linear damping models for structural vibration abstract linear damping models for structural vibration are examined first the familiar dissipation matrix model then the general linear model in both cases an approximation of small damping is used to obtain simple expressions for damped natural frequencies complex mode shapes and transfer functions results for transfer functions can be expressed in the form of very direct extensions of the familiar expression for the undamped case this allows a detailed discussion of the implications of the various damping models for the interpretation of measured transfer functions especially in the context of experimental modal analysis in the case of a dissipation matrix model it would be possible in principle to determine all the model parameters from measurements in the case of the general model however there is a fundamental ambiguity which prevents full determination of the model from measurements on a single structure

persistent random motion with maximally correlated fluctuations how often should a random walker change its direction of motion in order to maximize correlation in velocity fluctuations over a finite time interval we address this optimal diffusion problem in the context of the one dimensional persistent random walk where we evaluate the correlation and mutual information in velocity trajectories as a function of the persistence level and the observation time we find the optimal persistence level corresponds to the average number of direction reversals asymptotically scaling as the square root of the observation time this square root scaling law makes the relative growth between the average number of direction reversals and the persistence length invariant with respect to changes in the overall time duration of the random walk

on a general model for damping when a structure exhibits a damped dynamic behavior that does not conform to the classical and well known viscous or hysteretic models a more general approach must be sought several questions may then be raised like i in which theoretical background should one base the investigation or ii can one apply common modal analysis tools to solve the problem recent works have shown that some types of materials and therefore structures demand a more rigorous behavior description and that it seems possible to address the problem by means of the theory of fractional derivatives leading to a model in terms of general damping parameters such an approach reveals itself somewhat complicated to implement in practice and some simplifications are necessary the authors discuss the use of a generalized damping concept for modeling the dynamic behavior of linear systems and show how this concept allows for a clearer interpretation and explanation of the behavior displayed by the common viscous and hysteretic models

ising field theory in a magnetic field analytic properties of the free energy we study the analytic properties of the scaling function associated with the 2d ising model free energy in the critical domain t tc h 0 the analysis is based on numerical data obtained through the truncated free fermion space approach we determine the discontinuities across the yang lee and langer branch cuts we confirm the standard analyticity assumptions and propose extended analyticity roughly speaking the latter states that the yang lee branching point is the nearest singularity under langer s branch cut we support the extended analyticity by evaluating numerically the associated extended dispersion relation

on the impulse response precursor of an ideal linear hysteretic damper the model of the ideal linear hysteretic damper has been shown to possess a non causal impulse response precursor however the relevant characteristics of the impulse response precursor its extremum monotonicity and asymptotic property were not well comprehended in the literature in this paper an impulse response precursor expression was derived it was observed that the impulse response precursor achieves its only extremum which is negative at the origin the impulse response precursor monotonically increases from this extremum to zero while time retraces to the negative infinity the asymptotic rate of impulse response precursor approaching zero is o 1 t the non causal size gets stronger as the loss factor increases numerical computation also shows that the non causal extremum is even deeper than the first trough of the causal portion of the impulse response when the loss factor is greater than 0 77

approximating the hysteretic damping matrix by a viscous matrix for modelling in the time domain the paper is concerned with modelling the dynamic behaviour of a structure with damping hysteretic damping is commonly accepted to be reasonably accurate in some circumstances but can only be applied directly in the frequency domain dynamic time behaviour however is most conveniently predicted by a viscous model a damping matrix is constructed for use in the viscous equation which gives a dissipation of energy approximating to the hysteretic model the approximation is justified by comparing results in the frequency and time domains and against measured data from a loudspeaker diaphragm the ability of the matrix to reflect different damping in various components of the structure is considered together with predicted natural frequencies and modes

the 2 1 d ising model on a triangular lattice the 2 1 d ising model on a triangular lattice is explored for lattices of up to 5 5 sites finite size scaling techniques are used to estimate the critical parameters xc 0 2096 2 nu 0 627 4 beta 0 322 6 gamma 1 236 8 these agree with previous estimates within errors and with the hypotheses of universality and hyperscaling the behaviour at low temperatures is also studied and theoretical predictions of finite size scaling at a first order transition are confirmed

identification of linear non viscous damping with different kernel functions in the time domain abstract the non viscous damping model considers the complete velocity history via a convolution over the kernel functions in this paper a procedure is proposed for identifying a damping model involving different kernel functions in the time domain the method uses responses calculated by the generic time domain integration with the known mass matrix and the stiffness matrix the relaxation parameter in the kernel function is identified through a summation of the error function and the damping coefficient matrix is identified via the linear least squares method two examples show that reasonable estimates could be obtained by the proposed method

series analysis of the 3 state potts model in 2 1 dimensions both high temperature and low temperature series are used to locate and characterize the first order transition in the 3 state potts model in 2 1 dimensions on both square and triangular lattices estimates are presented for the vacuum energy latent heat magnetization susceptibility and mass gap at the transition the spontaneous magnetization and latent heat appear to display an approximate universality at this weak first order transition

the 3 state potts model in 2 1 dimensions the 3 state potts model in 2 1 dimensions is studied using series and monte carlo methods high temperature series for the vacuum energy mass gap and susceptibility are computed on the square and triangular lattices using linked cluster expansions monte carlo estimates are obtained by the stochastic truncation method the model is found to undergo a weak first order transition as in the euclidean version of the model

analytic continuation at first order phase transitions we study the analytic structure of thermodynamic functions at first order phase transitions in systems with short range interactions and in particular in the two dimensional ising model we analyze the nature of the approximation of the d 2 system by ann strip investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of h 0 in the complexh plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allh 0 this new function is used for numerical calculation of the coefficients cn in the power series expansions of the magnetizationm in the form m h 1 cn h h 0 n for various h0 0 the resulting series are studied by conventional methods we confirm recent series analysis results on the existence of the droplet model type essential singularity at h 0 evidence is found for a spinodal at h hsp ti 0

unraveling the structure of treelike networks from first passage times of lazy random walkers we study the problem of random search in finite networks with a tree topology where it is expected that the distribution of the first passage time f t decays exponentially we show that the slope of the exponential tail is independent of the initial conditions of entering the tree in general and scales exponentially or as a power law with the extent of the tree l depending on the tendency p to jump toward the target node it is unfeasible to uniquely determine l and p from measuring the tail slope or the mean first passage time mfpt of an ordinary diffusion along the tree to unravel the structure we consider lazy random walkers that take steps with probability m when jumping on the nodes and return with probability q from the leaves by deriving an exact analytical expression for the mfpt of the intermittent random walk we verify that the structural information of the tree can be uniquely extracted by measuring the mfpt for two randomly chosen types of tracer particles with distinct experimental parameters m and q we also address the applicability of our approach in the presence of disorder in the structure of the tree or statistical uncertainty in the experimental parameters

finite size scaling of critical cumulants near the ferromagnetic phase boundary abstract we employ the recently proposed scaling theory for first order transitions to derive a detailed prediction for the large argument behaviour of the critical point scaling function of the reduced fourth order cumulant g l 4 2 2 3 correct up to a term exponentially small in l t

stochastic truncation for the 2 1 d ising model the method of symmetrized stochastic truncation is applied to the 2 1 dimensional ising model to calculate the ground state energy mass gap magnetization and susceptibility on lattices of sizes up to 6 6 sites the method is shown to be a powerful and accurate monte carlo technique provided the lattice size is not too large and the model is suitably convergent finite size scaling estimates of the critical indices are nu 0 627 2 alpha 0 12 2 beta 0 324 3 and delta 1 23 1 an estimate of the combination gamma nu 2 beta nu 3 000 1 is obtained in outstanding agreement with the expected hyperscaling relation

metastability and analyticity in a dropletlike model we consider an urn model closely related to the fisher felderhof droplet model for the purpose of studying the relation between metastability and analytic continuation for this model both the statics and dynamics can be solved and we confirm the relation between the metastable decay rate and the imaginary part of the analytically continued free energy actually pressure in this model we also find that eigenvalue degeneracy an old theme for static aspects of phase transitions appears in the dynamics as well when approaching the phase transition from the stable side it is a degeneracy in the eigenvalues of the linear operator appearing in the master equation that causes the system to lock into a particular phase

finite size scaling study of a first order temperature driven symmetry breaking structural phase transition we present a study of finite size effects in a model exhibiting a first order temperature driven symmetry breaking structural phase transition in thel cylindrical geometry in thel limit exact studies demonstrate the applicability of our scaling ansatz even in the one dimensional limit making this model ideal for studying finite size effects the scaling ansatz similar to the previously developed ansatz for field driven transitions demonstrates that latent heat is crucial in driving these transitions this ansatz is supported by a 2 2 phenomenological transfer matrix based upon the symmetries of the system this produces an analytic free energy which has the scaling form order parameter probability distributions show that the high and low temperature phases coexist only in a small finite size affected regime near the bulk transition temperature this regime vanishes exponentially fast asl diverges

magnetisations from finite size scaling a method of obtaining the spontaneous magnetisation from finite lattice matrix elements of the magnetic field operator due to yang 1952 and uzelac 1980 is discussed the method is demonstrated for the case of the ising model in 1 1 dimensions and is shown to provide smooth and rapidly convergent finite lattice sequences applied to the case of the three state potts z3 model in 1 1 dimensions the method yields an estimate beta 0 111 09 or 0 000 05 for the critical exponent this confirms alexander s conjecture of universality with the hard hexagonal model

persistent random walk approach to anomalous transport of self propelled particles the motion of self propelled particles is modeled as a persistent random walk an analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk s displacement it is shown that the interplay of step length and turning angle distributions and self propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients the crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented

improved approximate methods for calculating frequency response function matrix and response of mdof systems with viscoelastic hereditary terms as we know it is difficult and unnecessary to obtain all the eigenpairs of a large scaled viscoelastic nonviscous or hysteretic damping systems which means that the mode truncation scheme is generally used and the mode truncated error is therefore introduced this study is aimed at eliminating the influence of the unavailable modes on the dynamic response of mdof systems with viscoelastic hereditary terms the energy dissipation terms of the system depend on the past history of motion via convolution integrals over some kernel functions therefore the system is a nonviscously damped system which has been considered as the most generalized damping model within the scope of a linear mechanical analysis to approximate frequency response function frf matrix and response without using the unavailable modes we suggest two methods which attempt to approximate the influence of the unavailable modes in terms of the lower modes and system matrices by using the first one or two terms of neumann expansion of the contribution of the unavailable modes in contrast with the frf matrix approximated in terms of the first two terms of neumann expansion these procedures cannot be extended to further high order terms since all of them will be affected by the frequency dependent variation of damping matrix from previous terms finally an example is shown that the two presented methods can make the mode truncated error reduce and may be used to approximate the influence of nonviscous modes contributed to frf matrix due to the fact that the nonviscous modes are difficult to be obtained accurately even if a small scaled model is used for some eigensolution methods

quantification of non viscous damping in discrete linear systems abstract the damping forces in a multiple degree of freedom engineering dynamic system may not be accurately described by the familiar viscous damping model the purpose of this paper is to develop indices to quantify the extent of any departures from this model in other words the amount of non viscosity of damping in discrete linear systems four indices are proposed two of these indices are based on the non viscous damping matrix of the system a third index is based on the residue matrices of the system transfer functions and the fourth is based on the measured complex modes of the system the performance of the proposed indices is examined by considering numerical examples

infinite range mean field percolation transfer matrix study of longitudinal correlation length two infinite range directed percolation models equivalent also to epidemic models are considered for a finite population finite number of sites n at each time directed axis step the general features of the transfer matrix spectrum evolution operator spectrum for the epidemic are studied numerically and compared with analytical predictions in the limitn one of the models is devised to allow numerical results to be obtained forn as high as nearly 800 for the largest longitudinal percolation correlation length relaxation time for epidemic the finite n behavior of this correlation length is studied in detail including scaling near the percolation transition exponential divergence withn above the percolation transition as well as other noncritical and critical point properties

finite element model updating with damping identification abstract most of finite element model updating techniques do not employ damping matrices and hence cannot be used for accurate prediction of complex frequency response functions frfs in this paper damped finite element model updating procedure is proposed and tested with the objective that the damped finite element updated model is able to predict the measured frfs accurately the proposed damped updating procedure is a two step procedure in the first step mass and stiffness matrices are updated using frf data and in the second step damping matrix is identified using updated mass and stiffness matrices that are obtained in the previous step the effectiveness of the proposed procedure is demonstrated by numerical examples as well as by actual experimental data firstly a study is performed using a numerical simulation based on fixed fixed beam structure with non proportional viscous damping model the numerical study is followed by case involving actual measured data for the case of f shaped test structure the results have shown that the proposed procedure can be used for accurate prediction of the complex frfs

a galerkin method for distributed systems with non local damping in this paper a non local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of euler bernoulli beams and kirchoff plates unlike ordinary local damping models the damping force in a non local model is obtained as a weighted average of the velocity field over the spatial domain determined by a kernel function based on distance measures the resulting equation of motion for the beam or plate structures is an integro partial differential equation rather than the partial differential equation obtained for a local damping model approximate solutions for the complex eigenvalues and modes with non local damping are obtained using the galerkin method numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions for non local and non viscous damping models and different kernel functions

a novel approach for distributed dynamic load reconstruction by space time domain decoupling abstract a novel inverse approach based on green s function method and orthogonal polynomial fitting technique is presented in this paper to reconstruct the distributed dynamic load acting on a structure this approach enables one to identify the time history and reconstruct the spatial distribution function separately it is first assumed in this paper that the distribution function and the time history of the distributed dynamic load are separable modal analysis proves the sameness of the form between the modal loads and the actual time history with the knowledge of corresponding green s functions and modal responses the modal loads are identified later approximating the spatial distribution function by a set of chebyshev orthogonal polynomials new distributed dynamic loads are constructed with each orthogonal polynomial performing as the spatial distribution function and the previously identified modal load acting as the time history fitting the modal loads the coefficients of each orthogonal polynomial are achieved and then the spatial distribution function recovered to overcome the intrinsic ill conditioned characteristic appropriate regularization methods are adopted in both the modal load identification and the distribution function reconstruction numerical examples demonstrate the validity and accuracy of the proposed method

finite size corrections for inclined interfaces in two dimensions exact results for ising and solid on solid models analysis of finite size corrections for the surface tension and surface stiffness coefficients in two dimensional models with inclined interfaces is presented we obtain a universal leading contribution proportional to lnl l for the 2d system of sizel by explicit calculations for restricted and unrestricted solid on solid models and the square lattice ising model we demonstrate the gaussian nature of rough interfaces with fixed ends and derive the leading 1 l type corrections for appropriate surface quantities

the 1d interacting bose gas in a hard wall box we consider the integrable one dimensional function interacting bose gas in a hard wall box which is exactly solved via the coordinate bethe ansatz the ground state energy including the surface energy is derived from the lieb liniger type integral equations the leading and correction terms are obtained in the weak and strong coupling regimes from both the discrete bethe equations and the integral equations this allows the investigation of both finite size and boundary effects in the integrable model we also study the luttinger liquid behaviour by calculating luttinger parameters and correlations the hard wall boundary conditions are seen to have a strong effect on the ground state energy and phase correlations in the weak coupling regime enhancement of the local two body correlations is shown by application of the hellmann feynman theorem

asymptotic degeneracy of the transfer matrix spectrum for systems with interfaces relation to surface stiffness and step free energy two and three dimensional ising type systems are considered in the finite cross section cylindrical geometry an interface is forced along the cylinder strip in 2d by the antiperiodic or boundary conditions detailed predictions are presented for the largest asymptotically degenerate set of the transfer matrix eigenvalues for rough interfaces i e for 0 t tc in 2d tr t tc in 3d the eigenvalues are split algebraically and the spectral gaps are governed by thesurface stiffness coefficient for rigid interfaces i e 0 t tr in 3d the eigenvalues are split exponentially with the gaps determined by thestep free energy

crossover finite size scaling at first order transitions in a recent paper we developed a method which allows one to control rigorously the finite size behavior in long cylinders near first order phase transitions at low temperature here we apply this method to asymmetric transitions with two competing phases and to theq state potts model as a typical model of a temperature driven transition whereq low temperature phases compete with one high temperature phase we obtain the finite size scaling of the firstn eigenvalues wheren is the number of competing phases of the transfer matrix in a periodic box of volumel l t and as a corollary the finite size scaling of the shape of the order parameter in a hypercubic box t l the infinite cylinder t and the crossover regime from hypercubic to cylindrical scaling for the two phase case n 2 we find that the crossover length l is given by o lw exp lv where is the inverse temperature is the surface tension and w 1 2 if v 1 2 whilew 0 if v 1 2 for the standard ising model we also consider free boundary conditions showing that l exp lv o lv 1 for any dimension v 1 2 for v 1 2 we finally discuss a class of boundary conditions which interpolate between free corresponding to the interpolating parameter g 0 and periodic boundary conditions corresponding to g 1 finding that l o lw exp lv withw 0 forg 0 andw 1 2 for 0 g 1

difference equations in statistical mechanics ii solid on solid models in two dimensions a review and some new results are presented for the solid on solid models of wetting in two dimensions i e line interfaces with an emphasis on the difference equations arising in the transfer matrix calculations for these models methods for solving the appropriate difference equations exactly or approximately are surveyed including specific results for short range long range power law and applied field like binding external potentials

analysis of the critical velocity of a load moving on a beam supported by a finite depth foundation abstract a detailed analysis of the critical velocity of a uniformly moving load is carried out in this paper it is assumed that the load is traversing an infinite beam supported by a finite depth foundation under plane strain condition the problem is solved analytically in the fourier domain respecting two formulations of the interface condition the critical velocity is determined as the velocity under which the undamped beam deflection tends to infinity i e by identifying double poles in the fourier image of the beam deflection situated on the real fourier variable axis results obtained are compared with the previously published results of this author where simplifying assumptions were imposed on the shear contribution of the foundation based on the results an addition to the previous formula for critical velocity estimate is proposed it is confirmed that there are several critical velocities but the lowest one which is the dominating one smoothly changes from the classical value to the lowest wave velocity of propagation in the foundation according to the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass particular situations where the first double pole cannot be formed in this model are discussed in detail in such cases a significant increase of deflection is observed in the vicinity of the expected location defining thus a pseudo critical velocity attention is paid to the cases where there are two or more very close critical velocities which causes an increased risk for practical applications in addition several options of damping are compared

comments on nonlinear vibration of viscoelastic beams described using fractional order derivatives abstract this discussion seeks to address some of the inconsistencies and concerns regarding fractional derivatives when applied to vibration analysis of viscoelastically damped beams 1 detailed numerical assessments of the major fractional derivatives of concern have been carried out with their relationships numerically examined numerical results have shown that two of the key equations of 1 are mathematically inappropriate and their applications could lead to serious modelling errors a simplified yet representative nonlinear system with fractional viscoelastic damping and cubic stiffness nonlinearity is used to illustrate the existence of periodic steady state solutions as well as amplitude frequency characteristics of such fractional nonlinear systems

correlation length of the three state potts model in three dimensions a monte carlo study is carried out for the three state potts model in three dimensions the correlation length is shown to remain finite and to be discontinuous at the transition point it is also shown that the transition exhibits genuine first order characteristics in all aspects

q state potts models in hamiltonian field theory for q 4 in 1 1 dimensions finite lattice sequence extrapolation methods are applied to the q state potts models in 1 1 d hamiltonian field theory thermal exponents nu 0 71 or 0 02 alpha 0 53 or 0 02 are obtained for the four state model methods are discussed for treating the first order transitions for q 4 and a sequence extrapolation is used to estimate the latent heat exact analytic formulae are derived for the ground state energy the mass gap and the latent heat at the transition point these are compared with the numerical results

surface tension from finite volume vacuum tunneling in the 3d ising model we measure the surface tension in the broken phase of the 3d ising model at a temperaturet 0 955t c with two different methods which are taken from quantum field theory in finite volumes both methods rely on finite size effects close to the phase transition the first one measures from the size dependence of the vacuum tunneling energy which is determined by the decay of a correlation giving 0 030 the second one extracts from the size dependence of the rate of flip events and its corresponding correlation time it leads to 0 027 both values agree reasonably with other calculations

series analysis of tricritical behaviour mean field model and slicewise pade approximants a mean field model is proposed as a test case for tricritical series analysis methods derivation of the 50th order series for the magnetization is reported as the first application this series is analysed by the traditional slicewise pade approximant method popular in earlier studies of tricriticality

latent heats from finite size scaling a method of obtaining the latent heat at a first order transition from finite lattice matrix elements is discussed and demonstrated for the case of the 1 1 d potts model the method is shown to provide smoothly convergent finite lattice sequences the structure of the finite lattice hamiltonian eigenvalues is exhibited and a characteristic signal of the first order transition is proposed the finite size scaling behaviour at the transition is also discussed

approximation of solutions for an initial and terminal value problem for the forced duffing equation with non viscous damping an algorithm to find explicit approximate solutions of an initial and terminal value problem for the forced duffing equation with non viscous damping is accomplished via a generalized quasilinearization method in fact we obtain a monotone sequence of approximate solutions converging uniformly and quadratically to a unique solution of the problem

damped lateral vibrations of straight and curved cables with no axial pre load abstract this paper presents a study of the lateral vibrations of straight and curved cables with no axial pre load for the computation of the vibration transmissibility we used finite elements based on the euler bernoulli theory the dissipation of energy was studied with viscous and structural damping models where the rayleigh coefficients and the frequency dependence of the loss factor were identified by using the equality between the measured and the computed natural frequencies the frequency dependence of the dynamic modulus of elasticity was estimated and used for all the studied types of cable the excitation was the result of moving the support in a direction perpendicular to the axis of the cable the mathematical model for the computation of the vibrations of the straight and curved cables was verified with experimental measurements in which the support excitation was achieved with an electrodynamic shaker and the amplitude force was measured at the fixed support with a dynamometer for the curved cable the mathematical model was verified for in plane and out off plane vibrations three straight cables of different lengths were analyzed for the dependence of the rayleigh coefficients on the length of the cables