Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams

A new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial. These new shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. The natural frequencies predicted by the proposed element are compared with an element with stiff-string, cubic polynomial and quintic polynomial shape functions. It is found that the new element exhibits superior convergence compared to the other basis functions.

Negative resistance mode of forced oscillations of a string

A new mode of driven nonlinear vibrations of a stretched string is investigated with reference to conditions of existence, properties, and regions of stability. It is shown that this mode exhibits negative resistance properties at all frequencies and driving force amplitudes. Discovery of this mode helps to fill certain gaps in the theory of forced nonlinear vibrations of strings.

On walls of marginal stability in N=2 string theories

We study the properties of walls of marginal stability for BPS decays in a class of N = 2 theories. These theories arise in N = 2 string compactifications obtained as freely acting orbifolds of N = 4 theories, such theories include the STU model and the FHSV model. The cross sections of these walls for a generic decay in the axion-dilaton plane reduce to lines or circles. From the continuity properties of walls of marginal stability we show that central charges of BPS states do not vanish in the interior of the moduli space. Given a charge vector of a BPS state corresponding to a large black hole in these theories, we show that all walls of marginal stability intersect at the same point in the lower half of the axion-dilaton plane. We isolate a class of decays whose walls of marginal stability always lie in a region bounded by walls formed by decays to small black holes. This enables us to isolate a region in moduli space for which no decays occur within this class. We then study entropy enigma decays for such models and show that for generic values of the moduli, that is when moduli are of order one compared to the charges, entropy enigma decays do not occur in these models.

Novel melody line identification algorithm for polyphonic MIDI music

The problem of automatic melody line identification in a MIDI file plays an important role towards taking QBH systems to the next level. We present here, a novel algorithm to identify the melody line in a polyphonic MIDI file. A note pruning and track/channel ranking method is used to identify the melody line. We use results from musicology to derive certain simple heuristics for the note pruning stage. This helps in the robustness of the algorithm, by way of discarding "spurious" notes. A ranking based on the melodic information in each track/channel enables us to choose the melody line accurately. Our algorithm makes no assumption about MIDI performer specific parameters, is simple and achieves an accuracy of 97% in identifying the melody line correctly. This algorithm is currently being used by us in a QBH system built in our lab.

Stiff-String Basis Functions for Vibration Analysis of High Speed Rotating Beams

A new rotating beam finite element is developed in which the basis functions are obtained by the exact solution of the governing static homogenous differential equation of a stiff string, which results from an approximation in the rotating beam equation. These shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. Using this new element and the Hermite cubic finite element, a convergence study of natural frequencies is performed, and it is found that the new element converges much more rapidly than the conventional Hermite cubic element for the first two modes at higher rotation speeds. The new element is also applied for uniform and tapered rotating beams to determine the natural frequencies, and the results compare very well with the published results given in the literature.

Non-Linear vibration of an elastic string

Equations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite medium, although this difference is usually negligible. After formulating the exact equations of motion for the string, a systematic procedure is described for obtaining approximations to these equations to any order, making only the assumption that the strain in the material of the string is small. The lowest order equations in this scheme are non-linear, and are used to describe the response of a string near resonance. Finally, it is shown that in the absence of damping, planar motion of a string is always unstable at sufficiently high amplitudes, the critical amplitude falling to zero at the natural frequency and its subharmonics. The effect of slight damping on this instability is also discussed.

A speech-music discriminator using HILN model based features

We propose a simple speech music discriminator that uses features based on HILN(Harmonics, Individual Lines and Noise) model. We have been able to test the strength of the feature set on a standard database of 66 files and get an accuracy of around 97%. We also have tested on sung queries and polyphonic music and have got very good results. The current algorithm is being used to discriminate between sung queries and played (using an instrument like flute) queries for a Query by Humming(QBH) system currently under development in the lab.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Radio interference measurements on a ceramic disc insulator string with field reduction electrode

This paper presents a laboratory study of the discharge radio noise generated by ceramic insulator strings under normal conditions. In the course of study, a comparison on the performance of two types of insulator strings under two different conditions was studied namely (a) normal disc insulators in a string and (b) disc insulators integrated with a newly developed field reduction electrode fixed to the disc insulator at the pin junction. The results obtained during the study are discussed and presented.

Finite data performance of MUSIC and minimum norm methods

In the direction of arrival (DOA) estimation problem, we encounter both finite data and insufficient knowledge of array characterization. It is therefore important to study how subspace-based methods perform in such conditions. We analyze the finite data performance of the multiple signal classification (MUSIC) and minimum norm (min. norm) methods in the presence of sensor gain and phase errors, and derive expressions for the mean square error (MSE) in the DOA estimates. These expressions are first derived assuming an arbitrary array and then simplified for the special case of an uniform linear array with isotropic sensors. When they are further simplified for the case of finite data only and sensor errors only, they reduce to the recent results given in [9-12]. Computer simulations are used to verify the closeness between the predicted and simulated values of the MSE.

Linear dynamics and active control of an elastically supported travelling string

In this paper, the linear dynamics and active control of a string travelling with uniform velocity is presented. Discrete elastic supports are introduced along the length of the string. Finite element formulation is adopted to obtain the governing equations of motion. The velocity of translation introduces gyroscopic terms in the system equations. The effect of translation and the discrete elastic supports on the free vibration solution is studied. The solution is utilized in actively controlling the string vibrations due to an initial disturbance. The control, affected in modal space, is optimal with respect to a quadratic performance index. Numerical results are presented to demonstrate the effectiveness of the control strategy in regulating the travelling string vibrations.

Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

Study of temperature distribution along an artificially polluted insulator string

Insulator becomes wet partially or completely, and the pollution layer on it becomes conductive, when collecting pollutants for an extended period during dew, light rain, mist, fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layer without initiating other stages of breakdown or it may bridge the gaps between sheds to promote flashover. The insulator with a conducting pollution layer being energized, can cause a surface leakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, the conducting pollution layer becomes broken by dry bands (at spots of high current density), interrupting the flow of leakage current. Voltage across insulator gets concentrated across dry bands, and causes high electric stress and breakdown (dry band arcing). If the resistance of the insulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminals causing flashover. The present paper concerns the evaluation of the temperature distribution along the surface of an energized artificially polluted insulator string.