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.

Microprocessor-based polynomial generator

A new method of generating polynomials using microprocessors is proposed. The polynomial is generated as a 16-bit digital word. The algorithm for generating a variety of basic 'building block' functions and its implementation is discussed. A technique for generating a generalized polynomial based on the proposed algorithm is indicated. The performance of the proposed generator is evaluated using a commercially available microprocessor kit.

On the sufficient conditions for the equality of the unassignable polynomial and Davison's fixed polynomial of strongly connected systems

In this technical note, it is established that the unassignable polynomial defined for a not strongly connected decentralized control system is not equal to Davison's fixed polynomial. This leads to a "sufficient condition" for the equality of the unassignable polynomial and Davison's fixed polynomial for strongly connected systems.

A parallel wilf algorithm for complex zeros of a polynomial

A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n 3 p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n 2 p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity.

Microprocessor-based polynomial generator

A new method of generating polynomials using microprocessors is proposed. The polynomial is generated as a 16-bit digital word. The algorithm for generating a variety of basic 'building block' functions and its implementation is discussed. A technique for generating a generalized polynomial based on the proposed algorithm is indicated. The performance of the proposed generator is evaluated using a commercially available microprocessor kit.

Multi-Tone Testing of Linear and Nonlinear Analog Circuits using Polynomial Coefficients

A method of testing for parametric faults of analog circuits based on a polynomial representation of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies in addition to DC. Classification or Cur is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. This testing method requires no design for test hardware as might be added to the circuit fly some other methods. The proposed method is illustrated for a benchmark elliptic filter. It is shown to uncover several parametric faults causing deviations as small as 5% from the nominal values.

On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.

On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Optimization of Helicopter Rotor Using Polynomial and Neural Network Metamodels

This study aims to determine optimal locations of dual trailing-edge flaps and blade stiffness to achieve minimum hub vibration levels in a helicopter, with low penalty in terms of required trailing-edge flap control power. An aeroelastic analysis based on finite elements in space and time is used in conjunction with an optimal control algorithm to determine the flap time history for vibration minimization. Using the aeroelastic analysis, it is found that the objective functions are highly nonlinear and polynomial response surface approximations cannot describe the objectives adequately. A neural network is then used for approximating the objective functions for optimization. Pareto-optimal points minimizing both helicopter vibration and flap power ale obtained using the response surface and neural network metamodels. The two metamodels give useful improved designs resulting in about 27% reduction in hub vibration and about 45% reduction in flap power. However, the design obtained using response surface is less sensitive to small perturbations in the design variables.

Substitution of chromium for univalent copper in superconducting Pb2Sr2(Ca,Y)Cu3O8+delta

Following considerations of geometry and the similarity between chromate and carbonate groups in terms of size and charge, we have investigated the possibility of replacing the two-coordinate Cu-I in superconducting lead cuprates of the general formula Pb2Sr2(Ca, Y)CU3O8 by Cr. A high-resolution electron microscopy study coupled with energy dispersive X-ray analysis on small crystals of the title phases suggests that between 10 and 15% of the Cu-I can be replaced by Cr. While from the present structural study using HRTEM and Rietveld refinement of X-ray powder data we are unable to precisely obtain the oxidation state and oxygen coordination of Cr, we suggest in analogy with Cr substitution in other similar cuprates that in the title phases (CuO2)-O-I rods are partially replaced by tetrahedral CrO42- groups. Infrared spectroscopy supports the presence of CrO42- groups. The phases Pb1.75Sr2Ca0.2Y0.8O8+delta and Pb1.75Sr2Ca0.2Y0.8CCu2.85Cr0.15O8+delta are superconducting as-prepared, but the substitution of Cr for Cu-I results in a decrease of the Te as well as the superconducting volume fraction. (C) 1996 Academic Press, lnc.

A polynomial bound on the number of light cycles in an undirected graph

Let G be an undirected graph with a positive real weight on each edge. It is shown that the number of minimum-weight cycles of G is bounded above by a polynomial in the number of edges of G. A similar bound holds if we wish to count the number of cycles with weight at most a constant multiple of the minimum weight of a cycle of G.

Uncertainty analysis of vibrational frequencies of an incompressible liquid in a rectangular tank with and without a baffle using polynomial chaos expansion

Polynomial chaos expansion (PCE) with Latin hypercube sampling (LHS) is employed for calculating the vibrational frequencies of an inviscid incompressible fluid partially filled in a rectangular tank with and without a baffle. Vibration frequencies of the coupled system are described through their projections on the PCE which uses orthogonal basis functions. PCE coefficients are evaluated using LHS. Convergence on the coefficient of variation is used to find the orthogonal polynomial basis function order which is employed in PCE. It is observed that the dispersion in the eigenvalues is more in the case of a rectangular tank with a baffle. The accuracy of the PCE method is verified with standard MCS results and is found to be more efficient.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Polynomial Coefficient Based Multi-Tone Testing of Analog Circuits

Abstract—A method of testing for parametric faults of analog circuits based on a polynomial representaion of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies apart from DC. Classification of CUT is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. The method needs very little augmentation of circuit to make it testable as only output parameters are used for classification. This procedure is shown to uncover several parametric faults causing smaller than 5 % deviations the nominal values. Fault diagnosis based upon sensitivity of polynomial coefficients at relevant frequencies is also proposed.