harmonic balance approach for an airfoil with a freeplay control surface the nonlinear aeroelastic response of a two dimensional airfoil including a control surface with freeplay placed in an incompressible flow is studied the model equations are formulated as a set of first order ordinary differential equations first the dynamic response is investigated by a time integration method and the time integration results are used for the verification of the harmonic balance results the interesting hysteresis phenomenon and the effect of initial conditions of the subcritical bifurcation are presented a higher order harmonic balance method is then derived to investigate the high harmonics of the airfoil motions the harmonic balance prediction is verified by comparison to the results from a numerical time marching integration and also by comparison to results from a previous experiment nomenclature a nondimensional distance of the elastic axis from the midchord with respect to the semichord b damping submatrix b semichord ch stiffness per unit span of wing in deflection c k generalized theodorsen function c c torsional stiffness per unit span of wing around a and of aileron around c c nondimensional distance of the control surface aileron hinge line from the midchord with respect to the semichord

optimal dimension and optimal auxiliary vector to construct calibration estimators of the distribution function the calibration technique deville and sarndal 1992 to estimate the finite distribution function has been studied in several papers calibration seeks for new weights close enough to sampling weights according to some distance function and that at the same time match benchmark constraints on available auxiliary information the non smooth character of the finite population distribution function causes certain complexities that are resolved by different authors in different ways one of these is to have consistency at a number of arbitrarily chosen points this paper deals with the problem of the optimal selection of the number of points and with the optimal selections of these points when auxiliary information is used by means of calibration

properties of estimators of the finite population distribution function two leading estimators of the finite population distribution function are studied their large sample mean squared errors are compared under a given model neither estimator is universally better circumstances are identified where the model based estimator would do poorly despite employing the correct model

an iterative procedure for nonlinear flutter analysis an iterative procedure in the frequency domain is presented for flutter analysis of large dynamic systems with multiple structural nonlinearities the major components of the procedure are the describing function approach for system linearization a structural dynamics modification method for shifting system mode shapes and frequencies and a complex eigenvalue algorithm for solution of the flutter equation the purpose of the procedure is to achieve alignment of the oscillatory amplitude in each nonlinear spring with the describing function prediction of stiffness before computing the final stability characteristics the result is a system tuned to the flutter frequency at the time of instability to support the development and validation of the procedure several describing functions are formulated and a quantitative measure of the errors in each is presented validation of the iterative method is accomplished through examples involving dynamic systems of increasing complexity coupled with various representations of the unsteady aerodynamic forces both numerical simulations and experimental data are used to compare with the iterative predictions in the cases studied the agreement is good to excellent with the method accurately predicting the amplitude of a limit cycle flutter as well as the initial disturbance required to produce flutter

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

optimal calibration estimators in survey sampling we show that the model calibration estimator for the finite population mean which was proposed by wu sitter 2001 through an intuitive argument is optimal among a class of calibration estimators we also present optimal calibration estimators for the finite population distribution function the population variance the variance of a linear estimator and other quadratic finite population functions under a unified framework the proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified a limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial the question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation

compact formulations as a union of polyhedra we explore one method for finding the convex hull of certain mixed integer sets the approach is to break up the original set into a small number of subsets find a compact polyhedral description of the convex hull of each subset and then take the convex hull of the union of these polyhedra the resulting extended formulation is then compact its projection is the convex hull of the original set and optimization over the mixed integer set is reduced to solving a linear program over the extended formulation the approach is demonstrated on three different sets a continuous mixing set with an upper bound and a mixing set with two divisible capacities both arising in lot sizing and a single node flow model with divisible capacities that arises as a subproblem in network design

an investigation of stability in the large behaviour of a control surface with structural non linearities in supersonic flow it is well known that the presence of non linearities may significantly affect the aeroelastic response of an aerospace vehicle structure in this paper the aeroelastic behaviour at high mach numbers of an all moving control surface with a non linearity in the root support is investigated very often a stable equilibrium point corresponding to zero displacement of the structure together with an unstable limit cycle arising from a sub critical hopf bifurcation results from the presence of the non linearity the stable equilibrium point will then possess a domain of attraction in this paper this situation is investigated by first applying the averaging method to obtain a new set of aeroelastic equations in which the limit cycle is replaced by an unstable equilibrium point a fourth order power series approximation to the stable manifold in the neighbourhood of this equilibrium point is then determined from the stable manifold predictions of the domain of attraction of the stable equilibrium point may then be made the method is applied to two examples in which the non linearity in the root support was due to either a cubic hardening restoring moment or the presence of freeplay the approximation to the stable manifold was sufficient to enable significant information about the domain of attraction of the stable equilibrium point of the control surface to be obtained agreement with predictions from numerical integration of the aeroelastic equations in the time domain was shown to be generally good in the cases considered though outside the region of validity of the stable manifold expansion discrepancies will occur the averaging method was shown to be sufficiently accurate for this analysis even when the non linearities could not be considered as weak

an investigation of stability of a control surface with structural nonlinearities in supersonic flow using zubov s method it is well known that the presence of nonlinearities may significantly affect the aeroelastic response of an aerospace vehicle structure in this paper the aeroelastic behaviour at high mach numbers of an all moving control surface with a nonlinearity in the root support is investigated very often under certain flight conditions a stable equilibrium point corresponding to zero displacement of the structure together with an unstable limit cycle arising from a sub critical hopf bifurcation results from the presence of the nonlinearity the dynamic aeroelastic response to external excitation is also of interest and when sinusoidal forcing is applied the stable equilibrium point may then be replaced by a periodic attractor and the limit cycle by an unstable multi periodic solution with or without this forcing there is an attractor which will possess a domain of attraction in this paper the problem of estimating these domains of attraction is tackled using zubov s method in the absence of forcing the method is applied directly to the aeroelastic equations while for the forced system the method of averaging is applied to approximate the aeroelastic equations by an autonomous system the behaviour of the system with forcing is also investigated for flight speeds below a threshold which may occur where the unstable limit cycle of the unforced system disappears in this regime the nonlinear system may nevertheless still possess multiple attractors and their domains of attraction are investigated again using an averaged form of the aeroelastic equations in this study the nonlinearity in the root support was assumed to be due to a cubic hardening restoring moment the zubov approach which always yields conservative estimates was shown to be capable of rapidly giving a good indication of stability domain boundaries under many conditions although this investigation focuses on an aeroelastic system the general form of equations considered arises in many other settings so that the approach would be relevant to a whole range of engineering applications

application of the centre manifold theory in non linear aeroelasticity abstract in this study a frequency relation for limit cycle oscillations of a two degree of freedom aeroelastic system with structural non linearities represented by cubic restoring spring forces is derived the centre manifold theory is applied to reduce the original system of nine dimensional first order ordinary differential equations to a governing system in two dimensions near the bifurcation point the principle of normal form is used to simplify the non linear terms of the lower dimensional system using the frequency relation and the amplitude frequency relationships derived from a previous study limit cycle oscillations lcos for self excited systems can be predicted analytically the mathematical technique proposed here has been applied to investigate lco near a hopf bifurcation for an aeroelastic system with cubic restoring forces not only that an excellent agreement is obtained compared to the numerical results from solving the original system of eight non linear differential equations by runge kutta time integration scheme but we also demonstrate that the use of a mathematical approach leads to a better understanding of non linear aeroelasticity

bias robust estimation in finite populations using nonparametric calibration a standard problem in sample survey inference is that of predicting the finite population total h of a function h y of a random variable y the model based approach to this problem first defines a working model for y and then predicts h by estimating its expectation under conditional on the sample values of y this approach leads to biased predictions if is incorrect we explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust but inefficient predictor of h and then calibrates this predictor for its bias under an application to prediction of the finite population distribution function of a population of australian beef farms is presented

median estimation in the presence of auxiliary information summary this paper deals with the estimation under simple random sampling of a finite population median in the presence of an auxiliary variable an estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach these estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known on the basis of the asymptotic properties derived and some simulation results the efficiencies of these estimators are compared it is shown that the two estimators proposed unlike that obtained from modifying the ratio estimator always dominate the sample median in mean squared error and that their efficiencies depend directly on the probability of concordance rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable when the linearity assumption is approximately satisfied the three estimators are seen to have comparable efficiencies while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumnption

estimating distribution functions from survey data summary a simple method for estimating population distribution functions and associated quantiles from sample survey data is described and some asymptotic theory for it presented the method assumes a model based approach to survey estimation and allows auxiliary population information to be directly incorporated into the estimation process monte carlo results comparing the proposed method with conventional design based methods are given these suggest that the model based approach offers significant gains when the auxiliary population information is linearly related to the survey variables of interest

asymptotic stability regions via extensions of zubov s method i on considere un systeme differentiel x f t x satisfaisant les hypotheses suivantes f r n 1 r n est analytique f t x est presque periodique en t pour chaque x r n f t 0 0 t r la matrice principale fondamentale t s de y f x t 0 y satisfait t s exp t s t s avec et des constantes positives f t x f x t o x 0 x uniformement en t quand x 0

bias calibrated estimation from sample surveys containing outliers we discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers we clarify the motivation for chambers s bias calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters we then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of chambers s estimator we also propose methodology based on the use of robust estimates and a bias calibrated form of the chambers and dunstan estimator of the population distribution function this proposal leads to a bias calibrated estimator of the population total which is an alternative to that of chambers we present a small simulation study to illustrate the utility of these estimators

an empirical study of the ratio estimator and estimators of its variance abstract this paper reports results from an empirical study of the ratio estimator for a finite population total from each of six real populations 1 000 simple random samples 1 000 restricted random samples and three nonrandom samples of size 32 are drawn performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using a prediction superpopulation models and b probability sampling distributions the results presented graphically show that theory based on prediction models can reveal relationships that are essential in making inferences but that are concealed in probability sampling analyses

a global analysis of an harmonically excited spring pendulum system with internal resonance abstract a non linear system can often have multiple attractors in this case it is important to study the global behavior of the system by determining the global domain of attraction of each attractor this paper is concerned with the global behavior of an harmonically excited spring pendulum system with internal resonance before studying the global behavior the local behaviors of the system around its steady state periodic solutions are examined two non linearly coupled second order non autonomous ordinary differential equations governing the spring pendulum system are transformed into a four dimensional autonomous system in amplitude and phase variables next the stability of equilibrium states of the autonomous system corresponding to steady state periodic solutions of the non autonomous system is examined when certain resonance conditions are satisfied the spring pendulum system has a very complex behavior including jump phenomena and hopf bifurcation global domains of attraction for the spring pendulum system are investigated when two stable steady state periodic solutions exist the interpolated mapping method a numerical method for determining global domains of attraction is presented so as to be applied to systems with dimension higher than two then the domains of attraction for a specific set of parameter values are obtained by the method it is shown that the interpolated mapping method can be an efficient tool for analyzing the global behaviors of higher dimensional systems also examined is how the global domains of attraction evolve as the forcing frequency is varied across critical values at which jump phenomena occur it is discovered that there exists a special plane in the four dimensional state space which contains all the attractors by using this plane called the principal plane the global domains of attraction can be discussed more effectively results show that knowledge of this evolution is essential to better understand the mechanism of the jump phenomena

bifurcation analysis of a two degree of freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation incremental method abstract a perturbation incremental pi method is presented for the computation continuation and bifurcation analysis of limit cycle oscillations lco of a two degree of freedom aeroelastic system containing a freeplay structural nonlinearity both stable and unstable lcos can be calculated to any desired degree of accuracy and their stabilities are determined by the floquet theory thus the present method is capable of detecting complex aeroelastic responses such as periodic motion with harmonics period doubling pd saddle node bifurcation neimark sacker bifurcation and the coexistence of limit cycles emanating branch from a pd bifurcation can be constructed this method can also be applied to any piecewise linear systems