phenomenon of stochastic resonance caused by multiplicative asymmetric dichotomous noise the exact expression of the first moment and the signal to noise ratio snr have been calculated for a linear system subject to an external periodic field as well as a multiplicative asymmetric dichotomous noise by using the shapiro loginov formula it has been found that the amplitude of the output signal and the snr respectively exhibit two kinds of the phenomena of stochastic resonance one is as the functions of the parameters of the asymmetric dichotomous noise such as the noise strength d and the parameter k describing the asymmetric degree of the dichotomous noise the other is as the function of the parameter of the input signal such as the input signal frequency ensuremath omega

noise induced chaos and phase space flux abstract we study the effect of additive noise on near integrable second order dynamical systems whose unperturbed flows have homoclinic or heteroclinic orbits the noise is represented by a type of shinozuka stochastic process capable of arbitrarily closely approximating gaussian noise with any specified spectrum we derive a formula for the flux factor applicable for any asymptotic mean stationary excitation this derivation shows that to first order the effect of the external excitation on the system is mediated by a linear filter associated with the system homoclinic or heteroclinic orbit it also shows that the stationary mean distribution of the filtered excitation determines the average phase space flux this is true for both random and nonrandom excitations and indicates that for the dynamical systems considered here these two classes of excitation play substantially equivalent roles in the promotion of chaos

agreement between two independent groups of raters we propose a coefficient of agreement to assess the degree of concordance between two independent groups of raters classifying items on a nominal scale this coefficient defined on a population based model extends the classical cohen s kappa coefficient for quantifying agreement between two raters weighted and intraclass versions of the coefficient are also given and their sampling variance is determined by the jackknife method the method is illustrated on medical education data which motivated the research

analysis of kinematic linked interpolation methods for reissner mindlin plate problems the approximation to the solution of reissner mindlin plate problem is considered in the framework of finite element techniques a general strategy involving a linking operator between rotations and vertical displacements is analyzed an abstract convergence result is provided examples of elements falling into this framework are presented and shown to be stable and locking free numerical tests detail the performances of the elements email lovadina ing unitn it

parametric tests for agreement amongst groups of judges summary series approximations to the logarithm of the probability of a permutation of the natural numbers 1 k using an extension of the thurstone model are investigated the asymptotic bias of the quadratic and cubic approximations using the normal density is shown to be small approximate likelihood ratio tests are considered for testing for agreement between and within groups of judges and x2 approximations seem adequate for significance levels

randomly disordered periodic induced chaos in a piezoelectric vibration energy harvester system with fractional order physical properties abstract the chaotic behavior of the piezoelectric vibration energy harvester veh system with fractional order physical properties under randomly disordered periodic excitations is investigated by using random melnikov method a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system the results indicate that the increase of the noise intensity will result in the occurrence of chaos and the changes of the possible chaotic region in phase space which first enlarging and then shrinking with a change in trend the threshold of amplitude of randomly disordered periodic for the onset of chaos is determined by the numerical calculation via the largest lyapunov exponent the effects of noise intensity on chaos are also investigated through the largest lyapunov exponent phase portraits poincare maps at the same time the effects of intensity of random frequency on the mean square voltage are further discussed which show that the square voltage is in positive proportion to the size of the chaotic region it is demonstrated that the essential changes of the dynamical behavior of the piezoelectric energy harvester system with fractional order physical properties will occur through changing the noise intensity which can not only induce or suppress the onset of the chaos but also raise or reduce the mean square voltage finally the 0 1 test of responses is used to quantify the responses of veh system which further supports the effects of noise intensity on chaotic behavior of the system

a class of nonparametric tests based on multiresponse permutation procedures summary a class of univariate rank tests based on multiresponse permutation procedures is introduced asymptotic equivalence is established between one member of this class and the kruskal wallis test simulated power comparisons for location shift detection indicate that another member of the class provides superior detection efficiency for location shifts of bimodal distributions and of heavy tailed unimodal distributions furthermore both tests possess substantial computational advantages over other members of the class

slow sweep through a period doubling cascade delayed bifurcations and renormalisation abstract we investigate analytically the effect on a period doubling cascade of slowly sweeping the bifurcation parameter by means of asymptotic calculations first we analyse the behaviour of the orbits when sweeping through one period doubling bifurcation there is still an effective bifurcation called a dynamic bifurcation but which is delayed we compute the delay sweeping in forward and backward directions yields qualitatively different results the presence of noise in the system even of small intensity turns out to play a key role we analyse the various behaviours as a function of the relative sizes of the sweep rate and the noise intensity in order to tackle the sweep through a whole cascade we extend the renormalisation theory for period doubling of one dimensional maps to non autonomous maps the particular we show that a slow linear of the parameter results in a new unstable eigenvalue which provides a scaling law for the sweep rate taking also into account the effect of noise we then derive an asymptotic scaling for the successive period doubling bifurcations as a result of the sweep and the noise only a finite number of doublings can be observed we estimate this maximum number we also show how to estimate the location of the real bifurcation of the real points from results of experiments with non zero sweep velocity when the functions involved to be analytic we show that the delay of a period doubling bifurcation due to sweep depends crucially on their degree of smoothness in both the analytic and non analytic cases we give insight into the geometry of some invariant curves reminiscent of an accordion our analysis explains numerical and experimental results on the problem

the patch test for mixed formulations this paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence the general algebraic conditions of babuska and brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems the test is also applied to mixed displacement strain formulations of elasticity and limiting formulations are noted

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

noise induced effects on period doubling bifurcation for integrate and fire oscillators this study provides a method for calculating first order approximations of the lyapunov exponents of systems with discontinuity in the presence of noise in order to characterize the stability of motions in those systems this paper in particular illustrates the results of the ways in which noise influences period doubling bifurcation in the parameter space of an integrate and fire model with a periodically modulated reset level for evaluating a stochastic version of period doubling bifurcation the first passage time problem of the ornstein uhlenbeck process is used to define a markov operator governing the transition of a reset level phase density the results on the stochastic bifurcation are thus compared with numerical computations of angles and moduli of eigenvalues of the markov operator that describes the firing properties of the model

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

melnikov s criteria and chaos in systems with fractional order deflection in this paper a qualitative analysis of the dynamic systems described with the second order differential equation with fractional order deflection function is considered the existence of fixed points closed orbits and the unions of fixed points and the trajectories connecting them is shown the homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form melnikov s procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function the critical parameter values for chaos are obtained analytically and proved numerically using the lyapunov exponents the bifurcation diagrams are plotted for various values of fractional order and the transition to chaos by period doubling is shown the phase plane diagrams and the poincare maps for certain fractional orders are obtained the control of chaos and the transformation to periodic motion is considered

augmented lagrangian finite elements for plate contact problems the present work investigates the unilateral frictionless contact between a plate and a rigid obstacle two sets of problems are studied a plate constrained through unilateral edge supports and a plate seating in its undeformed configuration at a given distance from a rigid support the attention is concentrated on two augmented lagrangian formulations the algorithmic implementation within a finite element scheme is presented and discussed the importance of using appropriate plate elements for the discretization of the structure is stressed new gap elements compatible with a robust plate element are derived computational aspects are emphasized a simple and effective numerical integration for the determination of the gap stiffnesses in partial contact with the support is proposed numerical results are carried out and compared with analytical solutions the convergence to the solution of the perfectly constrained problem is numerically investigated the inadequacy of the penalty method and the satisfactory performance obtained from only one augmented lagrangian procedure are emphasized

delayed feedback control of the lorenz system an analytical treatment at a subcritical hopf bifurcation we develop an analytical approach for the delayed feedback control of the lorenz system close to a subcritical hopf bifurcation the periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by a conventional delayed feedback control technique we utilize a modification based on an unstable delayed feedback controller the analytical approach employs the center manifold theory and the near identity transformation we derive the characteristic equation for the floquet exponents of the controlled orbit in an analytical form and obtain simple expressions for the threshold of stability as well as for an optimal value of the control gain the analytical results are supported by numerical analysis of the original system of nonlinear differential difference equations

linked interpolation for reissner mindlin plate elements part ii a simple triangle the formulation and shape functions given in part i are extended to develop a simple plate bending triangle with good performance in both thin and thick situations indeed its performance is better than that of other nine dof elements and its computer implementation simpler when used with selective reduced integration the element produces identical results as that of xu 1 2 to save space details given in part i are not repeated and some results are also presented in the figures of part i

orbits homoclinic to resonances with an application to chaos in a model of the forced and damped sine gordon equation abstract in this paper we develop new global perturbation techniques for detecting homoclinic and heteroclinic orbits in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two degree of freedom hamiltonian systems our methods are fundamentally different than other global perturbation methods e g standard melnikov theory in that we are seeking orbits homoclinic and heteroclinic to fixed points that are created in a resonance resulting from the perturbation our methods combine the higher dimensional melnikov theory with geometrical singular perturbation theory and the theory of foliations of invariant manifolds we apply our methods to a modified model of the forced and damped sine gordon equation developed by bishop et al we give explicit conditions in terms of the system parameters for the model to possess a symmetric pair of homoclinic orbits to a fixed point of saddle focus type chaotic dynamics follow from a theorem of silnikov this provides a mechanism for chaotic dynamics geometrically similar to that observed by bishop et al namely a random jumping between two spatially dependent states with an intermediate passage through a spatially independent state however in order for this type of silnikov dynamics to exist we require a different and unphysical type of damping compared to that used by bishop et al

chaotic motion of van der pol mathieu duffing system under bounded noise parametric excitation abstract the chaotic behavior of van der pol mathieu duffing oscillator under bounded noise is investigated by using random melnikov technique a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system the results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases which is further verified by the maximal lyapunov exponents of the system the effect of bounded noise on poincare map is also investigated in addition the numerical simulation of the maximal lyapunov exponents

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

monotonicity of the period function for u u up 0 with p r and p 1 abstract for p r and p 1 we consider the second order ordinary differential equation u u u p 0 which has a one parameter family of periodic solutions satisfying u 0 u 0 u 1 0 with u 1 0 1 we prove that the so called period function t u 1 which represents the period of the periodic solution is strictly decreasing on 0 1 this result is also applied to completely determine the global bifurcation diagram of interior single peak solutions in the neumann boundary value problem of u u u p 0 in 1 1 with u 1 0 where is a control parameter

event location for ordinary differential equations abstract an initial value problem for y f t y may have an associated event function g t y an event is said to occur at t when g t y t 0 we consider problems for which the definition of f t y changes at the time of an event a number of solvers locate events and restart the integration there so as to deal with the changes in f but there is little theoretical support for what is done here we prove that with reasonable assumptions about the problem and the solver the error of the numerical solution is qualitatively the same whether or not events occur numerical results obtained with a wide range of solvers confirm the theory developed here

an isostatic assumed stress triangular element for the reissner mindlin plate bending problem the paper describes a new assumed stress triangular element for reissner mindlin plates called tip3 with three nodes and three degrees of freedom per node the kinematics is constructed by means of the so called linked interpolation ruled by technically significant degrees of freedom i e one transversal displacement and two rotations per node without using additional bubble modes the static representation starts from a moment shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number the resulting element is locking free presents correct rank and passes the bending patch test even for very thin plates the good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature copyright 2007 john wiley sons ltd

a posteriori error analysis of finite element methods for reissner mindlin plates this paper develops an a posteriori error control theory of finite element methods for reissner mindlin plates which states that one can derive a uniformly reliable and efficient a posteriori error estimate for a given scheme by only 1 checking three conditions 2 designing three functions and one parameter 3 bounding the last three terms of the abstract estimator we apply this theory to two classes of methods and achieve robust a posteriori error controls for them

linked interpolation for reissner mindlin plate elements part i a simple quadrilateral in most plate elements using the reissner mindlin assumptions the interpolations used for the lateral displacements w and the rotation involve the independent representation of each variable by its nodal values usually with identical interpolations to ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element q4bl whose performance and robustness are good although it possesses one singularity if only three degrees of freedom are prescribed in part ii we apply the identical formulation to develop a triangular element t3bl which performs equally well and is fully robust

dichotomous noise induced chaos in a generalized duffing type oscillator with fractional order deflection abstract the chaotic behavior of a generalized duffing type oscillator with fractional order deflection under dichotomous noise excitation is discussed in detail using the melnikov method together with mean square criterion necessary conditions for the onsets of chaos are derived it is shown that with the increase of noise transition rate the threshold of noise amplitude for chaos firstly decreases to a minimum and then increases the effects of dichotomous noise on the duffing type oscillator are also obtained by vanishing the mean largest lyapunov exponent of the oscillator this is further verified by phase portraits and time histories with numerical simulations

generalized parametric resonance in electrostatically actuated microelectromechanical oscillators this paper investigates the dynamic response of a class of electrostatically driven microelectromechanical mem oscillators the particular systems of interest are those which feature parametric excitation that arises from forces produced by fluctuating voltages applied across comb drives these systems are known to exhibit a wide range of behaviors some of which have escaped explanation or prediction in this paper we examine a general governing equation of motion for these systems and use it to provide a complete description of the dynamic response and its dependence on the system parameters the defining feature of this equation is that both the linear and cubic terms feature parametric excitation which in comparison to the case of purely linear parametric excitation e g the mathieu equation significantly complicates the system s dynamics one consequence is that an effective nonlinearity for the overall system cannot be defined instead the system features separate effective nonlinearities for each branch of its nontrivial response as such it can exhibit not only hardening and softening nonlinearities but also mixed nonlinearities wherein the response branches in the system s frequency response bend toward or away from one another near resonance this paper includes some brief background information on the equation of motion under consideration an outline of the analytical techniques used to reach the aforementioned results stability results for the responses in question a numerical example explored using simulation of a mem oscillator which features this nonlinear behavior and preliminary experimental results taken from an actual mem device which show evidence of the analytically predicted behavior practical issues pertaining to the design of parametrically excited mem devices are also considered

criteria for chaos of a three well potential oscillator with homoclinic and heteroclinic orbits abstract criteria for chaotic vibrations of a non linear elastic beam having three stable and two unstable equilibrium positions are compared the responses of the system exhibit chaotic behavior in certain regions in the driving frequency and amplitude plane with the use of the melnikov technique necessary conditions for chaos are derived based on homoclinic and heteroclinic bifurcations of the system numerical simulations of the stable and unstable manifolds poincare maps lyapunov exponents and fractal basin boundaries are performed the results indicate that both homoclinic and heteroclinic bifurcations are necessary conditions for chaos thus at least two necessary conditions must be satisfied for any chaotic responses however the final steady state of motion for many initial conditions becomes unpredictable in the sense of fractal basin boundaries if at least one homoclinic or heteroclinic bifurcation occurs finally an experimental criterion for chaotic motion and an heuristic criterion based on classical methods in non linear dynamics are also obtained and compared with the bifurcation criteria as a function of forcing amplitude and frequency

using the extended melnikov method to study the multi pulse global bifurcations and chaos of a cantilever beam the aim of this paper is to investigate the multi pulse global bifurcations and chaotic dynamics for the nonlinear non planar oscillations of a cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end by using an extended melnikov method in the resonant case first the extended melnikov method for studying the shilnikov type multi pulse homoclinic orbits and chaos in high dimensional nonlinear systems is briefly introduced in the theoretical frame then this method is utilized to investigate the shilnikov type multi pulse homoclinic bifurcations and chaotic dynamics for the nonlinear non planar oscillations of the cantilever beam how to employ this method to analyze the shilnikov type multi pulse homoclinic bifurcations and chaotic dynamics of high dimensional nonlinear systems in engineering applications is demonstrated through this example finally the results of numerical simulation are given and also show that the shilnikov type multi pulse chaotic motions can occur for the nonlinear non planar oscillations of the cantilever beam which verifies the analytical prediction

specific poincare map for a randomly perturbed nonlinear oscillator the motion of a classical hamiltonian oscillator driven by a weak random force is examined by means of a deterministic approach we design the specific poincarmap to find domains of finite time stability in phase space the trajectories belonging to these domains remain stable by lyapunov criteria for the period of mapping t0 at least we derive the lower border for the time of phase correlations between close trajectories it is found that the lifetime of some stable domains significantly exceeds the correlation time of the external force the randomly driven morse oscillator is used as an example

approximations for motion of the oscillators with a non negative real power restoring force abstract oscillators with a non negative real power restoring force are considered in this paper this type of restoring force is related to systems with a quasi zero stiffness characteristic or those in which the restoring force is purely nonlinear in nature examples of these types of restoring force are grounded in real physical and engineering systems periodic motion of such conservative oscillators is described first in a novel way by means of the elliptic function the parameters of which are obtained from the energy conservation law and hamilton s variational principle then the approach is extended to non conservative oscillators by adjusting the elliptic krylov bogoliubov method the methods proposed for the conservative and non conservative systems under consideration have wider applications than the existing one with respect to the power of the restoring force several examples the majority of which are so far unsolved are given to illustrate the methods proposed and to demonstrate their generality which permits unforeseen solutions for motion containing higher harmonics and assuring consistent accuracy regardless of the value of the power of the restoring force the results obtained are compared with numerical results and have excellent accuracy

second order averaging and melnikov analyses for forced non linear oscillators abstract an analysis is presented of a class of periodically forced non linear oscillators the systems have centers and families of periodic orbits and may have homoclinic and or heteroclinic orbits when the forcing and damping terms are removed first birfucation behavior is analyzed near the unperturbed centers when primary subharmonic or superharmonic resonance occurs by using the second order averaging method second melnikov s method is applied and bifurcation behaviour near the unperturbed homoclinic heteroclinic and resonant periodic orbits is analyzed the limits of saddle node bifurcations of subharmonics near the unperturbed resonant periodic orbits as the resonant periodic orbits approach homoclinic and or heteroclinic orbits or centers are obtained the results of the second order averaging and melnikov analyses for saddle node bifurcations of subharmonics near centers are compared and their relation is discussed an example is given for the duffing oscillator with double well potential

a low order nonconforming finite element for reissner mindlin plates we propose a locking free element for plate bending problems based on the use of nonconforming piecewise linear functions for both rotations and deflections we prove optimal error estimates with respect to both the meshsize and the analytical solution regularity

finite element methods for a modified reissner mindlin free plate model the solution of the reissner mindlin plate problem with free boundary conditions presents a strong layer effect near the free edges as a consequence the solution is not even uniformly bounded even in h3 2 which implies that at most an o h1 2 uniform convergence rate can be reached by finite element methods in the h1 norm following instead the modified free boundary model presented by beirao da veiga and brezzi which gives more regular solutions better error estimates can be obtained in principle in this paper we present and analyze the extension of different families of well known optimal plate methods to this new model all the modified methods presented are proved to be optimal and free of locking

diversity as a concept and its measurement abstract this paper puts forth the view that diversity is an average property of a community and identifies that property as species rarity an intrinsic diversity ordering of communities is defined and is shown to be equivalent to stochastic ordering also the sensitivity of an index to rare species is developed culminating in a crossing point theorem and a response theory to perturbations diversity decompositions analogous to the analysis of variance are discussed for two way classifications and mixtures the paper concludes with a brief survey of genetic diversity linguistic diversity industrial concentration and income inequality

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

distortion immune nine node displacement based quadrilateral thick plate finite elements that satisfy constant bending patch test we employ the linked interpolation concept to develop a higher order 9 node quadrilateral plate finite element with curved sides which passes the constant bending patch test for arbitrary node positions the linked interpolation for the plate displacements is expanded with three bubble parameters to get polynomial completeness necessary to satisfy the patch test in contrast to some other techniques the elements developed in this way retain a symmetric stiffness matrix at a marginal computational expense at the element level two new elements are generated using this concept and tested on several examples with curved sides or some kind of geometric distortion

a shear deformable plate element with an exact thin limit abstract we present a quadrilateral finite element developed within the framework of a shear deformable plate theory the interpolation for the rotation takes advantage of internal rotational degrees of freedom through the use of bubble functions while the interpolation for the transverse displacement is linked to the nodal rotations a careful study of the element behavior is performed using an extensive set of mixed patch tests results from several numerical examples are also presented the element has proper rank and excellent interpolating capacity moreover without using any ad hoc assumption e g energy balancing schemes the element presents no locking effects at all in fact the shear energy may be set identically equal to zero without introducing any ill conditioning in the problem thus recovering a proper thin plate limit

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems we show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance in particular additive gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner results obtained for the logistic map and the lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems we attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments

stochastic dynamical analysis of a kind of vibro impact system under multiple harmonic and random excitations abstract there have been many contributions concerned with non smooth dynamics the purpose of this study is focused on the global stochastic dynamics of a kind of vibro impact oscillator under the multiple harmonic and bounded noisy excitations the well known cell to cell mapping method is firstly developed to investigate the incursive fractal boundaries between the attracting domains of different random attractors and a specific poincare map is then set up to explore the noise contaminated dynamical transitions in the system lastly the leading lyapunov exponents and the surrogate tests are used to identify the noise contaminated dynamics it is shown that several random attractors will coexist in the phase space of the randomly driven system by adjusting the parameters values and fractal boundaries may also arise between the attracting domains of different random attractors under the joint action of the harmonic excitation and the weak bounded noise excitation the noisy period doubling process similar to a deterministic one can appear in the poincare s global cross section by increasing the strength of the bounded noisy excitation moreover the noisy periodic the noisy chaotic and the random dominant dynamics are also distinguished from the noise contaminated signals

steady state self oscillations and chaotic behavior of a controlled electromechanical device by using the first lyapunov value and the melnikov theory abstract in this paper regular and chaotic oscillations in a controlled electromechanical transducer are investigated the nonlinear control laws are defined by an electric tension excitation and an external force applied to the mobile piece of the transducer the paper shows that an andronov poincare hopf bifurcation appears as long as adequate parameters are chosen for the nonlinear control laws the stability of the weak focuses associated to such bifurcation is examined according to the sign of the first lyapunov value showing that chaotic behavior can arise when the first lyapunov value is varied harmonically the appearance of a homoclinic orbit is investigated assuming an approximated model for the device on the basis of the parametric equations of the homoclinic orbit and the presence of harmonic disturbances on the platform it is demonstrated that chaotic oscillations can also appear and they have been examined by means of the melnikov theory chaotic behavior is corroborated by means of the sensitive dependence lyapunov exponents and power spectral density and it is applied to drive the transducer mobile piece to a predefined set point assuming that noise due to the measurement process can appear in the control signals the steady state error associated to such random noise is eliminated by adding a pi linear controller to the control force numerical simulations are used to corroborate the analytical results

a partial differential equation with infinitely many periodic orbits chaotic oscillations of a forced beam this paper delineates a class of time periodically perturved evolution equations in a banach space whose associated poincar e map contains a smale horseshoe this implies that such systems possess periodic orbits with arbitrarily high period the method uses techniques originally due to melnikov and applies to systems of the form x f0 x f1 x t where x f0 x is hamiltonian and has a homoclinic orbit we give an example from structural mechanics sinusoidally forced vibrations of a buckled beam

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

grazing bifurcations and basins of attraction in an impact friction oscillator abstract this paper describes some interesting global dynamic behavior in the response of a double sided harmonically forced impact oscillator including the influence of coulomb damping the system under study is modeled as piecewise linear in both its force deflection and force velocity characteristics grazing bifurcations caused by this latter effect are a new feature the paper has two distinct but related foci first the study of basins of attraction provides information regarding the complete solution set for the system given a specific set of parameters second grazing bifurcations represent the primary source of sudden change in qualitative behavior as a system parameter is varied the numerical technique of cell to cell mapping provides a useful insight into the relation between these two thus both local and global issues are addressed indeed it is the interplay of periodic attractors and their basins of attraction that dominates bifurcational behavior

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

oscillator with fraction order restoring force abstract in this paper a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced using the first integral of motion the exact period of vibration in the form of the euler beta function is obtained based on that value the approximate solution of the strong nonlinear fraction order differential equation is formed the suggested procedure is applied for various fraction values but also for the pure quadratic cubic and quintic oscillators the advantage of the suggested method is that is valid for all fraction values 1 the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time in the paper the fraction order differential equation with small linear and nonlinear terms is also considered the krylov bogolubov method is extended due to the fact that frequency of vibration depends on the amplitude of vibration the approximate solution is with time variable amplitude phase and frequency the linear damped fraction order oscillator is widely discussed the approximate solution of the differential equation which describes the vibrations of such oscillator is compared with exact numerical one and shows a good agreement

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

an improved estimator of dimension and some comments on providing confidence intervals abstract an estimator of dimension is described that has many advantages over the conventional implementation of the grassberger procaccia method it can in some circumstances provide a confidence interval for the dimension estimate for high dimension sets greater than about 3 5 the dimension estimate has a bias which depends on the structure of the set if one has suitable knowledge of the structure of the set it is possible to make a bias adjustment some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected the problem of providing confidence intervals for dimension estimates in general is not solved completely but we do take a step away from a meaningless number

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

the finite element patch test revisited a computer test for convergence validation and error estimates abstract the patch test was introduced in the mid 1960s first as a check of satisfactory performance for elements violating continuity requirements and later simply as a necessary condition which all elements had to satisfy and which frequently checked simple programming errors in its original form the patch test simply verified that the minimum local consistency error was achievable and that the programming was correct later it was established that the test could also be used to find the convergence order of any finite element type while consistency is one of the necessary requirements for convergence the second is of course that of stability in the original early work only displacement type structural elements were involved and thus stability was ensured by rejecting elements which could form mechanisms in a 1986 reformulation of the patch test this stability or solvability requirement was formalized to all element assemblies and the patch test extended to become a generally applicable sufficient and necessary condition for convergence of all element forms 1 2 although some misinterpretation of the patch test has occurred in literature 3 4 the authors believe that with certain restrictions on regularity of the problem dealt with the satisfaction of the patch test is equivalent to the satisfaction of the more mathematical babuska brezzi criteria 5 6 in recent years another important use of the patch test has been found by babuska and his coworkers 7 9 this work tests the asymptotic effectivity of various error estimating procedures used with various element patterns

a non simultaneous variational approach for the oscillators with fractional order power nonlinearities abstract this paper is concerned with a class of conservative oscillators the restitution force of which is of a power form which includes positive non integer exponents it is shown how an approximate lagrangian and hamilton s variational principle can be used to obtain a second order approximate solution for their free vibrations due to the fact that in a general case when the restoring force is multi term the period cannot be obtained from the energy conservation law in a closed form the problem is formulated as a one point boundary value problem and a non simultaneous variation is introduced the explicit expressions for the amplitudes and frequency of oscillations are derived in which there are no restrictions on the values of the non integer powers the analytically obtained results are compared with numerical results as well as with some approximate analytical results from the literature

intergroup concordance definition and estimation summary a coefficient of intergroup concordance is proposed which is consistent with the concept of intragroup concordance as measured by kendall s coefficient of concordance kendall babington smith 1939 this approach reconciles the approaches of schucany frawley 1973 and of hollander sethuraman 1978 to the problem of two group concordance estimation and test procedures for the population are based on jackknife procedures extension to the problem of multiple intergroup concordance when groups have factorial structure is noted

linked interpolation for reissner mindlin plate elements part iii an alternative quadrilateral an alternative quadrilateral element for reissner mindlin plates which extends the mixed formulation described in part 1 using linked interpolations is presented differently from element q4bl presented in part i this element q4bla employs four internal rotation nodes and a linear approximation for transverse shear forces it is shown that the element passes various patch tests it does not possess any zero energy mode and its performance is good for both thick and thin plates

a triangular element based on reissner mindlin plate theory a new triangular plate blending element based on the reissner mindlin theory is developed through a mixed formulation emanating from the hu washizu variational principle a main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges