a return mapping algorithm for isotropic elastoplasticity a return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces constructed from all three invariants of the stress tensor based on the first order backward euler difference formula bdf the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter the stresses are recovered afterwards the solution concept is applied to a pressure independent yield function expressed in terms of the second and third invariant of the stress tensor the numerical performance of the method is demonstrated with two examples

consistent tangent operator for plasticity models based on the plastic strain rate potential a stress updating integration algorithm is derived for use with plastic strain rate potentials and with the backward implicit euler method an explicit expression is also deduced for the consistent tangent modulus this analysis extends an earlier treatment developed for elastic perfectly plastic materials in that it applies to materials which harden isotropically the method is intended for use in finite element calculations that employ plasticity models based on the plastic strain rate potential it is particularly suitable for cases where the form of the plastic dual potential has been obtained from texture measurements or from crystallographic models that describe texture evolution during metal forming

solution procedures for j3 plasticity and viscoplasticity abstract a solution strategy for plasticity and viscoplasticity models with isotropic yield surfaces depending upon all the principal invariants of the stress tensor is presented basically it requires the inversion of a fourth order positive definite tensor g both for the solution of the constitutive problem and for the evaluation of the consistent tangent operator it is proved that the assumption of isotropic elastic behaviour and the isotropy of the yield criterion entail an explicit representation formula for g 1 as linear combination of dyadic and square tensor products further an analogous representation formula for the consistent tangent operator is provided by exploiting basic composition rules between dyadic and square tensor products along with rivlin s identities for tensor polynomials all tensor operations required to compute the coefficients of the adopted representation formula for g 1 are carried out in intrinsic form it is thus shown that the relevant computational burden essentially amounts to solving a linear system of order three the performances of the proposed approach are illustrated by means of some numerical examples referred to the argyris failure criterion

non linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method abstract the incremental harmonic balance method is improved by i reversing the order of increment and linearization to find the bifurcated solution branches ii using a fast fourier transform to compute the solution increments and the floquet matrix and iii finding the secondary path after a bifurcation by an improved arc length method a system of two duffing oscillators linked with a linear stiffness is taken as a numerical example the qualitative change of solution due to the change of the linking stiffness is studied in detail

analysis of forced bilinear oscillators and the application to cracked beam dynamics a new closed form solution based on the use of two square wave functions to model stiffness change is proposed for bilinear oscillators under low frequency excitation the solution procedure is extended to cases with bilinear forcing function which usually occur in the dynamics of damaged structures the proposed solution provides the spectral pattern and the magnitude of each harmonic component for a damaged rectangular beam according to the size and location of the crack the predicted spectral pattern and the magnitude of each harmonic component for a simply supported beam containing a fatigue crack are validated by numerical simulation experimental work has not been done the results show that the proposed solution may be used to predict efficiently spectral patterns of damaged structures while avoiding lengthy computation such a procedure may be developed into an attractive on line diagnostic tool

the analysis of dynamic instability of a bimaterial beam with alternating magnetic fields and thermal loads abstract in this study the dynamic instabilities and transient vibrations of a bimaterial beam with alternating magnetic fields and thermal loads are investigated materials are assumed isotropic and the physical properties are assumed to have unique values in each layer based on the hamilton s principle the equation of motion is derived in which the damping factor the electromagnetic force the electromagnetic torque and the thermal load are considered the solution of thermal effect is obtained by superposing certain fundamental linear elastic stress states which are compatible with euler bernoulli beam theory using the galerkin s method the equation of motion is reduced to a time dependent mathieu equation the numerical results of the regions of dynamic instability are determined by the incremental harmonic balance ihb method and the transient vibratory behaviors are presented by the fourth order runge kutta method the results show that the responses of the dynamic instability and transient vibrations of the system are influenced by the temperature increase the magnetic field the thickness ratio the excitation frequency and the dimensionless damping ratio the effects of using different values of parameters are presented to display the instability and steady vibrations and reveal some interesting characteristics such as beats and resonance phenomenon

the analysis of dynamic instability on the large amplitude vibrations of a beam with transverse magnetic fields and thermal loads abstract the dynamic instability of a pinned beam subjected to an alternating magnetic field and thermal load with the nonlinear strain and made of physically nonlinear thermoelastic material has been studied applying the hamilton s principle the equation of motion with damping factor induced current and thermal load is derived using the galerkin s method the governing equation is reduced to a time dependent mathieu equation the incremental harmonic balance ihb method is applied to analyse the dynamic instability the effects of non dimensional parameters frequency ratio load factor amplitude a damping factor k1 and temperature increment t on the dynamic instability are obtained and discussed results show that the characteristics of magnetoelastic instability for the beam having the large deformation are distinctive from those of the beam having small deformation

a tight upper bound of the average absolute error in a constant step size sign algorithm a direct performance index of the adaptive filtering sign algorithm sa is the average absolute error aae at the output of the filter adopting this performance index an easy analysis of sa is achieved under a weak assumption it is proved for both deterministic and random inputs to the filter that the aae has a tight upper bound that exceeds the minimum aae by half the product of the step size and power of the filter input the assumption used is existence of average squared and average absolute values of filter input signals a practical interest of the result is that it provides a formula for the biggest step size as a function of tolerable adaptation noise to desired signal ratio

a general approach to the evaluation of consistent tangent operators for rate independent elastoplasticity abstract we present a general approach to the derivation of the explicit expression of tangent operators consistent with the finite step integration schemes of the flow rule for rate independent elastoplastic models with mixed hardening by exploiting the model of generalized standard material we show that the algorithmic tangent operator can be obtained by inverting a suitable positive definite matrix use of the sherman morrison woodbury formula allows us to reduce to a half the burden associated with such inversion and to derive an expression of the consistent tangent operator prone to computer implementation the application of the proposed approach to the von mises yield criterion with linear kinematic and isotropic hardening shows that the closed form expression of the operator can be obtained by a straightforward procedure

solution diagram of non linear dynamic systems by the ihb method abstract it is well known that a number of solutions may coexist in non linear systems therefore a complete solution diagram is very important in solving non linear vibration problems in order to ensure that all possible solutions have been sought this paper is aimed at seeking solution diagrams by means of performing parametric studies in particular the incremental harmonic balance ihb method is used in the study by introducing a parameter this method can give solution diagrams of different non linear dynamic systems even with strong non linearity examples of van der pol oscillators and coupled oscillators are used to illustrate the effectiveness of the method and the importance of obtaining solution diagrams hopf bifurcations will also be discussed with these solution diagrams

forced periodic vibration of unsymmetric piecewise linear systems the forced steady response of a single degree of freedom system involving a large non linearity represented by unsymmetric piecewise linear stiffness is determined by a harmonic balance newton raphson method with the application of the fast fourier transformation fft algorithm all possible subharmonic harmonic and superharmonic responses are sought the responses of two systems involving subharmonic and superharmonic dominant motions are calculated by the newly developed method and compared with previously published findings the results obtained by using this method reveal the details of the response of the systems more efficiently than previous methods

algebraically computable piecewise linear nodal oscillators a family of piecewise linear oscillators whose oscillation can be completely characterized by algebraic methods is studied it represents up to the best of authors s knowledge the first planar example where all the oscillation properties can be determined for all the values of the bifurcation parameter in fact algebraic expressions for coordinates of representative points period and characteristic multiplier of the corresponding periodic orbit are provided thus the studied family of oscillators deserves to be considered a good benchmark for testing approximate methods of analysis in nonlinear oscillation theory the piecewise linear oscillators studied are called nodal oscillators since their relevant linear parts are of node type and they are not perturbations of the harmonic oscillator they represent real models in practice as it is shown for an electronic circuit modeling a piecewise linear version of the classical van der pol oscillator

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

convergence of the sign algorithm for adaptive filtering with correlated data convergence of a decreasing gain sign algorithm sa for adaptive filtering is analyzed the presence of the hard limiter in the algorithm makes a rigorous analysis difficult therefore there are few results available such results normally include restrictive assumptions such as the assumptions that successive observation vectors are independent and the new error signal of the adaptive filter has a time invariant probability density function the former assumption is not valid in the context of adaptive filtering since two successive observation vectors share most of their components while the latter assumption is a restriction on the adaptive weights whose evolution is a priori unknown in lieu of using these assumptions an almost sure convergence of the sa is proved under the assumption that the sequence of observation vectors is m dependent this assumption allows strong correlation between successive observations

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

a precise calculation of bifurcation points for periodic solution in nonlinear dynamical systems this paper presented a precise yet efficient algorithm to determine bifurcation points of periodic solutions in nonlinear dynamical systems period doubling and symmetry breaking points were obtained to an accuracy of 10 11 the bifurcation points can be directly determined without a tedious trail and error process calculations and analysis on bifurcations of periodic solutions has played a pivotal role in nonlinear dynamics researches this paper presents an efficient and precise approach based on the incremental harmonic balance ihb method to exactly determine the critical points at which periodic solutions exhibit bifurcations the presented method is based on a fact that some zero harmonic coefficients vary as non zeros during the bifurcation of a periodic solution equating one of these coefficients to an infinitesimal quantity the bifurcation value can be determined by the ihb method with the control parameter varying numerical examples show that the critical values for the control parameter where a symmetry breaking or period doubling happens can be calculated very accurately importantly each bifurcation value can be directly obtained without a tedious trail and error process

non linear dynamic analysis and control of chaos for a two degrees of freedom rigid body with vibrating support abstract the dynamic behaviors of a two degrees of freedom rigid body with vibrating support are studied in this paper both analytical and computational results are employed to obtain the characteristics of the system by using the lyapunov direct method the conditions of stability of the relative equilibrium position can be determined the incremental harmonic balance method ihb is used to find the stable and unstable periodic solutions for the strongly non linear system by applying various numerical results such as phase plane poincare map time history and power spectrum analysis a variety of periodic solutions and the phenomena of the chaotic motion is presented the effects of the changes of parameters in the system can be found in the bifurcation diagrams further the chaotic behavior is verified by using lyapunov exponents the modified interpolated cell mapping method micm is used to study the basins of attraction of periodic attractors and the fractal structure besides additions of a constant torque a periodic torque addition of dither signals delayed feedback control adaptive control and bang bang control are used to control the chaos phenomena effectively

tracking analysis of the sign algorithm in nonstationary environments a tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented under the assumption that the nonstationary can be modeled using a random disturbance it is shown that the long term time average of the mean absolute error is bounded and that there exists an optimal choice of the convergence constant mu which minimizes this quality applying the commonly used independence assumption and under the assumption that the nonstationarity is solely due to the time varying behavior of the optimal coefficients it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode finally under the additional assumption that the signals involved are zero mean and gaussian a set of nonlinear difference equations is derived that characterizes the mean and mean squared behavior of the filter coefficients and the mean squared estimation error during adaptation and tracking results of several experiments that show very good correlation with the theoretical analyses are presented

the harmonic balance method with arc length continuation in rotor stator contact problems there are a variety of abnormal running conditions in rotating machinery which lead to rotor stator interaction dynamics which in turn can cause a rich mixture of effects associated with rub related phenomena these effects manifest themselves in the occurrence of multiple solutions for steady state vibration response scenarios including amplitude jumps during rotor acceleration and vibration responses at different multiple frequencies of excitation forces such as unbalance this paper describes a numerical algorithm based on the harmonic balance method to calculate the periodic response of a non linear system under periodic excitation the algorithm also calculates the stability of the periodic solutions found marks turning and bifurcation points and follows a solution branch over varying system parameters via arc length continuation

bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method abstract the periodic motions of a non linear geared rotor bearing system are investigated by the incremental harmonic balance ihb method a path following procedure using arc length continuation technique is used to trace the bifurcation diagrams the system exhibits a period doubling route and a quasiperiodic route to chaos in different regions of excitation frequency the chaotic motions are investigated by numerical integration and the lyapunov exponents are computed the periodic solutions and subharmonic solutions obtained by the ihb method compare very well with those obtained by numerical integration

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

the analysis of dynamic instability and vibration motions of a pinned beam with transverse magnetic fields and thermal loads abstract dynamic instability and transient vibrations of a pinned beam with transverse magnetic fields and thermal loads are studied the magnetoelastic model whose beam thickness and the deflection are very small compared with the length is taken for analysis applying the hamilton s principle the equation of motion with damping factor is derived the governing equation is reduced to the mathieu equation by galerkin s method with the assumed mode shape the incremental harmonic balance ihb method is applied to analyze the dynamic instability the amplitude versus time behavior of the system is investigated by using the runge kutta method the study shows that the instability and transient vibratory behaviors of the beam are influenced by the magnetic fields thermal loads and the frequencies of oscillation of the transverse magnetic field the beat phenomenon and primary resonance are presented and discussed when the frequencies of the oscillating transverse magnetic field are close to the fundamental natural frequency of the system

convergence analysis of the sign algorithm without the independence and gaussian assumptions the paper is concerned with rigorous convergence analysis of the sign algorithm sa in the context of adaptive plant identification asymptotic time averaged convergence for the mean absolute weight misalignment is proved for all values of the algorithm step size and initial weight vector the paper has three main contributions with respect to available convergence results of the sa the first is the deletion of the gaussian assumption which is important when covering the case of discrete valued data no assumption about the distribution of the regressor sequence is used except for the usual assumption of positive definite covariance matrix the assumptions used about the noise allow nonexistence unboundedness and vanishing of the noise probability density function for arguments strictly different from zero the second contribution is the deletion of the assumption of independent successive regressors this deletion is important since in applications two successive regressors usually share all their components except two hence they are strongly dependent even for white plant input the case of colored noise is also analyzed finally the third contribution is the extension of the above results to the nonstationary case the used assumptions allow nonstationarity of the plant input plant noise and plant parameters

a frequency domain based numeric analytical method for non linear dynamical systems abstract in this paper a multiharmonic balancing technique is used to develop certain algorithms to determine periodic orbits of non liner dynamical systems with external parametric and self excitations essentially in this method the non linear differential equations are transformed into a set of non linear algebraic equations in terms of the fourier coefficients of the periodic solutions which are solved by using the newton raphson technique the method is developed such that both fast fourier transform and discrete fourier transform algorithms can be used it is capable of treating all types of non linearities and higher dimensional systems the stability of periodic orbits is investigated by obtaining the monodromy matrix a path following algorithm based on the predictor corrector method is also presented to enable the bifurcation analysis the prediction is done with a cubic extrapolation technique with an arc length incrementation while the correction is done with the use of the least square minimisation technique the under determined system of equations is solved by singular value decomposition the suitability of the method is demonstrated by obtaining the bifurcational behaviour of rolling contact vibrations modelled by hertz contact law

period one motions of a mechanical oscillator with periodically time varying piecewise nonlinear stiffness the dynamic behavior of a piecewise nonlinear mechanical oscillator with parametric and external excitations is investigated the viscously damped single degree of freedom oscillator is subjected to a periodically time varying piecewise nonlinear restoring function defined by a clearance surrounded by continuously nonlinear quadratic and cubic regions typical applications represented by this oscillator are highlighted a multi term harmonic balance formulation is used in conjunction with discrete fourier transforms and a parametric continuation scheme to determine steady state period 1 motions of the system due to both parametric and external excitations the accuracy of the analytical solutions is demonstrated by comparing them to direct numerical integration solutions floquet theory is applied to determine the stability of the steady state harmonic balance solutions at the end detailed parametric studies are presented to quantify the combined influence of clearance quadratic and cubic nonlinearities within reasonable ranges of all other system parameters a comparison between time varying and time invariant systems is also provided to demonstrate the influence of the parametric and external excitations on a piecewise nonlinear system

a return map algorithm for general isotropic elasto visco plastic materials in principal space we describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto visco plastic models whose yield function incorporates the third stress invariant the developments presented are based upon original results proved in the paper concerning the derivatives of eigenvalues and eigenprojectors of symmetric second order tensors with respect to the tensor itself and upon an original algebra of fourth order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument the analysis initially referred to the small strain case is then extended to a formulation for the large deformation regime for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the lagrangian description of large strain elastoplasticity copyright 2004 john wiley sons ltd

effect of smoothing piecewise linear oscillators on their stability predictions the effects of smoothing non smooth function on estimation of dynamical stability of the periodic response determined in the frequency domain are considered in this paper for that purpose a simple single degree of freedom system with piecewise linear force displacement relationship subjected to a harmonic force excitation is analyzed stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the floquet liapounov theorem results obtained are verified in the time domain by the method of piecing the exact solutions and runge kutta integration routine

large amplitude non linear normal modes of piecewise linear systems a numerical method for constructing non linear normal modes nnms for piecewise linear autonomous systems is presented these nnms are based on the concept of invariant manifolds and are obtained using a galerkin based solution of the invariant manifold s non linear partial differential equations the accuracy of the constructed non linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution in both time and frequency domains it is found that this construction approach can accurately capture the nnms over a wide range of amplitudes including those with strong non linear effects several interesting dynamic characteristics of the non linear modal motion are found and compared to those of linear modes a two degree of freedom example is used to illustrate the technique the existence stability and bifurcations of the nnms for this example are investigated

nonlinear analysis of a geared rotor system supported by fluid film journal bearings abstract this paper presents a novel approach for modeling and analyzing a geared rotor bearing system including nonlinear forces in the gear set and the supporting fluid film journal bearings the rotordynamics system model has five degrees of freedom that define the transverse displacements of the shaft gear centerlines and the relative displacement of the gear tooth contact point the journal bearing nonlinear forces are obtained via a solution of reynolds equation for lubricant film pressure utilizing the finite element method co existing steady state autonomous and non autonomous responses are obtained in an accurate and computationally efficient manner utilizing the multiple shooting and continuation algorithms this yields the full manifolds of the multiple bifurcation system chaos is identified with maximum lyapunov exponents frequency spectra poincare attractors etc the results reveal a dependence of the gear set contact conditions and system nonlinear response characteristics i e jump co existing responses subharmonic resonances and chaos on the choice of journal bearing parameters the results also show that hopf bifurcations which occur along with oil whirl in a journal bearing system can be attenuated by increasing the gear torque

a tangent secant approach to rate independent elastoplasticity formulations and computational issues a general and robust solution procedure for nonlinear finite element equations in small strain elastoplastic structural problems is presented its peculiar feature lies in the choice of the most suitable constitutive operator to be adopted at each iteration of a generic load step in order to ensure the utmost stability and convergence rate namely the consistent tangent operator is replaced by a secant one or vice versa whether the adopted norm of the residual does not or does conveniently decrease at the current iteration the secant operator is defined as to recover the finite step increment of the plastically admissible stress from the total not iterative strain increment the original formulation of the solution procedure consisting of alternate tangent and secant iterations is then extended to achieve an effective coupling with line searches the excellent performances of the two procedures are illustrated by numerical examples carried out for typical benchmark problems in plane strain and three dimensional cases

periodic forced vibration of unsymmetrical piecewise linear systems by incremental harmonic balance method abstract a single degree of freedom non linear system subjected to periodic excitation is considered the non linearity is in the restoring force and is represented by unsymmetrical piecewise linear stiffness the steady state response are analysed by an extended incremental harmonic balance ihb method all possible subharmonic harmonic and superharmonic resonances and bifurcations are sought the results reveal some interesting details of responses of unsymmetrical piecewise linear systems comparisons with available published findings are also made

a three invariant cap viscoplastic rate dependent damage model for cementitious materials with return mapping integration in haigh westergaard coordinate space abstract we present a new strain rate dependent elasto viscoplastic damage constitutive model for cementitious materials by incorporating duvaut lions viscoplasticity generalized to multi surface plasticity c f simo et al 1988b simo and hughes 1998 followed by strain rate dependent damage initiation and evolution under multiaxial loading to our previous inviscid elastoplastic damage model paliwal et al 2017 we also present a unique numerical scheme in which the integration algorithm for modeling elastoplastic response utilizes fully implicit backward euler method in which the governing system of non linear equations are solved in the space of invariants based on haigh westergaard coordinate system hardening parameter and discretized plastic multiplier it uses the framework by matzenmiller and taylor 1994 which is modified in this work this is particularly useful as the yield criteria flow rule and the non linear hardening utilize functions that are dependent on the pressure effective shear stress and lode angle components of the stress tensor to the best of authors knowledge such integration algorithm in haigh westergaard coordinate space has never been developed for lode angle dependent yield criteria and the flow rule and non linear hardening plasticity furthermore we also develop an accurate form for the algorithmic elastoplastic damage tangent modulus consistent with the proposed return mapping technique numerical simulations of uniaxial tension and compression cases demonstrate that both the local integration point algorithm as well as the global algorithm using the algorithmic elastoplastic damage tangent modulus exhibit quadratic convergence finally the predictive capability of the proposed model is demonstrated by virtue of several numerical examples under various loading conditions covering different stress paths and different dynamic strain rates these predictions are also compared against experimental results and experimentally observed features from tests on various concrete specimens and demonstrate excellent agreement

almost sure convergence of a decreasing gain sign algorithm for adaptive filtering the convergence analysis of a sign algorithm with decreasing gain when governing the weights of an adaptive filter is presented the analysis is done in a noiseless case a rigorous proof of almost sure convergence to the optimal filter is attained under a weak ergodicity assumption that includes the case important in practice of correlated observations

subharmonic resonances of a mechanical oscillator with periodically time varying piecewise nonlinear stiffness abstract the subharmonic period 1 motions of a piecewise nonlinear pn mechanical oscillator having parametric and external excitations are investigated the system is formed by a viscously damped single degree of freedom oscillator subjected to a periodically time varying pn stiffness defined by a clearance surrounded by continuous forms of nonlinearity a multiterm harmonic balance formulation in conjunction with discrete fourier transforms is used to determine steady state period motions of the system near the parametric instability regions the accuracy of analytical solutions is verified through a comparison with direct numerical integration results a parametric study is also presented to demonstrate the combined influence of a clearance and of cubic nonlinearities on period motions within typical ranges of system and excitation parameters

frequency response characteristics of a multi degree of freedom system with clearances abstract in an earlier study the frequency response characteristics of a single degree of freedom system with a clearance non linearity were studied the current study an extension of the earlier work is concerned with the frequency response characteristics of a multi degree of freedom system with clearances the method of harmonic balance is used to develop approximate analytical solutions of the undamped equations of motion of a multi degree of freedom system composed of three coupled non linear oscillators for primary resonances and a harmonic excitation general formulations are presented which can be used to study both the existence and the stability of the solutions these general formulations are used to discuss a number of modal spacing and modal coupling issues an analysis methodology for multi degree of freedom systems is introduced and illustrated by two special but practical cases a strongly non linear system and a weakly non linear system the results of the analysis of the special cases are validated by using analog simulation it is shown that an analysis of the special cases of the general multi degree of freedom non linear formulation can provide not only an improved understanding of the dynamic behavior of non linear systems but also can be used as the basis for the development of simplified approximate solutions the limitations of the current study and areas for further research are discussed

non linear real and complex modes of conewise linear systems abstract conewise piecewise linear non gyroscopic and gyroscopic autonomous systems are studied in detail first the general properties of such systems are examined then the non linear real and complex modes are obtained for both non gyroscopic and gyroscopic cases by means of analytical or numerical tools several interesting characteristics of non linear modes are found and compared to those of linear modes accurate analytical estimates of non linear mode periods are formulated for both non gyroscopic and gyroscopic systems the validity of such estimates is discussed in relation to a non linear mode bifurcation phenomenon which is located by using both characteristic multipliers and poincare mapping

numerical scheme of locating the periodic response of non smooth non autonomous systems of high dimension abstract the paper presents a numerical scheme of locating the periodic response of high dimensional systems with non smooth characters such as clearances constraints frictions the basic idea comes from the fact that an asymptotic stable periodic response of the system attracts its transient response and it may be extracted from the transient response somehow the paper thus suggests a novel iteration scheme to extrapolate the periodic response from a short time history of the transient response by curve fitting compared with the current schemes such as shooting incremental harmonic balancing and their improved forms the present scheme makes full use of the information within the transient response and the system characters so that the computational efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved

linearization and return mapping algorithms for elastoplasticity models the return mapping algorithm is one of the most efficient procedures to solve elasto plastic problems however a criticism that may be lodged against this method is the difficulty of the practical computation of the consistent tangent matrix when the return is non radial much research has been done to handle this matrix in this paper a unified approach is presented in such a way that a simple closed form expression gives the consistent tangent matrix for the classical constitutive relations von mises tresca mohr coulomb drucker prager the basic ideas are in the properties of eikonal equations appearing in several fields as image treatment short time computation in elastic waves and others the same kinds of ideas can be extended to non classical models copyright 2003 john wiley sons ltd

stochastic approximation with correlated data new almost sure convergence results for a special form of the multidimensional robbins monro stochastic approximation procedure are developed the results are applicable to cases where the training data is heavily correlated no conditional expectation properties or boundedness assumptions are required to apply the new results for example when the data sequence is normal and i m dependent ii autoregressive moving average or iii band limited the results can be used to establish the almost sure convergence of each algorithm treated the special form of the robbins monro procedure considered is motivated by a consideration of several algorithms that have been proposed for discrete time adaptive signal processing applications most of these algorithms can also be viewed as stochastic gradient following algorithm the ease with which the new results can be applied is illustrated

adaptive filtering with binary reinforcement recently there has been increased interest in high speed adaptive filtering where the usual stochastic gradient or least mean square lms algorithm is replaced with the simpler algorithm where adaptation is guided only by the polarity of the error signal in this paper the convergence of this binary reinforcement br algorithm is proved under the usual independence assumption and the surprising observation is made that unlike the lms algorithm convergence occurs for any positive value of the step size parameter while the stochastic gradient algorithm attempts to minimize a mean square error cost function the binary reinforcement algorithm in fact attempts to minimize a mean absolute error cost function it is proved for the binary reinforcement algorithm that the tap weight vector converges in distribution to a random vector that is suitably concentrated about the optimal value based on a least mean absolute error cost function for a sufficiently small step size the expected cost of the asymptotic weight vector can be made as close as desired to thc minimum cost attain ed by the optimum weight vector

comparison of the convergence of two algorithms for adaptive fir digital filters the convergence properties of two different algorithms for the updating of the coefficients of an adaptive fir digital filter are investigated and compared with one another these algorithms are the stochastic iteration algorithm and the sign algorithm in this latter algorithm a one bit gradient estimation is used which makes its implementation very simple the convergence is characterized by the residual echo variance after convergence and a parameter that indicates the speed of the convergence it is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained

dynamics and the periodic solutions of the delayed non smooth internet tcp red congestion control system via hb aft abstract this paper has attended to obtain the approximate analytical expressions of periodic solutions in the delayed non smooth internet tcp red congestion control system employing the semi analytical method named as the harmonic balance method with alternating frequency time hb aft domain technique for the first time the methodology presented herein provides the accurate approximate analytical expressions of periodic solutions including the non impacting periodic solutions and impacting periodic solutions in the non smooth dynamical system with time delays they agree very well with the results of numerical simulations by matlab it implies that the proposed method in this paper is accurate and effective furthermore rich dynamics of this delayed non smooth system is discovered in the present paper three kinds of bi stability i e coexistence of asymptotically stable equilibrium and equilibrium equilibrium and periodic solution periodic solution and periodic solution have been found in the system with the variation of the delay and the grazing solution the impacting solution traversing both the lower threshold tmin and the larger threshold tmax and a route to chaos i e intermittent to chaos have been also obtained by varying the delay employing numerical method

convergence of an adaptive linear estimation algorithm in this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations two complementary contributions are added to the famous 1977 ljung theorem first we drop the condition of nondivergence of the algorithm assumed by ljung while that condition can be ensured by adding a barrier the convergence of the suitably bounded algorithm itself is not established even on the basis of ljung theorem here the barrier problem is overcome by proving that it is not necessary for the convergence our second contribution is to generalize the model describing the correlated observations no state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed instead we use a decreasing covariance model that agrees with a very wide class of practical applications

optimization of nonlinear structural resonance using the incremental harmonic balance method abstract we present an optimization procedure for tailoring the nonlinear structural resonant response with time harmonic loads a nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinear vibration analysis an optimization procedure based on a gradient based algorithm is developed and we use the adjoint method for efficient computation of design sensitivities we consider several examples in which we find optimized beam width distributions that minimize or maximize fundamental or super harmonic resonant responses

a wavelet based method for the forced vibration analysis of piecewise linear single and multi dof systems with application to cracked beam dynamics abstract the present investigation outlines a method based on the wavelet transform to analyze the vibration response of discrete piecewise linear oscillators representative of beams with breathing cracks the displacement and force variables in the governing differential equation are approximated using daubechies compactly supported wavelets an iterative scheme is developed to arrive at the optimum transform coefficients which are back transformed to obtain the time domain response a time integration scheme solving a linear complementarity problem at every time step is devised to validate the proposed wavelet based method applicability of the proposed solution technique is demonstrated by considering several test cases involving a cracked cantilever beam modeled as a bilinear sdof system subjected to a harmonic excitation in particular the presence of higher order harmonics originating from the piecewise linear behavior is confirmed in all the test cases parametric study involving the variations in the crack depth and crack location is performed to bring out their effect on the relative strengths of higher order harmonics versatility of the method is demonstrated by considering the cases such as mixed frequency excitation and an mdof oscillator with multiple bilinear springs in addition to purporting the wavelet based method as a viable alternative to analyze the response of piecewise linear oscillators the proposed method can be easily extended to solve inverse problems unlike the other direct time integration schemes

steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non linearity a mechanical system exhibiting combined parametric excitation and clearance type non linearity is examined analytically and experimentally in an effort to explain complex behavior that is commonly observed in the steady state forced response of rotating machines the specific case of a preloaded mechanical oscillator having a periodically time varying stiffness function and subject to a symmetric backlash condition is considered a generalized solution methodology is proposed based on the harmonic balance method the resulting non linear algebraic equations are solved by using a direct newton raphson technique in which a closed form jacobian matrix is computed using frequency domain methods analytical solutions are validated by comparison with numerical integration results and experimental measurements obtained from a gear dynamics test rig

non linear dynamic interactions of a jeffcott rotor with preloaded snubber ring a two degrees of freedom model of a jeffcott rotor with a preloaded snubber ring subjected to out of balance excitation has been developed the purely impact interactions have been investigated the rotor makes intermittent contacts with the preloaded snubber ring and as a consequence it can be in one of five different contact regimes which boundaries have been found analytically the current location of the snubber ring has been determined using the principle of the minimum elastic energy in the snubber ring consequently a non linear piecewise smooth dynamical system has been obtained and studied numerically the results in form of bifurcation diagrams phase portraits and poincare maps show significant differences for the cases with and without preloading

asymptotic analysis of stochastic gradient based adaptive filtering algorithms with general cost functions this paper presents an analysis of stochastic gradient based adaptive algorithms with general cost functions the analysis holds under mild assumptions on the inputs and the cost function the method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates whereas previous stochastic analyses typically considered mean and mean square behavior the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time furthermore almost sure exponential bounds are given for the rate of convergence of the parameter estimates the asymptotic distribution of the parameter estimates is shown to be gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics specific adaptive algorithms that fall under the framework of this paper are signed error least mean square lms dual sign lms quantized state lms least mean fourth dead zone algorithms momentum algorithms and leaky lms

nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities abstract this paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities the galerkin method is employed to discretize the governing equations a high dimensional model that can take nonlinear model coupling into account is derived and the incremental harmonic balance ihb method is employed to obtain the steady state response of the curved beam the cases investigated include softening stiffness hardening stiffness and modal energy transfer the stability of the periodic solutions for given parameters is determined by the multi variable floquet theory using hsu s method particular attention is paid to the anti symmetric response with and without excitation as the excitation frequency is close to the first and third natural frequencies of the system the results obtained with the ihb method compare very well with those obtained via numerical integration

analysis of periodically forced nonlinear hill s oscillator with application to a geared system although nonlinear systems subject to combined parametric and external excitations have been examined in some depth very few of these investigations have addressed the influence of a mean time invariant load on the system response in particular the importance of the mean load effect has been highlighted in the study of whirling asymmetric shafts where significant changes in system response and stability occur under the influence of gravity the present paper intends to characterize the specific effect of mean load on the dynamic behavior of a hill s oscillator with a clearance type nonlinearity while also being subjected to a periodic base displacement excitation the parametric continuation technique and method of harmonic balance would be used for this purpose issues discussed would include the coupling between the mean load and the dynamic response amplitude interaction between the parametric excitation effect and the clearance nonlinearity and comparison between time invariant and time varying systems further a geared system has been analyzed as a practical application of the nonlinear hill s equation examined earlier studies on gear dynamics have been reexamined to provide improved correlation with prior experimental data new interpretations for some of the nonlinear phenomena in the experimental data has also been provided based on our study

bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method abstract in this paper an explicit formulation of the incremental harmonic balance ihb scheme for computation of periodic solutions of a harmonically excited oscillator which is asymmetric with both stiffness and viscous damping piecewise linearities is derived analysis of dynamical behavior as bifurcation and chaos of the non linear vibration system considered is effectively carried out by the ihb procedure showing that the system exhibits chaos via the route of period doubling bifurcation with coexistence of multiple periodic attractors observed and analyzed by the interpolated cell mapping method in addition numerical simulation by the ihb method is compared with that by the fourth order runge kutta numerical integration routine which shows that this method is in many respects distinctively advantageous over classical approaches and especially excels in performing parametric studies

optimum step size of sign algorithm for nonstationary adaptive filtering the adaptive filtering sign algorithm is analyzed in the case of nonstationary and correlated data the excess time average absolute estimation error eaae is used as a performance index of the algorithm it is proved that the eaae is the sum of two terms one proportional to the algorithm step size mu and the other proportional to 1 mu the optimum step size that minimizes the eaae is found equal to square root q p with q being the power of fluctuations of the optimal filter weights and p being the power of filter input this formula is derived under the assumption that increments of optimal filter weights are white computer simulations are used to examine the validity of the formula for other models of variation of the optimal filter simulation results show a good fit with the obtained optimum step size formula

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow