a generalized treatment of the energetics of translating continua part ii beams and fluid conveying pipes abstract the energetics of translating tensioned beams and fluid transporting pipes under fixed simply supported and free boundary conditions are analyzed in a generalized manner the conservative and non conservative forces acting at the boundaries lead to energy transfer between the translating continua and the boundary supports the forces and associated convective velocities are identified from the one dimensional transport theorem the group velocity and the wavenumber of propagating and evanescent waves in the dispersive continua are defined the time variation of total energy is represented in terms of the impedances and the reflection coefficients of the propagating waves in the continuum and the dynamic stability of the translating continua is discussed based on the energy expressions the critical fluid speed in a cantilevered pipe at which the resultant energy flux into the pipe at the free end vanishes is determined by the use of travelling wave solutions

the numerical study of the nonlinear dynamics of a light axially moving string abstract the vibration characteristics of a light axially moving band are investigated by a numerical study in the subcritical and supercritical speed ranges equations of motion for the geometrically nonlinear axially moving string are formulated using hamilton s principle and discretized by the finite element method the periodic nonlinear problem for the string is solved by the fourier galerkin newton fgn method the nonlinear dynamic behaviour of an axially moving band is examined through the dependences between the fundamental frequency axial velocity and vibration amplitude resulting from nonlinear free vibration in general the behaviour of the nonlinear axially moving string is similar to that of a nonlinear beam the most notable differences being the fact that the string does not undergo bifurcation from a straight configuration to curved equilibrium states in a supercritical transport speed regime nor does the equilibrium state remain straight

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

predicting phase shift effects for vibrating fluid conveying pipes due to coriolis forces and fluid pulsation abstract knowing the influence of fluid flow perturbations on the dynamic behavior of fluid conveying pipes is of relevance e g when exploiting flow induced oscillations of pipes to determine the fluids mass flow or density as done with coriolis flow meters cfm this could be used in the attempts to improve accuracy precision and robustness of cfms a simple mathematical model of a fluid conveying pipe is formulated and the effect of pulsating fluid flow is analyzed using a multiple time scaling perturbation analysis the results are simple analytical predictions for the transverse pipe displacement and approximate axial shift in vibration phase the analytical predictions are tested against pure numerical solution using representative examples showing good agreement fluid pulsations are predicted not to influence cfm accuracy since proper signal filtering is seen to allow the determination of the correct mean phase shift large amplitude motions which could influence cfm robustness do not appear to be induced by the investigated fluid pulsation pulsating fluid of the combination resonance type could however influence cfms robustness if induced pipe motions go unnoticed and uncontrolled during cfm operation by feedback control the analytical predictions offer an immediate insight into how fluid pulsation affects phase shift which is a quantity measured by cfms to estimate the mass flow and lead to hypotheses for more complex geometries i e industrial cfms the validity of these hypotheses is suggested to be tested using laboratory experiments or detailed computational models taking fluid structure interaction into account

nonconvex splitting for regularized low rank sparse decomposition we develop new nonconvex approaches for matrix optimization problems involving sparsity the heart of the methods is a new nonconvex penalty function that is designed for efficient minimization by means of a generalized shrinkage operation we apply this approach to the decomposition of video into low rank and sparse components which is able to separate moving objects from the stationary background better than in the convex case in the case of noisy data we add a nonconvex regularization and apply a splitting approach to decompose the optimization problem into simple parallelizable components the nonconvex regularization ameliorates contrast loss thereby allowing stronger denoising without losing more signal to the residual

dynamic characteristics and mode localization of elastically constrained axially moving strings and beams abstract the free vibration response of an axially moving string and euler bernoulli beam supported by an intermediate elastic constraint is studied the transfer function method is used to formulate the free response solution for the beam the elastic constraint can consist of either a transverse spring or both transverse and rotational springs the effects of both speed and tension on mode localization are studied a wave analysis is employed to further investigate the behaviour of the systems reflection and transmission coefficients are formulated to show the effects of the system parameters on the coupling of the subsystems the addition of the constraint is shown to increase the critical speed of the beam for low values of tension for the string mode localization increases as speed increases however the behaviour of the beam is shown to change significantly depending on both the system parameters and type of constraint the effects of tension and speed on the delocalization frequency of the weakly bi coupled beam are also presented

vibration of a flexible pipe conveying viscous pulsating fluid flow abstract the non linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow these partial differential equations are fully coupled through equilibrium of contact forces the normal compatibility of velocity at the fluid pipe interfaces and the conservation of mass and momentum of the transient fluid poisson coupling between the pipe wall and fluid is also incorporated in the model a combination of the finite difference method and the method of characteristics is employed to extract displacements hydrodynamic pressure and flow velocities from the equations a numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

coupled longitudinal transverse dynamics of an axially accelerating beam abstract the coupled longitudinal transverse nonlinear dynamics of an axially accelerating beam is numerically investigated this problem is classified as a parametrically excited gyroscopic system the axial speed is assumed to be comprised of a constant mean value along with harmonic fluctuations hamilton s principle is employed to derive the equations of motion of the system which are in the form of two coupled partial differential equations the equations are discretized using the galerkin method which yields a set of coupled second order nonlinear ordinary differential equations with time dependent coefficients the sub critical dynamics of the system is examined via the pseudo arclength continuation technique while the global dynamics is investigated using direct time integration the mean axial speed and the amplitude of the speed variations are varied so as to construct the bifurcation diagrams of poincare maps the vibration specifications of the system are investigated more detailed via plotting time histories phase plane portraits and fast fourier transforms ffts

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

divergence and flutter instabilities of nanobeams in moving state accounting for surface and shear effects abstract transverse vibrations of elastically rested moving beam like nanostructures accounting for surface effect are of high concern the role of nonlocality on the free dynamic response of moving nanobeams has been revealed in recent years nevertheless the influence of the surface energy on the mechanical behavior of such elements has not been explained yet in this paper equations of motion of rested nanoscaled beams in the moving state are derived carefully via surface energetic shear deformable beam models subsequently the transverse vibrations of the nanostructure are evaluated using galerkin based assumed mode method the explicit expressions of divergence velocities are obtained analytically and these are successfully verified with the results of a numerical approach the roles of crucial parameters on the first divergence velocity are addressed in some detail additionally the stable and unstable regions are determined systematically and the influence of both surface energy and shear energy on the stability of moving nanostructure is discussed

a horizontal fluid conveying cantilever spatial coherent structures beam modes and jumps in stability diagram the proper orthogonal decomposition method is used to obtain a low dimensional model for the planar non linear dynamics of a horizontal fluid conveying cantilever undergoing a limit cycle oscillation the finite dimensional approximation of the non linear partial differential equation pde describing the oscillation is carried out by a galerkin projection scheme using both the cantilever beam modes and proper orthogonal modes coherent structures as projection bases which leads to a finite set of coupled ordinary differential equations the proper orthogonal modes are obtained semi analytically using the cantilever beam modes as a basis a systematic study is then carried out focusing on the jumps in the linear stability diagram of a horizontal fluid conveying cantilever vis a vis the order of the finite dimensional model obtained using either the beam modes or the proper orthogonal modes depending on the mass ratio of the cantilever while the order of the finite dimensional model using the beam mode basis increases steadily up to 10 the corresponding order when the proper orthogonal modes are used to span the solution of the pde remains unaltered only two

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

hamilton s principle for external viscous fluid structure interaction abstract hamilton s principle is extended so as to be able to model external flow structure interaction this is accomplished by using reynold s transport theorem in this form hamilton s principle is hybrid in the sense that it has an analytical part as well as a part that depends on experimentally derived functions examples are presented the discussion on implications and extensions is extensive in this work a general theory is developed for the case where the configuration is not prescribed at the end times of the variational principle this leads to a single governing equation of motion this limitation can be removed by prescribing the end times as usually done this is outlined in the present paper and will be the subject of a future paper a detailed discussion is also presented of the experimental work performed in parallel with and in support of the theoretical developments as a true fluid structural model it is necessary to fully couple the dynamics this has been the foundation of our formulation

transverse vibration of an axially accelerating string abstract the transverse vibration of an axially accelerating string is investigated the equation of motion is developed using hamilton s principle the resulting partial differential equations are discretized using galerkin s method assuming the axial velocity to be periodic a stability analysis is performed using floquet theory one two three four six and eight term series approximations are considered in the galerkin s method the one term approximation leads to a mathieu equation the solution of which is well known the numerical results for one term are compared with the analytical solution for the mathieu equation and they are in full agreement the two term approximation leads to gyroscopically coupled equations and the solutions differ significantly from that of the one term approximation whereas the three term approximation solutions look similar to the one term approximation solutions the analysis is carried out for higher order even approximations and the solutions are in qualitative agreement the two and four term approximation solutions are compared with the analytical results from hsu s method and are in reasonable agreement the results show that instabilities occur at much higher amplitudes and frequencies of the periodic axial velocity than that of typical devices such as tape machines and band saws

new non linear modelling for vibration analysis of a straight pipe conveying fluid abstract a new non linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends using the euler bernoulli beam theory and the non linear lagrange strain theory from the extended hamilton s principle the coupled non linear equations of motion for the longitudinal and transverse displacements are derived these equations of motion are discretized by using the galerkin method after the discretized equations are linearized in the neighbourhood of the equilibrium position the natural frequencies are computed from the linearized equations on the other hand the time histories for the displacements are also obtained by applying the generalized time integration method to the non linear discretized equations the validity of the new modelling is provided by comparing results from the proposed non linear equations with those from the equations proposed by paidoussis

vibrations of an axially moving beam with time dependent velocity the dynamic response of an axially accelerating elastic tensioned beam is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity these systems experience a coriolis acceleration component which renders such systems gyroscopic the equation of motion is solved by using perturbation analysis principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for different flexural stiffness values and for the first two modes

estimation of the parameters of sinusoidal signals in non gaussian noise accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications in this paper the problem is investigated under the assumption of non gaussian noise in general and laplace noise in particular it is proven mathematically that the maximum likelihood estimator derived under the condition of laplace white noise is able to attain an asymptotic cramer rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares it is also proven that when applied to non laplace situations the laplace maximum likelihood estimator which may also be referred to as the nonlinear least absolute deviations estimator can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails a computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function simulation results are provided to validate the analytical findings

dynamics of a beam moving over multiple supports abstract the equations of motion of a beam moving over multiple supports are formulated based on hamilton s principle and the assumed mode method the supports are either roller supports which impart motion to the beam or frictionless supports with the beam being pushed or pulled over them in both cases the supports are regarded as very stiff springs acting on the moving beam a feature of the present formulation is that its complexity does not increase with an increased number of supports results of numerical simulations are presented for various prescribed motions of the beam

towards a mathematical theory of super resolution this paper develops a mathematical theory of super resolution broadly speaking super resolution is the problem of recovering the fine details of an object the high end of its spectrum from coarse scale information only from samples at the low end of the spectrum suppose we have many point sources at unknown locations in 0 1 and with unknown complex valued amplitudes we only observe fourier samples of this object up to a frequency cutoff fc we show that one can super resolve these point sources with infinite precision i e recover the exact locations and amplitudes by solving a simple convex optimization problem which can essentially be reformulated as a semidefinite program this holds provided that the distance between sources is at least 2 fc this result extends to higher dimensions and other models in one dimension for instance it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well we also show that the theory and methods are robust to noise in particular in the discrete setting we develop some theoretical results explaining how the accuracy of the super resolved signal is expected to degrade when both the noise level and the super resolution factor vary 2014 wiley periodicals inc

existence of solutions for generalized vector quasi variational like inequalities without monotonicity in this paper we introduce and study four kinds of generalized vector quasi variational like inequalities without monotonicity or pseudomonotonicity in hausdorff topological vector spaces by means of fixed point theorem we obtain some existence theorems of solutions for four kinds of generalized vector quasi variational like inequalities

existence of solutions for generalized implicit vector variational like inequalities abstract in this paper we introduce a new class of generalized implicit vector variational like inequalities in hausdorff topological vector spaces and banach spaces which contain implicit vector equilibrium problems implicit vector variational inequalities and implicit vector complementarity problems as special cases we derive some new results by using the kkm fan theorem under compact and noncompact assumptions on underlying convex sets

complex dynamics of high speed axially moving systems in this paper the dynamic response of a simply supported travelling beam subjected to a transverse load is investigated in the super critical speed range the well known axially moving beam theory is considered and a simple viscous damping mechanism has been introduced the displacement field is expanded in a series of the buckling modes a sine series and different techniques have been used in analyzing the response of the dynamical system periodic oscillations are studied by means of continuation techniques while non stationary dynamics are investigated through direct simulations a comparison with the literature and a convergence test on the series expansion are performed a sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability and direct simulations of global postcritical dynamics a complex scenario of alternate regular and chaotic motions is found in a large range of the main parameters

static elastica formulations of a pine conveying fluid an elastic pipe in an equilibrium configuration of arbitrary large deflection discharging fluid from its end experiences static centrifugal and frictional drag forces along its complete length these are however entirely equivalent to an end follower force of magnitude av 2 this equivalence is examined in detail by using the intrinsic field equations which are suitable for closed form solutions in terms of elliptic integrals once the pipe moves it also experiences gyroscopic coriolis forces along its length but these are not considered in this static examination it is shown in detail how a discharging pipe with end forces and moments is statically equivalent to a beam or strut with the same end forces and moments plus the reversed momentum vector av 2 it is seen that a cantilevered pipe with a free end can have no statical equilibrium states at all at either large or small deflections while pipes with constrained ends have large static deflections identical to those of the equivalent struts

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

maximum likelihood estimation of 2 d superimposed exponential signals the problem of maximum likelihood estimation of the parameters i e frequencies amplitudes and noise variance of 2 d superimposed exponential signals is considered in this paper a polynomial rooting approach is proposed to obtain the estimates of the 2 d frequencies strong consistency and limiting distribution are established for the estimates of the parameters furthermore the covariance matrix of the limiting distribution attains the cramer rao lower bound

convex low rank approximation low rank approximation is an important tool in many applications given an observed matrix with elements corrupted by gaussian noise it is possible to find the best approximating matrix of a given rank through singular value decomposition however due to the non convexity of the formulation it is not possible to incorporate any additional knowledge of the sought matrix without resorting to heuristic optimization techniques in this paper we propose a convex formulation that is more flexible in that it can be combined with any other convex constraints and penalty functions the formulation uses the so called convex envelope which is the provably best possible convex relaxation we show that for a general class of problems the envelope can be efficiently computed and may in some cases even have a closed form expression we test the algorithm on a number of real and synthetic data sets and show state of the art results

spectral analysis for the transverse vibration of an axially moving timoshenko beam the use of frequency dependent spectral element matrix or exact dynamic stiffness matrix in structural dynamics is known to provide very accurate solutions while reducing the number of degrees of freedom to resolve the computational and cost problems thus in the present paper the spectral element model is formulated for the axially moving timoshenko beam under a uniform axial tension the high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions the effects of the axial velocity and axial tension on the vibration characteristics the dispersion relation and the stability of a moving timoshenko beam are analytically and numerically investigated

supercritical stability of an axially moving beam part i model and equilibrium analysis axially moving material problems consider the dynamic response vibration and stability of long slender members which are in a state of translation this study focuses on the response of axially moving beam like elements at translation speeds that exceed the classical critical speed stability limit a non linear model for an axially moving beam is derived that accounts for the initial beam curvature induced by supporting pulleys or wheels presently the model is used to determine steady responses at critical and supercritical translation speeds the properties of the equilibrium problem are examined using an approximate linear solution and an exact non linear solution the deficiency of the linear solution is illustrated by its inability to capture essential features of the equilibrium problem particularly near and above the critical speed in this high speed region the translating beam undergoes large overall buckling deformations leading to multiple and bifurcated equilibrium states the stability of the equilibria is assessed in part ii

dynamic modeling of beams with non material deformation dependent boundary conditions abstract in conventional problems of structural mechanics both kinematic boundary conditions and external forces are prescribed at fixed material points that are known in advance if however a structure may move relative to its supports the position of the imposed constraint relations generally changes in the course of motion a class of problems which inherently exhibits this particular type of non material boundary conditions is that of axially moving continua despite varying in time the positions of the supports relative to the material points of the body have usually assumed to be known a priori throughout the deformation process in previous investigations this requirement is abandoned in the present paper where the dynamic behavior of a structure is studied which may move freely relative to one of its supports as a consequence the position of such a non material boundary relative to the structure does not only change in time but also depends on the current state of deformation of the body the variational formulation of the equilibrium relations of a slender beam that may undergo large deformations is presented to this end a theory based on reissner s geometrically exact relations for the plane deformation of beams is adopted in which shear deformation is neglected for the sake of brevity before a finite element scheme is developed a deformation dependent transformation of the beam s material coordinate is introduced by which the varying positions of the constraint relations are mapped onto fixed points with respect to the new non material coordinate by means of this transformation additional convective terms emerge from the virtual work of the inertia forces whose symmetry properties turn out to be different from what has previously been presented in the literature in order to obtain approximate solutions a finite element discretization utilizing absolute nodal displacements as coordinates is subsequently used in characteristic numerical examples which give an insight into the complex dynamic behavior of problems of this type on the one hand the free vibrations of a statically pre deformed beam are investigated on the other hand an extended version of the sliding beam problem is studied

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

asymptotic behavior of maximum likelihood estimates of superimposed exponential signals strong consistency and asymptotic normality are derived for the maximum likelihood estimates mles of the unknown parameters omega sub 1 omega sub p alpha sub 1 alpha sub p and sigma sup 2 in the superimposed exponential model for signals y sub t sigma alpha exp it omega sub k e sub t where the summation is from k 1 to p t 0 1 n 1 and sigma sup 2 is the variance of the complex normal distribution of e sub t as a by product it is found that the mles of the parameters attain the cramer rao lower bound for the asymptotic covariance matrix

dynamic stiffness matrix development and free vibration analysis of a moving beam abstract the dynamic stiffness matrix of a moving bernoulli euler beam is developed and used to investigate its free flexural vibration characteristics in order to develop the dynamic stiffness matrix it is necessary to derive and solve the governing differential equation of motion of the moving beam in closed analytical form the solution is then used to obtain the general expressions for both responses and loads boundary conditions are applied to determine the constants in the general solution leading to the formation of the frequency dependent dynamic stiffness matrix of the moving beam relating the amplitudes of the harmonically varying loads to those of the corresponding responses the application of the resulting dynamic stiffness matrix using the wittrick williams algorithm is demonstrated by some illustrative examples numerical results for both simply supported and fixed fixed end conditions of the beam are discussed and wherever possible some are compared with those available in the literature

vector variational like inequalities and non smooth vector optimization problems abstract in this paper we establish relationships between vector variational like inequality problems and non smooth vector optimization problems under non smooth invexity we identify the vector critical points the weakly efficient points and the solutions of the non smooth weak vector variational like inequality problems under non smooth pseudo invexity assumptions these conditions are more general than those existing in the literature

short kernel fifth order interpolation an explicit analytical formula for a short kernel fifth order polynomial interpolator is obtained it is also possible to obtain the explicit forms of even higher order interpolation kernels with the method of calculation used but it is seen that these local kernels become remainder dominated as the order increases the frequency domain properties and the accuracies of the obtained kernel and the known convolution kernels are compared frequency domain comparison with the cubic b spline interpolators is also given some cases of proper use of the calculated kernels have been pointed out

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

vandermonde decomposition of multilevel toeplitz matrices with application to multidimensional super resolution the vandermonde decomposition of toeplitz matrices discovered by caratheodory and fejer in the 1910s and rediscovered by pisarenko in the 1970s forms the basis of modern subspace methods for 1 d frequency estimation many related numerical tools have also been developed for multidimensional md especially 2 d frequency estimation however a fundamental question has remained unresolved as to whether an analog of the vandermonde decomposition holds for multilevel toeplitz matrices in the md case in this paper an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each toeplitz block a numerical method for searching for a decomposition is also proposed when the matrix rank is higher the new results are applied to study the md frequency estimation within the recent super resolution framework a precise formulation of the atomic ell 0 norm is derived using the vandermonde decomposition practical algorithms for frequency estimation are proposed based on the relaxation techniques extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared with the existing atomic norm and subspace methods

on the generalized vector variational inequality problem abstract in this paper we study vector variational inequalities with set valued mappings the concept of c x pseudomonotone mapping is introduced by employing the fan lemma we establish several existence results the new results extend and unify existence results of vector variational inequalities for single valued operators under the banach space setting

transition behaviour from string to beam for an axially accelerating material an approximate analytical expression for the natural frequency is given for the problem for velocity profiles harmonically varying about a mean velocity stability borders are determined analytically for fluctuation frequency versus amplitudes beam effects cause the stability boundaries to shift to higher frequency values

on generalized vector variational like inequalities abstract in this paper we consider a vector version of minty s lemma and obtain existence theorems for two kinds of variational like inequality a fixed point theorem is also discussed

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

stability in parametric resonance of axially accelerating beams constituted by boltzmann s superposition principle stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated the governing equation is derived from newton s second law boltzmann s superposition principle and the geometrical relation when the axial speed is a constant mean speed with small harmonic variations the governing equation can be treated as a continuous gyroscopic system with small periodically parametric excitations and a damping term the method of multiple scales is applied directly to the governing equation without discretization the stability conditions are obtained for combination and principal parametric resonance numerical examples demonstrate that the increase of the viscosity coefficient causes the lager instability threshold of speed fluctuation amplitude for given detuning parameter and smaller instability range of the detuning parameter for given speed fluctuation amplitude the instability region is much bigger in lower order principal resonance than that in the higher order

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

on the existence of solutions to generalized vector variational like inequalities abstract in this paper we consider a vector version of generalized minty s lemma and obtain existence theorems of solutions for two kinds of vector variational like inequalities

the non linear equations of motion of pipes conveying fluid abstract the non linear equations of motion of pipes conveying fluid are derived in simple and accessible terms by energy and newtonian methods different derivations are made for cantilevered pipes where the centreline is assumed inextensible and for pipes with both ends fixed it is shown that the derivations the origin of the various terms and the structure of the equations are distinctly different in these two cases the equations of motion are then compared with those already in existence e g by holmes rousselet and herrmann and lundgren sethna and bajaj at the same time clarifying the derivations and assumptions made and discussing the validity and completeness of the final equations some of the equations are found to be fully correct indeed superior to those derived here while others are found to be deficient because of assumptions made or inconsistencies in the derivations for pipes with both ends fixed the equations given in this paper are considered to be the most complete and correct

supercritical stability of an axially moving beam part ii vibration and stability analyses abstract this paper focuses on the stability of axially moving beam like materials e g belts bands paper and webs which translate at speeds near to and above the so called critical speed stability limit in the companion paper a theoretical model for an axially moving beam was presented which accounted for geometrically non linear beam deflections and the initial beam curvature generated by supporting wheels and pulleys in that paper analysis of steady response revealed that the beam possesses multiple non trivial equilibrium states when translating at supercritical speeds the equations of motion are presently linearized about these equilibria and their stability is predicted from the eigenvalue problem for free response asymptotic and numerical solutions to the eigenvalue problem are presented for the respective cases of small and arbitrary equilibrium curvature the solutions illustrate that the translating beam has multiple stable equilibrium states in the supercritical speed regime the solutions confirm that the critical speed behavior for axially moving materials is extremely sensitive to system imperfections such as initial curvature

nonlinear dynamics of cantilevered extensible pipes conveying fluid abstract in this paper the nonlinear planar dynamics of a fluid conveying cantilevered pipe is investigated the centreline of the pipe is considered to be extensible i e coupled longitudinal and transverse displacements are considered the extended version of the lagrange equations for systems containing non material volumes is employed to derive the equations of motion resulting directly in a set of coupled nonlinear ordinary differential equations the pseudo arclength continuation technique along with direct time integration are used to solve these equations bifurcation diagrams of the system are constructed as the flow velocity is increased these diagrams are supplemented by time traces phase plane portraits and fast fourier transforms for some sets of system parameters as opposed to the case of an inextensible pipe an extensible pipe elongates in the axial direction as the flow velocity is increased from zero depending on the system parameters this static elongation can be considerable at the critical flow velocity the system loses stability via a supercritical hopf bifurcation emerging from the trivial solution for the transverse displacement and leading to a flutter

a parameter estimation scheme for damped sinusoidal signals based on low rank hankel approximation most of the existing algorithms for parameter estimation of damped sinusoidal signals are based only on the low rank approximation of the prediction matrix and ignore the hankel property of the prediction matrix we propose a modified kumaresan tufts mkt algorithm exploiting both rank deficient and hankel properties of the prediction matrix computer simulation results demonstrate that compared with the original kumaresan tufts 1982 algorithm and the matrix pencil algorithm the mkt algorithm has a lower noise threshold and can estimate the parameters of signal with larger damping factors

on the dynamic properties of axially moving systems abstract the objective of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems such important mechanical systems exhibit interesting dynamic behaviors homoclinic orbits sub harmonic responses amplitude modulations and chaos these dynamics have been obtained numerically and in some cases have been experimentally observed using recent techniques of the non linear time series analysis the response of axially moving systems has been studied for a large variety of test cases the correlation dimension of the time series which is deeply related to the minimal dimension of a system able to reproduce the dynamics is estimated lyapunov exponents are evaluated in order to quantify the response regularity the present work gives a contribution towards understanding the complex dynamics observed both in conservative and dissipative systems the dynamical phenomena are analyzed within the unified framework of the non linear time series analysis in the case of experimental data the new non linear filtering techniques based on the embedding techniques have been applied to reduce high noise when classical techniques give bad results

fe analysis of a moving beam using lagrangian multiplier method lagrangian multiplier technique is employed to develop a h p version finite element model for a certain class of dynamics problems legendre polynomials are used as shape functions owing to its orthogonality property variational principle is the basis of this formulation with essential conditions applied via lagrangian multipliers the example considered here is a problem of a beam moving over supports response behavior of the beam is investigated for various longitudinal motions the present finite element model is validated by comparing the results with previous research work lagrangian multiplier implementation of the problem with finite element technique is very effective compared to other global methods such as assumed mode technique the inconsistencies in the model presented by lee 1993 are also pointed out

vibrations of an axially accelerating beam with small flexural stiffness transverse vibrations of an axially moving beam are considered the axial velocity is harmonically varying about a mean velocity the equation of motion is expressed in terms of dimensionless quantities the beam effects are assumed to be small since in this case the fourth order spatial derivative multiplies a small parameter the mathematical model becomes a boundary layer type of problem approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions results of both methods are contrasted with the outer solution

superfast approximative implementation of the iaa spectral estimate in this correspondence we develop superfast approximative one dimensional algorithms for the computationally efficient implementation of the recent iterative adaptive approach iaa spectral estimate the proposed methods are based on rewriting the iaa algorithm with suitable gohberg semencul representations solving the resulting linear systems of equations using the preconditioned conjugate gradient method where a novel preconditioning is applied using an incomplete factorization of the toeplitz matrix numerical simulations illustrate the efficiency of both the proposed preconditioning as well as the overall algorithm offering a computational reduction of up to two orders of magnitude as compared to our recently proposed efficient and exact iaa implementation

performance of high resolution frequencies estimation methods compared to the cramer rao bounds an explicit expression for the cramer rao bounds crbs and a calculation of the statistical perturbation of the covariance matrix due to additive noise are presented the results are applied to a statistical efficiency analysis of the main frequency estimation methods based on eigenvalue decomposition for the covariance matrix in order to characterize the perturbation of the signal subspace only the component of the perturbation of the eigenvectors orthogonal to the subspace is considered this gives a simpler and more significant form of the error covariance the treatment includes the cases of forward backward and moving averages the crb and estimation variances are calculated in the presence of additive random noise but for a given set of amplitudes characterized by their sample covariance matrix this approach is more realistic for the evaluation of efficiency in the small sample case

a new frequency estimation method for equally and unequally spaced data spectral estimation is an important classical problem that has received considerable attention in the signal processing literature in this contribution we propose a novel method for estimating the parameters of sums of complex exponentials embedded in additive noise from regularly or irregularly spaced samples the method relies on kronecker s theorem for hankel operators which enables us to formulate the nonlinear least squares problem associated with the spectral estimation problem in terms of a rank constraint on an appropriate hankel matrix this matrix is generated by sequences approximating the underlying sum of complex exponentials unequally spaced sampling is accounted for through a proper choice of interpolation matrices the resulting optimization problem is then cast in a form that is suitable for using the alternating direction method of multipliers admm the method can easily include either a nuclear norm or a finite rank constraint for limiting the number of complex exponentials the usage of a finite rank constraint makes in contrast to the nuclear norm constraint the method heuristic in the sense that the problem is non convex and convergence to a global minimum can not be guaranteed however we provide a large set of numerical experiments that indicate that usage of the finite rank constraint nevertheless makes the method converge to minima close to the global minimum for reasonably high signal to noise ratios hence essentially yielding maximum likelihood parameter estimates moreover the method does not seem to be particularly sensitive to initialization and performs substantially better than standard subspace based methods

an alternative approach for the analysis of nonlinear vibrations of pipes conveying fluid based on a novel extended version of the lagrange equations for systems containing non material volumes the nonlinear equations of motion for cantilever pipe systems conveying fluid are deduced an alternative to existing methods utilizing newtonian balance equations or hamilton s principle is thus provided the application of the extended lagrange equations in combination with a ritz method directly results in a set of nonlinear ordinary differential equations of motion as opposed to the methods of derivation previously published which result in partial differential equations the pipe is modeled as a euler elastica where large deflections are considered without order of magnitude assumptions for the equations of motion a dimensional reduction with arbitrary order of approximation is introduced afterwards and compared with existing lower order formulations from the literature the effects of nonlinearities in the equations of motion are studied numerically the numerical solutions of the extended lagrange equations of the cantilever pipe system are compared with a second approach based on discrete masses and modeled in the framework of the multibody software hotint mbs instability phenomena for an increasing number of discrete masses are presented and convergence towards the solution for pipes conveying fluid is shown

nonlinear vibrations of axially moving timoshenko beams under weak and strong external excitations in this paper nonlinear vibrations under weak and strong external excitations of axially moving beams are analyzed based on the timoshenko model the governing nonlinear partial differential equation of motion is derived from newton s second law accounting for the geometric nonlinearity caused by finite stretching of the beams the complex mode approach is applied to obtain the transverse vibration modes and the natural frequencies of the linear equation the method of multiple scales is employed to investigate primary resonances nonsyntonic excitations superharmonic resonances and subharmonic resonances some numerical examples are presented to demonstrate the effects of a varying parameter such as axial speed external excitation amplitudes and nonlinearity on the response amplitudes for the first and second modes when other parameters are fixed the stability of the response amplitudes is investigated and the boundary of instability is located

fast nearly ml estimation of the parameters of real or complex single tones or resolved multiple tones this paper presents new computationally efficient algorithms for estimating the parameters frequency amplitude and phase of one or more real tones sinusoids or complex tones cisoids in noise from a block of n uniformly spaced samples the first algorithm is an interpolator that uses the peak sample in the discrete fourier spectrum dfs of the data and its two neighbors we derive cramer rao bounds crbs for such interpolators and show that they are very close to the crb s for the maximum likelihood ml estimator the new algorithm almost reaches these bounds a second algorithm uses the five dfs samples centered on the peak to produce estimates even closer to ml enhancements are presented that maintain nearly ml performance for small values of n for multiple complex tones with frequency separations of at least 4 spl pi n rad sample unbiased estimates are obtained by incorporating the new single tone estimators into an iterative cyclic descent algorithm which is a computationally cheap nonlinear optimization single or multiple real tones are handled in the same way the new algorithms are immune to nonzero mean signals and provided n is large remain near optimal in colored and non gaussian noise

analysis of the dynamic stability of collar stiffened pipes conveying fluid abstract the dynamic stability of a collar stiffened pipe conveying fluid was examined by using the euler bernoulli beam theory the pipe considered consists of identical substructures or cells connected in an identical fashion each substructure or cell comprises a uniform pipe segment and a collar a finite element model was developed to predict the dynamic stability of the stiffened pipe under the action of the flowing fluid stability maps were obtained for clamped free collar stiffened pipes of various design parameters the design parameters included the arrangement and the geometry of the identical cells the stability maps demonstrated that the collar stiffened pipe exhibits unique stability characteristics when compared to a uniform pipe it was found that the stable region in the stability map enlarges for the collar stiffened pipe when compared to a uniform pipe to give clearer insight into the pipe dynamic behavior the dynamic response and eigenvalue branches were presented for a number of collar stiffened pipes

efficient implementation of iterative adaptive approach spectral estimation techniques this paper presents computationally efficient implementations for several recent algorithms based on the iterative adaptive approach iaa for uniformly sampled one and two dimensional data sets considering both the complete data case and the cases when the data sets are missing samples either lacking arbitrary locations or having gaps or periodically reoccurring gaps by exploiting the method s inherent low displacement rank together with the development of suitable gohberg semencul representations and the use of data dependent trigonometric polynomials the proposed implementations are shown to offer a reduction of the necessary computational complexity by at least one order of magnitude numerical simulations together with theoretical complexity measures illustrate the achieved performance gain

a constrained assumed modes method for solution of a new dynamic equation for an axially moving beam flexible beams with prismatic joints have complicated differential equations this complexity is mostly due to axial motion of the beam in the present research a horizontal flexible link sliding through a passive prismatic joint while attached to a rigid link of a robot moving in a vertical direction is considered a body coordinate system is used which aids in obtaining a new and rather simple form of the differential equation without the loss of generality to model the passive prismatic joint the motion differential equation is written in a form of virtual displacement next a solution method is presented for the lateral vibrations of the beam referred to as constrained assumed modes method unlike the traditional assumed modes method in the proposed constrained assumed modes method the assumed mode shapes do not each satisfy the geometrical boundary conditions of the point where passive prismatic joint is located instead by writing additional constraint equations the combination of the assumed modes will satisfy the geometrical boundary conditions at location of the passive prismatic joint two case studies for the effect of axial motion on lateral vibration of the beam are presented approximate analytical results are compared with fem results

hankel matrix nuclear norm regularized tensor completion for n dimensional exponential signals signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry biology and medical imaging for fast data acquisition or other inevitable reasons however only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic but existing approaches cannot efficiently recover n dimensional exponential signals with n geq 3 in this paper we study the problem of recovering n dimensional particularly n geq 3 exponential signals from partial observations and formulate this problem as a low rank tensor completion problem with exponential factor vectors the full signal is reconstructed by simultaneously exploiting the candecomp parafac tensor structure and the exponential structure of the associated factor vectors the latter is promoted by minimizing an objective function involving the nuclear norm of hankel matrices experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank

towards generalized fri sampling with an application to source resolution in radioastronomy it is a classic problem to estimate continuous time sparse signals like point sources in a direction of arrival problem or pulses in a time of flight measurement the earliest occurrence is the estimation of sinusoids in time series using prony s method this is at the root of a substantial line of work on high resolution spectral estimation the estimation of continuous time sparse signals from discrete time samples is the goal of the sampling theory for finite rate of innovation fri signals both spectral estimation and fri sampling usually assume uniform sampling but not all measurements are obtained uniformly as exemplified by a concrete radioastronomy problem we set out to solve thus we develop the theory and algorithm to reconstruct sparse signals typically sum of sinusoids from nonuniform samples we achieve this by identifying a linear transformation that relates the unknown uniform samples of sinusoids to the given measurements these uniform samples are known to satisfy the annihilation equations a valid solution is then obtained by solving a constrained minimization such that the reconstructed signal is consistent with the given measurements and satisfies the annihilation constraint thanks to this new approach we unify a variety of fri based methods we demonstrate the versatility and robustness of the proposed approach with five fri reconstruction problems namely dirac reconstructions with irregular time or fourier domain samples fri curve reconstructions dirac reconstructions on the sphere and point source reconstructions in radioastronomy the proposed algorithm improves substantially over state of the art methods and is able to reconstruct point sources accurately from irregularly sampled fourier measurements under severe noise conditions

on the boundary conditions for axially moving beams axially moving beam typed structures are of technical importance and present in a wide class of engineering problem as the axial speed of a beam may significantly affect the dynamic characteristics of the structure even at a low velocity it is important to accurately predict the dynamic characteristics and stability of such structures in most previous studies the net energy flux through the left end and right end boundaries of the finite beam over two simple supports has been implicitly assumed to be zero by completely ignoring the effects of its left incoming and right outgoing semi infinite beam parts or by applying fixed boundary conditions for its longitudinal vibration which seems to be very non realistic from the physical point of view thus this paper investigates the effects of the continuously incoming and outgoing semi infinite beam parts on the dynamic characteristics and stability of an axially moving beam by using the spectral element method the spectral element model is formulated from the equations of motion derived by using the hamilton s principle extended for the systems of changing mass it is numerically shown that the effects of the continuously incoming and outgoing semi infinite beam parts should be taken into account for further accurate prediction of the dynamic characteristics and stability for such axially moving beams

comments on non linear formulations for travelling string and beam problems abstract kinematic aspects of non linear travelling structure problems are reviewed and clarified in this paper the description of the motion of a structure can be based on two different formulations eulerian or mixed eulerian lagrangian the mixed formulation leads to simpler equations but it requires comprehensive restrictions these restrictions and the formulation itself are considered and explained the inertia terms of the equations of motion are derived and are shown to be the same as those in the earlier papers

vibration and stability of a cracked translating beam abstract the vibration and stability characteristics of a cracked beam translating between fixed supports are investigated using hamilton s principle and elementary fracture mechanics the equations of motion for the beam are developed throughout this analysis it is assumed that the crack is shallow and always remains open i e crack closure and the associated impact conditions are not considered in order to restrict attention to the open crack scenario parameter regimes corresponding to 1 a fully open crack 2 a fully closed crack and 3 a partly open partly closed crack are clearly identified for parameter values in regime 1 the free vibration characteristics are studied via an eigenanalysis this shows that the natural frequencies im and stability characteristics re fluctuate as the crack translates along with the beam between the two supports for the shallow cracks being considered the fluctuations are attributed primarily to the localized drop in the mass per unit length occurring at the crack rather than from the increased flexibility furthermore the magnitudes of these fluctuations are shown to vary with both the axial transport speed and the crack depth and are mapped in the control parameter space implications for the free and forced vibration problems are discussed

existence of solutions for vector optimization problems we define the generalized efficient solution which is more general than the weakly efficient solution for vector optimization problems and prove the existence of the generalized efficient solution for nondifferentiable vector optimization problems by using vector variational like inequalities for set valued maps

on generalized implicit vector equilibrium problems in banach spaces let x and y be real banach spaces k be a nonempty convex subset of x and c k 2 y be a multifunction such that for each email protected k c u is a proper closed and convex cone with intc u email protected where intc u denotes the interior of c u given the mappings t k 2 l x y a l x y l x y f 1 l x y xkxk y f 2 kxk y and g k k we introduce and consider the generalized implicit vector equilibrium problem find u k such that for any email protected k there is s tu satisfying f 1 as v g u f 2 v g u intc u by using the kkm technique and the well known nadler s result we prove some existence theorems of solutions for this class of generalized implicit vector equilibrium problems our theorems extend and improve the corresponding results of several authors

existence of vector quasi variational like inequalities for fuzzy mappings abstract the purpose of this paper is to study the existence problem of solutions for vector quasi variational like inequalities in fuzzy locally convex hausdorff topological vector spaces by using maximal element theorem and under suitable conditions some existence theorems for two types of vector quasi variational like inequalities are proved

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

new fluid velocity expression in an extensible semi circular pipe conveying fluid a new expression for fluid velocity is presented for a fluid conveying semi circular pipe with an extensible centreline the proposed fluid velocity expression is obtained from the material derivative while the previous velocity expressions are from love s kinematical relations in order to show that the new fluid velocity expression is more reasonable than the previous velocity expressions the equations of in plane motion derived with the new expression are compared to the equations derived with the previous expressions furthermore the equilibrium positions natural frequencies and mode shapes obtained with both the new and previous expressions are analysed and discussed

wave propagation in and vibration of a travelling beam with and without non linear effects part i free vibration the relation between the wave propagation and the free vibration in a travelling beam with simple supports has been thoroughly investigated the frequency equation of such a beam has been derived using the phase closure principle since the characters of the waves change drastically as the axial speed is increased beyond a certain value the phase closure principle has been applied differently in these two speed regimes the justifications for some approximate methods of obtaining the natural frequencies are also discussed lastly the non linear normal modes are derived again using the phase closure principle the computation of the forced response using the wave propagation approach is discussed in part ii

galerkin methods for natural frequencies of high speed axially moving beams in this paper natural frequencies of planar vibration of axially moving beams are numerically investigated in the supercritical ranges in the supercritical transport speed regime the straight equilibrium configuration becomes unstable and bifurcate in multiple equilibrium positions the governing equations of coupled planar is reduced to two nonlinear models of transverse vibration for motion about each bifurcated solution those nonlinear equations are cast in the standard form of continuous gyroscopic systems by introducing a coordinate transform the natural frequencies are investigated for the beams via the galerkin method to truncate the corresponding governing equations without nonlinear parts into an infinite set of ordinary differential equations under the simple support boundary numerical results indicate that the nonlinear coefficient has little effects on the natural frequency and the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters and the integro partial differential equation yields results quantitatively closer to those of the coupled equations

unitary esprit how to obtain increased estimation accuracy with a reduced computational burden esprit is a high resolution signal parameter estimation technique based on the translational invariance structure of a sensor array previous esprit algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary the authors present a simple and efficient method to constrain the estimated phase factors to the unit circle if centro symmetric array configurations are used unitary esprit the resulting closed form algorithm has an esprit like structure except for the fact that it is formulated in terms of real valued computations throughout since the dimension of the matrices is not increased this completely real valued algorithm achieves a substantial reduction of the computational complexity furthermore unitary esprit incorporates forward backward averaging leading to an improved performance compared to the standard esprit algorithm especially for correlated source signals like standard esprit unitary esprit offers an inexpensive possibility to reconstruct the impinging wavefronts signal copy these signal estimates are more accurate since unitary esprit improves the underlying signal subspace estimates simulations confirm that even for uncorrelated signals the standard esprit algorithm needs twice the number of snapshots to achieve a precision comparable to that of unitary esprit thus unitary esprit provides increased estimation accuracy with a reduced computational burden

a finite element formulation for sliding beams part i we use the updated lagrangian and the co rotational finite element methods to obtain solutions for geometrically non linear flexible sliding beams finite element formulations are normally carried out for fixed domains since the sliding beam is a system of changing mass first we discretize the system by introducing a variable domain beam element and model the sliding beam by a fixed number of elements with changing length second we transform the system governing equations of motion to a fixed domain and use conventional finite elements fixed size and number to discretize the system then our investigation is followed by a comparison between two formulations finally we use the co rotational method in conjunction with a variable domain beam element to obtain the discretized system equations to do so we consider the beam to slide with respect to a fixed channel and later we consider a formulation in which the beam remains at rest and the channel slides with a prescribed velocity we show that both formulations end up with identical discretized equations of motion 1998 john wiley sons ltd

on asymptotic normality of nonlinear least squares for sinusoidal parameter estimation this correspondence revisits the asymptotic normality question of the nonlinear least squares estimator for sinusoidal parameter estimation and fills a gap in the literature by providing a complete proof of the asymptotic normality under the assumption of additive non gaussian white noise the result shows that the nonlinear least squares estimator is able to asymptotically attain the cramer rao lower bound derived under the gaussian white noise assumption in situations where the actual noise distribution is non gaussian

on the transversal vibrations of an axially moving continuum with a time varying velocity transient from string to beam behavior in this paper an initial boundary value problem for a linear equation describing an axially moving stretched beam will be considered the velocity of the beam is assumed to be time varying since the order of magnitude of the bending stiffness terms depends on the vibration modes and the frequencies involved a combination of two simplified models that is a string equation for the lower frequencies and a beam with string effect equation for the higher frequencies will be used to describe the transversal vibrations of the system accurately based on the calculations of the natural frequencies the regions of applicability of these sub models will be determined a two time scales perturbation method will be used to construct formal asymptotic approximations of the solutions non resonant and some resonant cases will be studied for four different values of the relative errors an important implication of the earlier results in the literature is that for these types of axially moving continua problems the use of only string like models is not appropriate to describe the dynamics of these types of axially moving continua problems correctly one has to include small bending stiffness in the model in this paper it is explicitly shown how to work with a combined model that is a string model at the low frequencies and a tensioned beam model at the higher frequencies

generalized vector variational type inequalities solvabilities of generalized vector variational type inequalities gvvti are discussed in this work first the solvability of gvvti without monotone assumption for mappings is considered in reflexive banach spaces by using brouwer fixed point theorem browder fixed point theorem second the solvability of gvvti with monotone assumption for mappings is considered in reflexive banach spaces by using ky fan lemma