minority below current assay detection limits. Here, we employ stochastic simulations and a mathematical model to estimate the frequencies of strains carrying different combinations of the common nevirapine resistance mutations K103N, V106A, Y181C, Y188C, and G190A in chronically infected HIV-1 patients naive to nevirapine. We estimate the relative fitness of mutant strains from an independent analysis of previous competitive growth assays. We predict that single mutants are likely to preexist in patients at frequencies (similar to 0.01% to 0.001%) near or below current assay detection limits (>0.01%), emphasizing the need for more-sensitive assays. The existence of double mutants is subject to large stochastic variations. Triple and higher mutants are predicted not to exist. Our estimates are robust to variations in the recombination rate, cellular superinfection frequency, and the effective population size. Thus, with 10(7) to 10(8) infected cells in HIV-1 patients, even when undetected, nevirapine-resistant genomes may exist in substantial numbers and compromise efforts to prevent mother-to-child transmission of HIV-1, accelerate the failure of subsequent antiretroviral treatments, and facilitate the transmission of drug resistance.

Stochastic Aeroelastic Analysis of Composite Helicopter Rotor

The effect of uncertainty in composite material properties on the aeroelastic response, vibratory loads, and stability of a hingeless helicopter rotor is investigated. The uncertainty impact on rotating natural frequencies of the blade is studied with Monte Carlo simulations and first-order reliability methods. The stochastic aeroelastic analyses in hover and forward flight are carried out with Monte Carlo simulations. The flap, lag, and torsion responses show considerable scatter from their baseline values, and the uncertainty impact varies with the azimuth angle. Furthermore, the blade response shows finite probability of resonance-type conditions caused by modal frequencies approaching multiples of the rotor speed. The 4/rev vibratory forces show large deviations from their baseline values. The lag mode damping shows considerable scatter due to uncertain material properties with an almost 40% probability of instability in hover.

From the Icosahedron to Natural Triangulations of CP(2) and S(2) x S(2)

We present two constructions in this paper: (a) a 10-vertex triangulation CP(10)(2) of the complex projective plane CP(2) as a subcomplex of the join of the standard sphere (S(4)(2)) and the standard real projective plane (RP(6)(2), the decahedron), its automorphism group is A(4); (b) a 12-vertex triangulation (S(2) x S(2))(12) of S(2) x S(2) with automorphism group 2S(5), the Schur double cover of the symmetric group S(5). It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of S(2) x S(2). Both constructions have surprising and intimate relationships with the icosahedron. It is well known that CP(2) has S(2) x S(2) as a two-fold branched cover; we construct the triangulation CP(10)(2) of CP(2) by presenting a simplicial realization of this covering map S(2) x S(2) -> CP(2). The domain of this simplicial map is a simplicial subdivision of the standard cell structure of S(2) x S(2), different from the triangulation alluded to in (b). This gives a new proof that Kuhnel's CP(9)(2) triangulates CP(2). It is also shown that CP(10)(2) and (S(2) x S(2))(12) induce the standard piecewise linear structure on CP(2) and S(2) x S(2) respectively.

Adaptive control of vibration transmission in a strut system

In this article, theoretical and the experimental studies are reported on the adaptive control of vibration transmission in a strut system subjected to a longitudinal pulse train excitation. In the control scheme, a magneto-strictive actuator is employed at the downstream transmission point in the secondary path. The actuator dynamics is taken into account. The system boundary parameters are first estimated off-line, and later employed to simulate the system dynamics. A Delayed-X Filtered-E spectral algorithm is proposed and implemented in real time. The underlying mechanics based filter construction allows for the time varying system dynamics to be taken into account. This work should be of interest for active control of vibration and noise transmission in helicopter gearbox support struts and other systems.

Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation

We address a certain inverse problem in ultrasound-modulated optical tomography: the recovery of the amplitude of vibration of scatterers [p(r)] in the ultrasound focal volume in a diffusive object from boundary measurement of the modulation depth (M) of the amplitude autocorrelation of light [phi(r, tau)] traversing through it. Since M is dependent on the stiffness of the material, this is the precursor to elasticity imaging. The propagation of phi(r, tau) is described by a diffusion equation from which we have derived a nonlinear perturbation equation connecting p(r) and refractive index modulation [Delta n(r)] in the region of interest to M measured on the boundary. The nonlinear perturbation equation and its approximate linear counterpart are solved for the recovery of p(r). The numerical results reveal regions of different stiffness, proving that the present method recovers p(r) with reasonable quantitative accuracy and spatial resolution. (C) 2011 Optical Society of America