modal identification using the frequency scale domain decomposition technique of ambient vibration responses abstract this paper proposes a new modal identification method of ambient vibration responses the application of the singular value decomposition to continuous wavelet transform of power spectral density matrix gives singular values and singular vectors in frequency scale domain analytical development shows a direct relation between local maxima in frequency scale representation of singular values and modal parameters this relation is then carried on for the identification of modal parameters via a complete practical procedure the main novelties of this work involve the new formulation in frequency scale domain and the capacity for the identification of modal parameters without the step of ridges extraction in comparison with previous wavelet based modal identification methods

hamiltonian principle based stress singularity analysis near crack corners of multi material junctions this paper presents a new method for the stress singularity analysis near the crack corners of a multi material junctions the stress singularities near the crack corners of multi dissimilar isotropic elastic material junctions are studied analytically in terms of the methods developed in hamiltonian system the governing equations of plane elasticity in a sectorial domain are derived in hamiltonian form via variable substitution and variational principle respectively both of the methods of global state variable separation and symplectic eigenfunction expansion are used to find the analytical solution of the problem the relationships among the state vectors in different material spaces are obtained by means of coordinate transformation and consistent conditions between the two adjacent domains the expression of the original problem is thus changed into a new form where the solutions of symplectic generalized eigenvalues and eigenvectors are needed the closed form of expressions is established for the stress singularity analysis near the corner with arbitrary vertex angles numerical results are presented with several chosen angles and multi material constants to show the potential of the new method proposed a semi analytical finite element is furthermore developed for the numerical analysis of crack problems

wavelet analysis for hopf bifurcations with aeroelastic applications abstract a wavelet analysis on the output signal of a non linear system in the neighbourhood of a hopf bifurcation i e a limit cycle oscillation has been performed to point out the linear and non linear signatures of the system indeed this kind of non linear behaviour is characterized not only by a simple harmonic oscillation in developed steady state condition but also by an initial transitory phase with a complex time evolution of the spectral signal content both these issues could be described in an analytical way via a singular perturbation analysis but they could be also directly analyzed by a signal processing tool via wavelet analysis continuous wavelet transform cwt this is obtained by using the wavelet capability in describing efficiently the time evolution of the spectrum of the signal i e a non linear signature of a hopf bifurcation furthermore the analytical results given by the singular perturbation analysis for the same class of non linear problems have allowed one to interpret correctly the results obtained by the wavelet analysis in this paper this theoretical link between the wavelet analysis and the output signal of a dynamical system recently achieved for linear mechanical damped systems has been extended to non linear systems in the neighbourhood of a hopf bifurcation this kind of analysis is of natural interest in aeroelastic applications where an efficient and noise insensitive analysis of the output signal recorded during the flight tests performed in the neighbourhood of the critical condition flutter may be desirable together with the capability to record the non linear system signature the time scale decompositions cwt have given the opportunity to analyze pre and post critical transient behaviour of a non linear aeroelastic system and thus upon considering the analytical tool given by the singular perturbation analysis to identify its linear and non linear features applications include either two non linear coupled oscillators or a typical section in a supersonic flow

asymptotic approach to analyze singular stress state in anisotropic multi material application to the rivets the problem of stress singularities due to multi material junctions is described in this paper a semi analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions the advantage of the present method is the quasi explicit knowledge of the stress and displacement fields around the junctions thus after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials numerical results are presented concerning various configurations of an assembly with rivets included in a bi layer composite that illustrate this method

minimizing error in the logarithmic decrement method through uncertainty propagation abstract logarithmic decrement is a well known approach for estimating the damping ratio from a time history this paper uses uncertainty propagation to unveil how uncertainties in different quantities can impact damping ratio estimates more specifically the trade off between the number of periods n between the first and final peaks and measurement noise is addressed the insights gained from this analysis are condensed into a single graphic or guide which provides the ideal number of periods n to use for a common range of measurement uncertainties and damping ratios the guide is then applied to experimental data derived from image processing to estimate the damping ratio

singular hypersingular and singular free electromagnetic fields at wedge tips in metamaterials the engineering response of metamaterials has a dramatic impact on the physics optics and engineering communities because they offer electromagnetic properties that are difficult or impossible to achieve with conventional materials in this paper an asymptotic analysis of the electromagnetic fields at multi material wedges composed of metamaterials is proposed this is made possible by removing the assumption of positive electric permittivities and magnetic permeabilities an hypothesis which usually applies to conventional materials exploring the whole range of variability of these electromagnetic properties it is shown that in addition to the classical real eigenvalues 0 1 leading to power law singularities of the type o r 1 as r 0 it is also possible to find imaginary eigenvalues leading to hypersingular solutions as well as nonsingular configurations for a suitable choice of the negative electric permittivities and magnetic permeabilities of the media moreover to fully characterize the asymptotic fields the analysis is not only restricted to the determination of the lowest real and complex eigenvalues but is also extended to the evaluation of the higher order nonsingular ones the obtained analytical results collected in synthetic diagrams are expected to have impact on the design of micro and nano electro mechanical systems

the plane elasticity problem of an isotropic wedge under normal and shear distributed loading application in the case of a multi material problem the problem of a multi material composite wedge under a normal and shear loading at its external faces is considered with a variable separable solution the stress and displacement fields are determined using the equilibrium conditions for forces and moments and the appropriate airy stress function the infinite isotropic wedge under shear and normal distributed loading along its external faces is examined for different values of the order n of the radial coordinate r the proposed solution is applied to the elastostatic problem of a composite isotropic k materials infinite wedge under distributed loading along its external faces applications are made in the case of the two materials composite wedge under linearly distributed loading along its external faces and in the case of a three materials composite wedge under a parabolically distributed loading along its external faces

damping identification using a continuous wavelet transform application to real data a continuous wavelet transform cwt based on the gabor wavelet function is used to identify the damping of a multi degree of freedom system the common procedures are already known especially the identification with a morlet cwt this study gives special attention to the following a description of the instantaneous noise the edge effect of the cwt the frequency shift of the cwt the bandwidth of the wavelet function and the selection of the parameter of the gabor wavelet function of the cwt the procedures are demonstrated using several numerical examples and on signals acquired from the lateral vibration of a uniform beam the study demonstrates the advantages of using the amplitude and phase methods both of which provide information about the instantaneous noise the procedures presented are appropriate for automating the identification process

the order of stress singularities for bonded and disbonded three material junctions abstract in plane solutions are given for the order of the stress singularity at an internal point in an elastic isotropic solid where three wedges of different materials meet the three interfaces are either all perfectly bonded or a disbond is introduced along one interface one feature of this three material junction that is not present for the corresponding two material case is that each interface is geometrically different and therefore the singular behavior is dependent on which interface is disbonded each material and geometrical combination therefore gives rise to four problems one with perfect bonding at all interfaces and three cases of an interface disbond numerical results are presented for selected three material junctions new results for two material junctions and wedges that serve as special cases for the present study are also presented

stress singularities in anisotropic multi material wedges and junctions abstract the general problem of stress singularities in anisotropic multi material wedges and junctions due to geometric and material discontinuities is investigated the anisotropic wedges and junctions discussed here comprise two or three materials with different geometric configurations and different material properties the interfaces in multi material junctions are either all perfectly bonded or a disbond is introduced along one interface the order of stress singularities is obtained by solving the characteristic equations that are developed from the boundary conditions of the problem numerical examples for the order of stress singularities are given for the general problem including two and three material wedges a crack terminating at an interface between two materials bonded and disbonded two and three material junctions as well an extra root of the characteristic equations in addition to three roots corresponding to higher singular stresses is observed for the cases of disbonded anisotropic two and three material junctions the stress singularities affected by geometric configurations and material properties of anisotropic materials are also investigated

finite element analysis of anisotropic materials with singular inplane stress fields abstract a finite element formulation is developed for the analysis of singular stress states at material and geometric discontinuities in anisotropic materials loaded inplane the displacement field of the sectorial element is quadratic in the angular coordinate direction and exponential in the radial direction measured from the singular point the formulation of yamada and okumura 1983a b is extended to take into account the anisotropy of the material the stress and displacement fields are obtained when the order of the stress singularity is real as well as complex when the order of the stress singularity is complex it is shown that the angular variation of the stress and displacement fields can be expressed in an infinite number of ways results for the displacement and stress fields obtained when the order of the stress singularity is complex can be made to match already published results once a similarity transformation is applied the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and rate of convergence associated with the element suggests that it could be used in developing enriched elements for use with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries

enrichment of finite elements with numerical solutions for singular stress fields enriched 2 d and 3 d finite elements are formulated for analysis of solids having multi material junction and wedge configurations that create singular stress fields due to the material and or geometric discontinuities the order and angular variation of the displacements associated with the singular fields are determined from a separate special finite element eigenanalysis and used in the enrichment process the use of these numerically determined singular fields allows enriched elements to be developed for complex configurations for which analytical fields are not available in addition to this added flexibility of application the current formulation applies to elements that may or may not be in direct contact with the singular point this allows multiple layers of enriched elements to be used around the singular point and traditional mesh refinement studies to be carried out in the enriched element region previous enriched formulations have not provided this important capability for cases where analytical fields are available such as cracked solids the performance of elements developed with the current approach is shown to be equivalent to that obtained using analytically enriched elements mesh refinement techniques using enriched elements are described that allow accurate stress distributions and generalized stress intensity factors to be directly determined the importance of high order numerical integration use of multiple layers of enriched elements and proper choice of the size of the enriched region are demonstrated by comparison to existing solutions for solids with cracks application of enriched element modelling to a 2 d bi material wedge and a 3 d stepped thickness anisotropic composite laminate is demonstrated 1997 john wiley sons ltd

hilbert transform and its engineering applications the hilbert transform is useful in calculating instantaneous attributes of a time series especially the envelope amplitude and instantaneous frequency the instantaneous envelope is the amplitude of the complex hilbert transform the instantaneous frequency is the time rate of change of the instantaneous phase angle these properties can be applied to identify dynamic characteristics of a linear as well as a nonlinear system however the conventional discrete hilbert transform which is based on fast fourier transform and inverse fourier transform has shown the lack of accuracy for time derivative calculations in this paper we first introduce the hilbert transform and its applications to the nonlinear system parameter identification then we address the practical issues in applying the hilbert transform to engineering applications to increase the accuracy of the envelope detection we propose a hilbert transform technique based on local maxima interpolation analyses and simulations are carried out to demonstrate the advantages of the proposed technique finally we employ the proposed local maxima interpolation technique in identifying the nonlinear dynamic characteristics of industrial examples

a new variable order singular boundary element for two dimensional stress analysis a new variable order singular boundary element for two dimensional stress analysis is developed this element is an extension of the basic three node quadratic boundary element with the shape functions enriched with variable order singular displacement and traction fields which are obtained from an asymptotic singularity analysis both the variable order of the singularity and the polar profile of the singular fields are incorporated into the singular element to enhance its accuracy the enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour integral methods numerical examples involving crack notch and corner problems in homogeneous materials and bimaterial systems show the singular element s great versatility and accuracy in solving a wide range of problems with various orders of singularities the stress intensity factors which are obtained agree very well with those reported in the literature copyright 2002 john wiley sons ltd

identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform we consider the free response of a nonlinear vibrating system using the ridges and skeletons of the continuous wavelet transform we identify weak nonlinearities on damping and stiffness and estimate their physical parameters the crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform the method is applied to simulated single degree of freedom systems and multi degree of freedom systems with nonlinearities on damping and stiffness experimental validation of the nonlinear identification and parameter estimation method is presented the experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor

stochastic processes evolutionary spectrum estimation via harmonic wavelets the problem of estimating the power spectrum of non stationary stochastic processes using dyadic generalized and filtered harmonic wavelets is addressed explicit relationships between the statistical moments of the coefficients of the wavelets based representation of the process and of its evolving spectral values are given it is shown that the popular concept of a separable evolutionary spectrum involving a deterministic modulating envelope is subject to interpretation further mathematical expressions elucidating the analogy between the wavelets based spectral representation and the traditional one involving trigonometric functions are derived finally the applicability and the physical soundness of the developed procedure are demonstrated by applying it to records of the kocaeli turkey earthquake 8 17 1999

analysis of wavelets in chaotic states for a one degree of freedom system with viscoelastic restraints a qualitative numerical technique is presented for identifying chaotic states of a non linear one sided constrained one degree of freedom 1 d o f deterministic system under a dynamic non conservative load discrete wavelet analysis in its classic and packet versions was used to search for the boundaries of chaotic and non chaotic solutions the results obtained were verified by an analysis of the lyapunov exponents of the investigated system on the basis of numerical tests one can state that wavelet analysis may be a fast and reliable tool suitable for searching for the boundaries of chaotic and non chaotic solutions

an analysis of weighted eigenspace methods in the presence of sensor errors among all direction finding methods eigenspace based spectral methods are of interest because they are known to yield asymptotically unbiased and efficient estimates these algorithms require knowledge of the array geometry and its elements characteristics in real systems only approximate knowledge of the required array characterization is available there is valid concern that deviation of nominal sensor gain and phase values can result in degradation of doa estimates we analyze the effects of sensor gain and phase perturbation on weighted eigenspace methods wems we quantify the sensitivity of wems by first and second order statistical analyses simulation results are included to validate our analytical results

damping identification in multi degree of freedom systems via a wavelet logarithmic decrement part 1 theory a wavelet based formula similar to the logarithmic decrement formula is introduced to estimate damping in multi degree of freedom systems from time domain responses both analytical and numerical approaches are investigated

continuous wavelet transform for modal identification using free decay response abstract this paper deals with the use of the continuous wavelet transform for system identification purposes the wavelet analysis of the free responses of a linear mechanical system allows the estimation of its natural frequencies viscous damping ratios and mode shapes using either the modulus or the phase of the wavelet transform a complete procedure for modal identification from free responses based on the continuous wavelet transform is presented two difficulties during the implementation of this technique are highlighted the edge effect and the choice of the time frequency localization of the wavelet transform some upper and lower bounds for the mother wavelet s parameters are given in order to improve the numerical computation three complex valued mother wavelets are studied and the full procedure is applied to a damped discrete system the correct choice of the mother wavelet s parameters leads to an accurate identification of the modal parameters

stress singularity analysis in three dimensional bonded structure abstract stress analysis for joints between two isotropic materials is performed using three dimensional boundary element method with rongved s fundamental solution rongved l 1955 force interior to one of two joined semi infinite solids in second midwestern conf on solid mechanics pp 1 13 which satisfies boundary conditions at the interface the stress distribution around the vertex of the joint is precisely examined and the order of stress singularity obtained in three dimensional analysis is compared with that in two dimensional analysis it is shown that the order of the stress singularity along the stress singularity line which is the intersection of the interface with the free surface varies from the value in plane strain to that in plane stress as the opposite side free surface is approached the order of stress singularity in the spherical coordinates centered at the vertex is next investigated when singularity lines with a singularity order meet with each other at the vertex the order of stress singularity is larger than that for plane strain and plane stress when the vertex angle between two side free surfaces is varied the order of stress singularity is also altered in particular a bound at which singularity disappears at the plane for dundurs composite parameters is examined for a cubic dissimilar material it is demonstrated that the bound varies little in comparison with the one obtained from the two dimensional theory

bias and variance of direction of arrival estimates from music min norm and fine we derive variance and bias expressions of direction of arrival doa estimates for min norm and fine these expressions for arbitrarily configured arrays are valid and accurate over wide ranges of snr and number of snapshots using these expressions we illustrate that both min norm and fine have smaller estimate bias and further fine has comparable estimate variance compared to music

natural frequencies and damping estimation using wavelet transform of a frequency response function this paper deals with a general wavelet transform of frfs for linear systems complex fractional functions are used as wavelets and properties of the wavelet transform are studied then an efficient method for estimating natural frequencies and dampings is proposed the efficiency of the method is illustrated with both analytical and experimental data of frequency response functions

an assessment of damping identification methods a study is carried out into the philosophy and performance of different approaches for the determination of linear viscous damping in elasto mechanical systems the methods studied include a closed form solution identification methods based on inverting the matrix of receptances energy expressions developed from single frequency excitation and responses as well as first order perturbation methods the work is concentrated particularly upon modal truncation and how this affects the distribution of matrix terms and the ability of the identified damping together with known mass and stiffness terms to reproduce the complex eigenvalues and eigenvectors of the full order system a simulated example is used to illustrate various points covered in the theoretical discussion of the methods considered

influence of the intermediate material on the order of stress singularity in three phase bonded structure the plane problem for dissimilar materials composed of three isotropic homogeneous wedges with arbitrary angles under surface tractions is analysed using the theory of elasticity the order of singularity in stress fields near the apex of a three phase bonded structure is investigated it is first demonstrated how the order of stress singularity varies with several combinations of material with different properties in cases where the angles of wedge are of 3 3 3 and 2 2 2 when the materials and wedge angles of the side regions are identical the order of stress singularity is additionally studied in detail with the wedge angle of the intermediate region varying in cases where the total angle of the bonded wedge geometry is fixed and not fixed a method reducing the stress singularity in a two phase bonded structure is finally proposed

a finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear a finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading the displacement field of the sectorial element is quadratic in the angular co ordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura14 for in plane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries

modal identification based on continuous wavelet transform and ambient excitation tests abstract this paper deals with the use of the continuous wavelet transform for modal identification from ambient vibration tests the wavelet analysis of the free responses of a linear mechanical system has been used to estimate its natural frequencies viscous damping ratios and mode shapes using either the modulus or the phase of the wavelet transform with ridge and skeleton notions this technique is extended in this paper to the response from ambient excitation tests based on the equivalent formulation between the free response and the correlation function of a linear mechanical system under stationary stochastic excitation the main novelties involve the new formulation of continuous wavelet transform and the use of the singular value decomposition algorithm for ridges and skeleton detection under the noisy conditions of ambient vibration tests a complete procedure for modal identification of ambient response including these new formulations is presented and then applied to numerical examples and experimental test to illustrate its validity

second order statistical analysis of totally weighted subspace fitting methods we analyze the effects of a limited number of snapshots on a general class of multidimensional signal subspace estimation methods termed totally weighted subspace fitting twsf methods this class is an extension of the weighted subspace fitting technique that includes row weighting and column weighting of the signal subspace matrix we quantify the asymptotic statistical properties of the twsf method by means of a second order statistical analysis the main contribution of this article is that it provides for the first time the estimator bias some simulation results are included to validate our analytical results

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

identification of damping in mdof systems using time scale decomposition abstract a method of damping identification in multi degree of freedom systems is presented the method is based on the time scale decomposition of the system impulse response the continuous wavelet transform is used to decompose the impulse response into the time scale domain three techniques based on the wavelet tranform are used to estimate damping these are the wavelet transform cross section procedure the impulse response recovery procedure based on wavelet domain filtering and the wavelet ridge detection procedure the methods are applied to simulated multi degree of freedom systems

identification of coupled non linear modes from free vibration using time frequency representations abstract a new method based on time frequency representations is presented for identifying the non linear modal parameters of a multi degree of freedom non linear lightly damped mechanical system the coupled non linear modes are first introduced it is shown that by using the coupled non linear modes the free response can be expressed as a linear combination of frequency and amplitude modulated components this suggests the use of time frequency methods to characterize these modulation laws and then identify the coupled non linear modes these modulation laws are extracted by using an extended definition of the so called ridges of the continuous gabor transform which enables a more accurate estimation an identification procedure of the coupled non linear modes is proposed and the validity of the whole process is confirmed by performing computer simulations of different types of non linear elastic dynamic systems

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

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels