Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow

Rotor flap-lag stability in forward flight is studied with and without dynamic inflow feedback via a multiblade coordinate transformation (MCT). The algebra of MCT is found to be so involved that it requires checking the final equations by independent means. Accordingly, an assessment of three derivation methods is given. Numerical results are presented for three- and four-bladed rotors up to an advance ratio of 0.5. While the constant-coefficient approximation under trimmed conditions is satisfactory for low-frequency modes, it is not satisfactory for high-frequency modes or for untrimmed conditions. The advantages of multiblade coordinates are pronounced when the blades are coupled by dynamic inflow.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

The dynamic stability of degenerate systems under parametric excitation

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Systematic variation in bond lengths of peptides

The lengths of the carbonyl as well as of the adjacent C-N and C-C bonds in peptides are shown to vary systematically with the central C-N bond length. Results of ab initio calculations on N-methylacetamide and its Li+, Na+ and Mg2+ complexes are also discussed.

On a generalized dynamic model of bi-state social interaction processes

A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Temporal variation of tonal spectrum of tambura

Tambura is an essential drone accompaniment used in Indian music concerts. It acts as an immediate reference of pitch for both the artists and listeners. The four strings of Tambura are tuned to the frequency ratio :1:1: . Careful listening to Tambura sound reveals that the tonal spectrum is not stationary but is time varying. The object of this study is to make a detailed spectrum analysis to find out the nature of temporal variation of the tonal spectrum of Tambura sound. Results of the analysis are correlated with perceptual evaluation conducted in a controlled acoustic environment. A significant result of this study is to demonstrate the presence of several notes which are normally not noticed even by a professional artist. The effect of bridge in Tambura in producing the so called “live tone” is explained through time and frequency parameters of Tambura sounds.

Automatic Path Planning and Control Design for Autonomous Landing of UAVs using Dynamic Inversion

In this paper a nonlinear control has been designed using the dynamic inversion approach for automatic landing of unmanned aerial vehicles (UAVs), along with associated path planning. This is a difficult problem because of light weight of UAVs and strong coupling between longitudinal and lateral modes. The landing maneuver of the UAV is divided into approach, glideslope and flare. In the approach UAV aligns with the centerline of the runway by heading angle correction. In glideslope and flare the UAV follows straight line and exponential curves respectively in the pitch plane with no lateral deviations. The glideslope and flare path are scheduled as a function of approach distance from runway. The trajectory parameters are calculated such that the sink rate at touchdown remains within specified bounds. It is also ensured that the transition from the glideslope to flare path is smooth by ensuring C-1 continuity at the transition. In the outer loop, the roll rate command is generated by assuring a coordinated turn in the alignment segment and by assuring zero bank angle in the glideslope and flare segments. The pitch rate command is generated from the error in altitude to control the deviations from the landing trajectory. The yaw rate command is generated from the required heading correction. In the inner loop, the aileron, elevator and rudder deflections are computed together to track the required body rate commands. Moreover, it is also ensured that the forward velocity of the UAV at the touch down remains close to a desired value by manipulating the thrust of the vehicle. A nonlinear six-DOF model, which has been developed from extensive wind-tunnel testing, is used both for control design as well as to validate it.

Regional variation in the composition and structure of mixed-species bird flocks in the Western Ghats and Sri Lanka

Mixed-species bird flocks are attractive models for the investigation of geographical variation in animal communities, as they represent a subset of the avifauna in most forested regions of the world. Yet studies of the regional variation in flock size and the composition of flocks are few, due to the predominance of studies carried out at single study site. Here, we review nine studies of mixed-species flocks conducted at 16 sites along the Western Ghats in India and in Sri Lanka. We find that flock size varies as much within this region as it does globally, with observation time being a confounding variable. Flock composition, however, is predictably related to elevation. Flocks at high elevations (>1200 m) in the Western Ghats strongly resemble flocks at high elevations in the mountain ranges of Sri Lanka in their composition, especially at the family level. We compare these flocks to flocks of other regions and make recommendations on study methodology that can facilitate comparisons across studies.

Spatial variation of sequestered calcium in the multicellular stage of Dictyostelium discoideum as assayed by chlortetracycline fluorescence

Abstract. We have used chlortetracycline (CTC) as a fluorescent probe to detect the distribution of sequestered calcium in multicellular stages of Dictyostelium discoideum. Tips of late aggregates, slugs and early culminating masses fluoresce very strongly. Most of the fluorescence is intracellular in origin and emanates from a small number of intense punctate sources. The sources correspond in part to autophagic vacuoles viz. neutral-red staining, acidic digestive vesicles, and may also include intracellular organelles; cytoplasmic fluorescence is much weaker in comparison. The level of fluorescence drops in the middle portion of slugs and rises again in the posteriormost region, though not to as high a level as in the tip. This holds good irrespective of whether CTC is applied only in the neighbourhood of the aggregate centre, only in the aggregate periphery, or to the whole aggregate. We infer that there must be a good deal of mixing in the stages leading from aggregation to slug formation; thus the serial order in which cells enter an aggregate does not bear any relation to their ultimate fates. The other implication of our study is that calcium sequestration is much more extensive in prestalk and anterior-like cells than in prespore cells. These findings are discussed with regard to possible implications for pattern formation.

Dynamic viscosity of ternary mixtures of dichlorodifluoromethane (R-12), chlorodifluoromethane (R-22), and dichlorotetrafluoroethane (R-114) vapors

The viscosities of ternary mixtures of R-12, R-22, and R-114 vapors were determined at ambient temperature and pressure within +-1% by using an oscillating disk viscometer. The empirical viscosity obtained by Wllke's equation compares very well with the experimental results obtained with this vlscometer. In the case of this ternary vapor mixture, as long as the molar fraction ratio of R-12 to R-114 Is maintained at approximately 2"' (=Inverse ratio of thelr molecular weights) the viscosity of the ternary mixture at ambient temperature and pressure remalns constant irrespective of the percentage of R-22 present in the mixture.

Dynamic pressure modulation for solar desalination system

Obtaining drinking water from seawater is usually done through the process of desalination. The conventional desalination processes at present are centralized, require huge capital cost, and enormous amount of concentrated energy from fossil fuel. Issues like optimal chamber pressure, pressure control and energy savings for desalination are not adequately addressed. This paper proposes a novel pressure control method by means of dynamic pressure modulation within the evaporation chamber. A performance index is proposed that results in a dynamic optimal external pressure and maximum energy saving for a specific flow rate. Experimental results from the laboratory setup that validate the proposed concepts are presented in the paper. (C) 2009 Elsevier B.V. All rights reserved.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography

Purpose: A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography. Methods: Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms. Results: These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, requir O(NN3) and O(NN6) operations, with ``NN'' being the number of unknown parameters in the optical image reconstruction procedure. Conclusions: This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.

Compact fiber Bragg grating dynamic strain sensor cum broadband thermometer for thermally unstable ambience

An instrument for simultaneous measurement of dynamic strain and temperature in a thermally unstable ambience has been proposed, based on fiber Bragg grating technology. The instrument can function as a compact and stand-alone broadband thermometer and a dynamic strain gauge. It employs a source wavelength tracking procedure for linear dependence of the output on the measurand, offering high dynamic range. Two schemes have been demonstrated with their relative merits. As a thermometer, the present instrumental configuration can offer a linear response in excess of 500 degrees C that can be easily extended by adding a suitable grating and source without any alteration in the procedure. Temperature sensitivity is about 0.06 degrees C for a bandwidth of 1 Hz. For the current grating, the upper limit of strain measurement is about 150 mu epsilon with a sensitivity of about 80 n epsilon Hz(-1/2). The major source of uncertainty associated with dynamic strain measurement is the laser source intensity noise, which is of broad spectral band. A low noise source device or the use of optical power regulators can offer improved performance. The total harmonic distortion is less than 0.5% up to about 50 mu epsilon, 1.2% at 100 mu epsilon and about 2.3% at 150 mu epsilon. Calibrated results of temperature and strain measurement with the instrument have been presented. Traces of ultrasound signals recorded by the system at 200 kHz, in an ambience of 100-200 degrees C temperature fluctuation, have been included. Also, the vibration spectrum and engine temperature of a running internal combustion engine has been recorded as a realistic application of the system.