on the computation of the coefficients associated with high order normal forms a new procedure for obtaining high order normal forms and the associated coefficients is presented it is assumed that the jacobian of the system considered is in a diagonal form in comparison with existing normal form approaches this procedure lends itself more readily to symbolic calculations like maple and the calculations of high order normal forms together with the associated coefficients are carried out much more conveniently to illustrate the approach five examples are presented examples 1 and 3 also contain a comparison of the results obtained by the methods of normal forms and averaging

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

a recursive approach to compute normal forms normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations particularly when singularities close to a bifurcation are to be characterized however the computation of a normal form up to an arbitrary order is numerically hard this paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms a computer program to reduce the system to its normal form on a center manifold is developed using the maple symbolic language however it should be stressed that the program relies essentially on recursive numerical computations while symbolic calculations are used only for minor tasks some strategies are proposed to save computation time examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension

applying the method of normal forms to second order nonlinear vibration problems vibration problems are naturally formulated with second order equations of motion when the vibration problem is nonlinear in nature using normal form analysis currently requires that the second order equations of motion be put into first order form in this paper we demonstrate that normal form analysis can be carried out on the second order equations of motion in addition for forced damped nonlinear vibration problems we show that the invariance properties of the first and second order transforms differ as a result using the second order approach leads to a simplified formulation for forced damped nonlinear vibration problems

detection of stellate distortions in mammograms malignant densities in mammograms have an irregular appearance and frequently are surrounded by a radiating pattern of linear spicules in this paper a method is described to detect such stellate patterns this method is based on statistical analysis of a map of pixel orientations if an increase of pixels pointing to a region is found this region is marked as suspicious especially if such an increase is found in many directions orientations of the image intensity map are determined at each pixel using a multiscale approach at a given scale accurate line based orientation estimates are obtained from the output of three directional second order gaussian derivative operators the orientation at the scale at which these operators have maximum response is selected if a line like structure is present at a given site this method provides an estimate of the orientation of this structure whereas in other cases the image noise will generate a random orientation the pixel orientation map is used to construct two operators which are sensitive to radial patterns of straight lines combination of the output of these operators using a classifier allows for detection of stellate patterns different classification methods have been compared and results obtained on a common database are presented around 90 of the malignant cases were detected at rate of one false positive fp per image

renormalization of the voter model in equilibrium we consider the d dimensional voter model for d 3 our interest is the large scale limit of the equilibrium state of the voter model where we prove the d 3 results of 1 for d 4 which turn out to be of a different nature than for d 3 for this purpose we use the historical process we establish some surprising facts about the green s function of random walks in dimension d 4 which lead to the different features in d 3 versus d 4 secondly we prove an analogous result for the voter model on the hierarchical group

markov random field for tumor detection in digital mammography a technique is proposed for the detection of tumors in digital mammography detection is performed in two steps segmentation and classification in segmentation regions of interest are first extracted from the images by adaptive thresholding a further reliable segmentation is achieved by a modified markov random field mrf model based method in classification the mrf segmented regions are classified into suspicious and normal by a fuzzy binary decision tree based on a series of radiographic density related features a set of normal 50 and abnormal 45 screen film mammograms were tested the latter contained 48 biopsy proven malignant masses of various types and subtlety the detection accuracy of the algorithm was evaluated by means of a free response receiver operating characteristic curve which shows the relationship between the detection of true positive masses and the number of false positive alarms per image the results indicated that a 90 sensitivity can be achieved in the detection of different types of masses at the expense of two falsely detected signals per image the algorithm was notably successful in the detection of minimal cancers manifested by masses spl les 10 mm in size for the 16 such cases in the authors dataset a 94 sensitivity was observed with 1 5 false alarms per image an extensive study of the effects of the algorithm s parameters on its sensitivity and specificity was also performed in order to optimize the method for a clinical observer performance study

reduced order models for large amplitude vibrations of shells including in plane inertia non linear normal modes nnms are used in order to derive reduced order models for large amplitude geometrically non linear vibrations of thin shells the main objective of the paper is to compare the accuracy of different truncations using linear and non linear modes in order to predict the response of shells structures subjected to harmonic excitation for an exhaustive comparison three different shell problems have been selected i a doubly curved shallow shell simply supported on a rectangular base ii a circular cylindrical panel with simply supported in plane free edges and iii a simply supported closed circular cylindrical shell in each case the models are derived by using refined shell theories for expressing the strain displacement relationship as a consequence in plane inertia is retained in the formulation reduction to one or two nnms shows perfect results for vibration amplitude lower or equal to the thickness of the shell in the three cases and this limitation is extended to two times the thickness for two of the selected models 2008 elsevier b v all rights reserved

an efficient bi convex fuzzy variational image segmentation method abstract image segmentation is an important and well known ill posed inverse problem in computer vision it is a process of assigning a label to each pixel in a digital image so that pixels with the same label have similar characteristics chan vese model which belongs to partial differential equation approaches has been widely used in image segmentation tasks chan vese model has to optimize a non convex problem it usually converges to local minima furthermore the length penalty item which is critical to the final results of chan vese model makes the model be sensitive to parameter settings and costly in computation in order to overcome these drawbacks a novel bi convex fuzzy variational image segmentation method is proposed it is unique in two aspects 1 introducing fuzzy logic to construct a bi convex object function in order to simplify the procedure of finding global optima and 2 efficiently combining the length penalty item and the numerical remedy method to get better results and to bring robustness to parameter settings and greatly reduce computation costs experiments on synthetic natural medical and radar images have visually or quantitatively validated the superiorities of the proposed method compared with five state of the art algorithms

an amplitude phase formulation for nonlinear modes and limit cycles through invariant manifolds the aim of this paper is to show how the concept of nonlinear modes can be used to characterize periodic orbits and limit cycles in multi degree of freedom nonlinear mechanical systems in line with previous studies by shaw and pierre the concept of nonlinear modes is introduced here in the framework of invariant manifold theory for dynamical systems a nonlinear mode is defined in terms of amplitude phase frequency damping coefficient and mode shape where the last three quantities are amplitude and phase dependent an amplitude phase transformation is performed on the nonlinear dynamical system giving the time evolution of the nonlinear mode motion via the two first order differential equations governing the amplitude and phase variables as well as the geometry of the invariant manifold the system of formulation adopted here is suitable for use with a galerkin based computational procedure the existence and stability of periodic orbits such as limit cycles on the associated invariant manifolds can be studied from the differential equations governing the amplitude and phase variables the examples given here involve adding gyroscopic and or negative nonlinear damping terms of van der pol type and nonlinear restoring force to the system equations

biologically inspired feature manifold for scene classification biologically inspired feature bif and its variations have been demonstrated to be effective and efficient for scene classification it is unreasonable to measure the dissimilarity between two bifs based on their euclidean distance this is because bifs are extrinsically very high dimensional and intrinsically low dimensional i e bifs are sampled from a low dimensional manifold and embedded in a high dimensional space therefore it is essential to find the intrinsic structure of a set of bifs obtain a suitable mapping to implement the dimensionality reduction and measure the dissimilarity between two bifs in the low dimensional space based on their euclidean distance in this paper we study the manifold constructed by a set of bifs utilized for scene classification form a new dimensionality reduction algorithm by preserving both the geometry of intra bifs and the discriminative information inter bifs termed discriminative and geometry preserving projections dgpp and construct a new framework for scene classification in this framework we represent an image based on a new bif which combines the intensity channel the color channel and the c1 unit of a color image then we project the high dimensional bif to a low dimensional space based on dgpp and finally we conduct the classification based on the multiclass support vector machine svm thorough empirical studies based on the usc scene dataset demonstrate that the proposed framework improves the classification rates around 100 relatively and the training speed 60 times for different sites in comparing with previous gist proposed by siagian and itti in 2007

phase transitions for the long time behavior of interacting diffusions let xi t i zd t 0 be the system of interacting diffusions on 0 defined by the following collection of coupled stochastic differential equations dxi t j zd a i j xj t xi t dt bxi t dwi t i z t 0 here a is an irreducible random walk transition kernel on z z b 0 is a diffusion parameter and wi t i zd t 0 is a collection of independent standard brownian motions on r the initial condition is chosen such that xi 0 i zd is a shift invariant and shift ergodic random field on 0 with mean 0 the evolution preserves the mean we show that the long time behaviour of this system is the result of a delicate interplay between a and b in contrast to systems where the diffusion function is subquadratic in particular let i j 12 a i j a j i i j z denote the symmetrised transition kernel we show that a if is recurrent then for any b 0 the system locally dies out b if is transient then there exist b b2 0 such that b1 the system converges to an equilibrium with mean if 0 b b3 has a finite 2 nd moment if and only if 0 b2 the equilibrium is shown to be associated and mixing for all 0 b2 we further conjecture that the system locally dies out at b b for the case where a is symmetric and transient we further show that c there exists a sequence b2 b3 b4 0 such that c1 has a finite m th moment if and only if 0 bm c3 b2 m 1 bm 2 c4 limm m 1 bm c supm 2 m 1 bm mathematisches institut universitat erlangen nurnberg bismarckstrasse 1 1 2 d 91504 erlangen germany greven mi uni erlangen de mathematical institute leiden university p o box 9512 2300 ra leiden the netherlands denholla math leidenuniv nl eurandom p o box 513 5600 mb eindhoven the netherlands

a new formulation for the existence and calculation of nonlinear normal modes a new formulation is presented here for the existence and calculation of nonlinear normal modes in undamped nonlinear autonomous mechanical systems as in the linear case an expression is developed for the mode in terms of the amplitude mode shape and frequency with the distinctive feature that the last two quantities are amplitude and total phase dependent the dynamic of the periodic response is defined by a one dimensional nonlinear differential equation governing the total phase motion the period of the oscillations depending only on the amplitude is easily deduced it is established that the frequency and the mode shape provide the solution to a 2 periodic nonlinear eigenvalue problem from which a numerical galerkin procedure is developed for approximating the nonlinear modes the procedure is applied to various mechanical systems with two degrees of freedom

mammographic mass segmentation embedding multiple features in vector valued level set in ambiguous regions mammographic mass segmentation plays an important role in computer aided diagnosis systems it is very challenging because masses are always of low contrast with ambiguous margins connected with the normal tissues and of various scales and complex shapes to effectively detect true boundaries of mass regions we propose a feature embedded vector valued contour based level set method with relaxed shape constraint in particular we initially use the contour based level set method to obtain the initial boundaries on the smoothed mammogram as the shape constraint to prevent the contour leaking and meanwhile preserve the radiative characteristics of specific malignant masses afterward we relax the obtained shape constraint by analyzing possible valid regions around the initial boundaries the relaxed shape constraint is then used to design a novel stopping function for subsequent vector valued level set method since texture maps gradient maps and the original intensity map can reflect different characteristics of the mammogram we integrate them together to obtain more accurate segmentation by incorporating the new stopping function into the newly proposed feature embedded vector valued contour based level set method the experimental results suggest that the proposed feature embedded vector valued contour based level set method with relaxed shape constraint can effectively find ambiguous margins of the mass regions comparing against existing active contours methods the new scheme is more effective and robust in detecting complex masses

analysis of critical and post critical behaviour of non linear dynamical systems by the normal form method part ii divergence and flutter abstract the normal form method nfm presented in part i 1 is applied to the analysis of systems near two basic bifurcation conditions divergence and flutter the reduced systems and the normalizing transformation obtained by means of a computer routine implementing the normalization formulae of part i are utilized to determine a the stability of the bifurcating singular point b the local equilibrium paths associated with divergence bifurcation and c the amplitude and frequency or more generally the waveform of post flutter oscillations

analysis of non linear dynamical systems by the normal form theory abstract a method is proposed for calculating the periodic solutions of non linear mechanical systems with analytical non linearities the jordan normalization procedure for the case of non linear autonomous systems is described and generalized to dampened harmonically excited oscillators non linear modes for hamiltonian systems are introduced normal forms simplify the analysis of bifurcation it is shown how to extend the modal synthesis procedure the proposed non linear modes obtained from free vibrations are used to construct a superposition technique to describe the forced response of harmonically excited systems these results are tested for one and two degrees of freedom systems with cubic non linearities the results are compared with expressions obtained by classical analytical methods averaging or multiple scales methods or runge kutta numerical methods

an analytical approach for detecting isolated periodic solution branches in weakly nonlinear structures this paper considers isolated responses in nonlinear systems both in terms of isolas in the forced responses and isolated backbone curves i e the unforced undamped responses as isolated responses are disconnected from other response branches reliably predicting their existence poses a significant challenge firstly it is shown that breaking the symmetry of a two mass nonlinear oscillator can lead to the breaking of a bifurcation on the backbone curves generating an isolated backbone it is then shown how an energy based analytical method may be used to compute the points at which the forced responses cross the backbone curves at resonance and how this may be used as a tool for finding isolas in the forced responses this is firstly demonstrated for a symmetric system where an isola envelops the secondary backbone curves which emerge from a bifurcation next an asymmetric configuration of the system is considered and it is shown how isolas may envelop a primary backbone curve i e one that is connected directly to the zero amplitude solution as well as the isolated backbone curve this is achieved by using the energy based method to determine the relationship between the external forcing amplitude and the positions of the crossing points of the forced response along with predicting the existence of the isolas this technique also reveals the nature of the responses thus simplifying the process of finding isolas using numerical continuation

approximate invariant manifolds up to exponentially small terms abstract this paper is devoted to analytic vector fields near an equilibrium for which the linearized system is split in two invariant subspaces e 0 dim m 0 e 1 dim m 1 under light diophantine conditions on the linear part we prove that there is a polynomial change of coordinate in e 1 allowing to eliminate in the e 1 component of the vector field all terms depending only on the coordinate u 0 e 0 up to an exponentially small remainder this main result enables to prove the existence of analytic center manifolds up to exponentially small terms and extends to infinite dimensional vector fields in the elliptic case our results also proves with very light assumptions on the linear part in e 1 that for initial data very close to a certain analytic manifold the solution stays very close to this manifold for a very long time which means that the modes in e 1 stay very small

gradient and texture analysis for the classification of mammographic masses computer aided classification of benign and malignant masses on mammograms is attempted in this study by computing gradient based and texture based features features computed based on gray level co occurrence matrices gcms are used to evaluate the effectiveness of textural information possessed by mass regions in comparison with the textural information present in mass margins a method involving polygonal modeling of boundaries is proposed for the extraction of a ribbon of pixels across mass margins two gradient based features are developed to estimate the sharpness of mass boundaries in the ribbons of pixels extracted from their margins a total of 54 images 28 benign and 26 malignant containing 39 images from the mammographic image analysis society mias database and 15 images from a local database are analyzed the best benign versus malignant classification of 82 1 with an area a sub z of 0 85 under the receiver operating characteristics roc curve was obtained with the images from the mias database by using gcm based texture features computed from mass margins the classification method used is based on posterior probabilities computed from mahalanobis distances the corresponding accuracy using jack knife classification was observed to be 74 4 with a sub x 0 67 gradient based features achieved a sub x 0 6 on the mias database and a sub z 0 76 on the combined database the corresponding values obtained using jack knife classification were observed to be 0 52 and 0 73 for the mias and combined databases respectively

resonant response functions for nonlinear oscillators with polynomial type nonlinearities in this paper we consider the steady state response of forced damped weakly nonlinear oscillators with polynomial type nonlinearities in particular we define general expressions that can be used to compute resonant response functions which define the steady state constant amplitude oscillatory response at the primary resonance and the associated harmonics the resonant response functions are derived using a normal form transformation which is carried out directly on the second order nonlinear oscillator the example of a forced van der pol oscillator with an additional cubic stiffness nonlinearity is used to demonstrate how the general analysis can be applied

normal form of double hopf bifurcation in forced oscillators a general four dimensional normal form of a double hopf bifurcation is considered as a particular case the normal form of a forced non autonomous non linear oscillator having two frequencies namely the linear natural frequency and the excitation frequency is studied in detail when these two frequencies form two purely imaginary sub blocks of order two in the real jordan block the system constitutes a double hopf bifurcation in this paper the normal form of the double hopf bifurcation is reduced when the two frequencies are not in resonance in order to use the method of normal form the non autonomous problem is transformed into an autonomous one by a generalized co ordinate transformation the method of undetermined coefficients is used to find the double hopf bifurcation normal form the coefficients of similar monomials rather than similar powers of e are compared to get the normal form to various orders the steady state periodic solutions and the bifurcation equations of the forced non linear vibration system in the case of non resonant are studied a mathematica program is designed to find the normal form three examples are given to use the mathematica program and to compare them with the existing results

nonlinear modes of clarinet like musical instruments the concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments using a modal expansion of the impedance of the instrument and by projecting the equation for the acoustic pressure on the normal modes of the air column a system of second order ordinary differential equations is obtained the equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed the system is treated using an amplitude phase formulation for nonlinear modes where the frequency and damping functions as well as the invariant manifolds in the phase space are unknowns to be determined the formulation gives without explicit integration of the underlying ordinary differential equation access to the transient the limit cycle its period and stability the process is illustrated for a model reduced to three normal modes of the air column

fast bayesian identification of a class of elastic weakly nonlinear systems using backbone curves this paper introduces a method for the identification of the parameters of nonlinear structures using a probabilistic bayesian framework employing a markov chain monte carlo algorithm this approach uses analytical models to describe the unforced undamped dynamic responses of structures in the frequency amplitude domain known as the backbone curves the analytical models describing these backbone curves are then fitted to measured responses found using the resonant decay method to investigate the proposed identification method a nonlinear two degree of freedom example structure is simulated numerically and analytical expressions describing the backbone curves are found these expressions are then used in conjunction with the backbone curve data found through simulated experiment to estimate the system parameters it is shown that the use of these computationally cheap analytical expressions allows for an extremely efficient method for modelling the dynamic behaviour providing an identification procedure that is both fast and accurate furthermore for the example structure it is shown that the estimated parameters may be used to accurately predict the existence of dynamic behaviours that are well away from the backbone curve data provided specifically the existence of an isola is predicted

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

normal form analysis of a forced aeroelastic plate abstract a nonlinear elastic plate in a supersonic unsteady flow forced by a dynamic excitation and a biaxial compressive load is studied the physical behavior of the plate is modelized by the von karman equations and the aerodynamic loads are modeled by using the piston theory including nonlinearities up to the third order the space continuum model is space discretized by a galerkin projection and then studied by a perturbation approach based on the normal form method in order to reduce the system to a simpler and essential form defined by its resonance conditions a physical interpretation of the involved small divisors is given by analyzing how different equation parameters influence the reduced normal form model in the neighborhood of both static and dynamic bifurcation points

variational and pca based natural image segmentation this paper introduces a novel variational segmentation method within the fuzzy framework which solves the problem of segmenting multi region color scale images of natural scenes we call this kind of images as natural images the advantages of our segmentation method are 1 by introducing the pca descriptors our segmentation model can partition color texture images better than classical variational based segmentation models 2 to preserve geometrical structure of each fuzzy membership function we propose a nonconvex regularization term in our model 3 to solve our segmentation model more efficiently we design a fast iteration algorithm in which we integrate the augmented lagrange multiplier method and the iterative reweighting we conduct comprehensive experiments to measure the segmentation performance of our model in terms of visual evaluation and we also demonstrate the efficiency of the corresponding algorithm in terms of a variety of quantitative indices the proposed model achieves better segmentation results compared with some other well known models such as the level set model and the fuzzy region competition model while the proposed algorithm is much more efficient than the algorithm of the state of the art natural image segmentation model

numerical computation of nonlinear normal modes in mechanical engineering this paper reviews the recent advances in computational methods for nonlinear normal modes nnms different algorithms for the computation of undamped and damped nnms are presented and their respective advantages and limitations are discussed the methods are illustrated using various applications ranging from low dimensional weakly nonlinear systems to strongly nonlinear industrial structures

efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization the fuzzy c partition entropy has been widely adopted as a global optimization technique for finding the optimized thresholds for multilevel image segmentation however it involves expensive computation as the number of thresholds increases and often yields noisy segmentation results since spatial coherence is not enforced in this paper an iterative calculation scheme is presented for reducing redundant computations in entropy evaluation the efficiency of threshold selection is further improved through utilizing the artificial bee colony algorithm as the optimization technique finally instead of performing thresholding for each pixel independently the presented algorithm oversegments the input image into small regions and uses the probabilities of fuzzy events to define the costs of different label assignments for each region the final segmentation results is computed using graph cut which produces smooth segmentation results the experimental results demonstrate the presented iterative calculation scheme can greatly reduce the running time and keep it stable as the number of required thresholds increases quantitative evaluations over 20 classic images also show that the presented algorithm outperforms existing multilevel segmentation approaches

analysis of critical and post critical behaviour of non linear dynamical systems by the normal form method part i normalization formulae abstract a method based on normal form theory is presented to study the dynamical behaviour of a system in the neighbourhood of a nearly critical equilibrium state associated with a bifurcation condition explicit formulae for the normalization procedure are derived these formulae can be numerically programmed avoiding usual complicated algebraic calculations and making the method effectively applicable for n dimensional systems rather general bifurcations can be included e g non linear flutter hopf bifurcation divergence and internal resonance

a wavelet galerkin procedure to investigate time periodic systems transient vibration and stability analysis abstract a wavelet galerkin procedure is introduced in order to obtain transient and periodic solutions of multi degree of freedom d o f s dynamical systems with time periodic coefficients numerical comparisons achieved with a runge kutta method emphasize that the wavelet based procedure is reliable even in the case of problems involving both smooth or non smooth parametric excitations and a relatively large number of degrees of freedom the procedure is then applied to study the vibrations of some theoretical parametrically excited systems since problems of stability analysis of non linear systems are often reduced after linearization to problems involving linear differential systems with time varying coefficients the method is shown to be effective for the computation of the floquet exponents that characterize stable unstable parameters areas and consequently allows estimators for stability instability levels to be provided stability diagrams of some theoretical examples including a single degree of freedom mathieu oscillator and a two degree of freedom parametrically excited system illustrate the relevance of the method finally future studies are outlined for the extension of the wavelet method to the non linear case

hardening softening behaviour in non linear oscillations of structural systems using non linear normal modes the definition of a non linear normal mode nnm as an invariant manifold in phase space is used in conservative cases it is shown that normal form theory allows one to compute all nnms as well as the attendant dynamics onto the manifolds in a single operation then a single mode motion is studied the aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results using single non linear mode motion predicts the correct behaviour hence the nonlinear change of co ordinates allowing one to pass from the linear modal variables to the normal ones linked to the nnms defines a framework to properly truncate non linear vibration pdes two examples are studied a discrete system a mass connected to two springs and a continuous one a linear euler bernoulli beam resting on a non linear elastic foundation for the latter a comparison is given between the developed method and previously published results

a method for nonlinear modal analysis and synthesis application to harmonically forced and self excited mechanical systems abstract the recently developed generalized fourier galerkin method is complemented by a numerical continuation with respect to the kinetic energy which extends the framework to the investigation of modal interactions resulting in folds of the nonlinear modes in order to enhance the practicability regarding the investigation of complex large scale systems it is proposed to provide analytical gradients and exploit sparsity of the nonlinear part of the governing algebraic equations a novel reduced order model rom is developed for those regimes where internal resonances are absent the approach allows for an accurate approximation of the multi harmonic content of the resonant mode and accounts for the contributions of the off resonant modes in their linearized forms the rom facilitates the efficient analysis of self excited limit cycle oscillations frequency response functions and the direct tracing of forced resonances the rom is equipped with a large parameter space including parameters associated with linear damping and near resonant harmonic forcing terms an important objective of this paper is to demonstrate the broad applicability of the proposed overall methodology this is achieved by selected numerical examples including finite element models of structures with strongly nonlinear non conservative contact constraints

post buckling longterm dynamics of a forced nonlinear beam a perturbation approach abstract the aim of this paper is to determine by a singular perturbation approach the dynamic response of a harmonically forced system experiencing a pitchfork bifurcation the model of an extensible beam forced by a harmonic excitation and subject to an axial static buckling is space discretized by a galerkin approach and studied by the normal form method for different values of equation parameters influencing the nonlinear dynamic behavior like damping coefficient load amplitude and frequency a relevant issue in the perturbation methods is the concept of small and zero divisors which are related to the possibility to build a transformation that simplifies the original studied problem i e to obtain the normal form by eliminating as much as possible nonlinearities in the equations for nonconservative systems like structural damped systems there are no conditions in the prior literature that define what small means relatively to a divisor in the present paper some conditions about the order of magnitude of the divisors with respect to the perturbation entity are given and related to some physical parameters in the governing equations in order to estimate the relevance of some nonlinear effects

asymptotic approach for non linear periodical vibrations of continuous structures abstract an asymptotic approach for determining periodic solutions of non linear vibration problems of continuous structures such as rods beams plates etc is proposed starting with the well known perturbation technique the independent displacement and frequency is expanded in a power series of a natural small parameter it leads to infinite systems of interconnected non linear algebraic equations governing the relationships between modes amplitudes and frequencies a non trivial asymptotic technique based on the introduction of an artificial small parameter is used to solve the equations an advantage of the procedure is the possibility to take into account a number of vibration modes as examples free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non linear restoring force are considered resonance interactions between different modes are investigated and asymptotic formulae for corresponding backbone curves are derived

image quality assessment based on multiscale geometric analysis reduced reference rr image quality assessment iqa has been recognized as an effective and efficient way to predict the visual quality of distorted images the current standard is the wavelet domain natural image statistics model wnism which applies the kullback leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion however wnism fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells in addition wavelet transforms are optimal greedy approximations to extract singularity structures so they fail to explicitly extract the image geometric information e g lines and curves finally wavelet coefficients are dense for smooth image edge contours in this paper to target the aforementioned problems in iqa we develop a novel framework for iqa to mimic the human visual system hvs by incorporating the merits from multiscale geometric analysis mga contrast sensitivity function csf and the weber s law of just noticeable difference jnd in the proposed framework mga is utilized to decompose images and then extract features to mimic the multichannel structure of hvs additionally mga offers a series of transforms including wavelet curvelet bandelet contourlet wavelet based contourlet transform wbct and hybrid wavelets and directional filter banks hwd and different transforms capture different types of image geometric information csf is applied to weight coefficients obtained by mga to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in hvs jnd is finally introduced to produce a noticeable variation in sensory experience thorough empirical studies are carried out upon the live database against subjective mean opinion score mos and demonstrate that 1 the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images 2 different transforms in mga under the new framework perform better than the standard wnism and some of them even perform better than the standard full reference iqa model i e the mean structural similarity index and 3 hwd performs best among all transforms in mga under the framework

analysis of forced non linear undamped oscillators by a time transformation method the recently developed time transformation method 1 3 is extended to the analysis of forced vibration of the strongly non linear undamped oscillator u u ef u p t where f u is a non linear function of the displacement u t and e is not necessarily small two types of external loading p t are considered a step input and a simple harmonic input the frequency amplitude relation is obtained through a slight modification of the results developed in reference 2 for the unforced oscillator a comparison with the results of numerical and other analytic methods is made it can be deduced that the time transformation approach offers simple and accurate approximations for the oscillators considered

interpreting the forced responses of a two degree of freedom nonlinear oscillator using backbone curves in this paper the backbone curves of a two degree of freedom nonlinear oscillator are used to interpret its behaviour when subjected to external forcing the backbone curves describe the loci of dynamic responses of a system when unforced and undamped and are represented in the frequency amplitude projection in this study we provide an analytical method for relating the backbone curves found using the second order normal form technique to the forced responses this is achieved using an energy based analysis to predict the resonant crossing points between the forced responses and the backbone curves this approach is applied to an example system subjected to two different forcing cases one in which the forcing is applied directly to an underlying linear mode and the other subjected to forcing in both linear modes additionally a method for assessing the accuracy of the prediction of the resonant crossing points is then introduced and these predictions are then compared to responses found using numerical continuation

nonlinear normal modes for damped geometrically nonlinear systems application to reduced order modelling of harmonically forced structures in order to build efficient reduced order models roms for geometrically nonlinear vibrations of thin structures a normal form procedure is computed for a general class of nonlinear oscillators with quadratic and cubic nonlinearities the linear perturbation brought by considering a modal viscous damping term is especially addressed in the formulation a special attention is focused on how all the linear modal damping terms are gathered together in order to define a precise decay of energy onto the invariant manifolds also defined as nonlinear normal modes nnms then this time independent formulation is used to reduce the dynamics governing the oscillations of a structure excited by an external harmonic force the validity of the proposed roms is systematically discussed and compared with other available methods in particular it is shown that large values of the modal damping of the slave modes may change the type of nonlinearity hardening softening behaviour of the directly excited master mode two examples are used to illustrate the main features of the method a two degrees of freedom dof system allows presentation of the main results through a simple example then a water filled circular cylindrical shell with external resonant forcing is considered in order to show the ability of the method to substantially reduce the dynamics of a continuous structure 2006 elsevier ltd all rights reserved

non linear stability analysis of a complex rotor stator contact system in this paper a non linear strategy based on the centre manifold the rational approximants and the alternating frequency time domain method has been developed in order to study the non linear dynamical behaviour of a system in the neighbourhood of a critical steady state equilibrium point the stability analysis and the non linear dynamics of a complex braking system with a non linear rotor stator contact are presented moreover one of the most important steps of this paper is the determination of the non linear behaviour and the limit cycle amplitudes of this complex system in order to conduct this study the dynamic response is evaluated by using applying the centre manifold the rational approximants and the alternating frequency time domain method that permit to obtain rapidly and efficiently the non linear behaviour of the system the dynamic response obtained by applying this method is compared with that evaluated through numerical integration

modal analysis of mechanical systems with impact non linearities limitations to a modal superposition this paper presents an attempt to generalize the modal superposition formula to mechanical systems with impact type non linearities following the procedure introduced for smooth non linearities the study is restricted to simple one and two degree of freedom systems with a unilateral constraint on one of the degrees of freedom for which the response can be analytically determined generalized frequencies modes and masses are built in the procedure the results obtained for various sets of parameters point out some limitations to the validity of a general modal superposition formula