from one cell to the whole froth a dynamical map we investigate two and three dimensional shell structured inflatable froths which can be constructed by a recursion procedure adding successive layers of cells around a germ cell we prove that any froth can be reduced into a system of concentric shells there is only a restricted set of local configurations for which the recursive inflation transformation is not applicable these configurations are inclusions between successive layers and can be treated as vertices and edges decorations of a shell structured inflatable skeleton the recursion procedure is described by a logistic map which provides a natural classification into euclidean hyperbolic and elliptic froths froths tiling manifolds with different curvatures can be classified simply by distinguishing between those with a bounded or unbounded number of elements per shell without any a priori knowledge on their curvature a result associated with maximal orientational entropy is obtained on topological properties of natural cellular systems the topological characteristics of all experimentally known tetrahedrally close packed structures are retrieved

numerical analysis of a new space time variable fractional order advection dispersion equation many physical processes appear to exhibit fractional order behavior that may vary with time and or space the continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable in this paper we consider a new space time variable fractional order advection dispersion equation on a finite domain the equation is obtained from the standard advection dispersion equation by replacing the first order time derivative by coimbra s variable fractional derivative of order x 0 1 x 0 1 and the first order and second order space derivatives by the riemann liouville derivatives of order x t 0 1 x t 0 1 and x t 1 2 x t 1 2 respectively we propose an implicit euler approximation for the equation and investigate the stability and convergence of the approximation finally numerical examples are provided to show that the implicit euler approximation is computationally efficient

variable order fractional differential operators in anomalous diffusion modeling abstract the purpose of this paper is to offer a unified discussion of variable order differential operators in anomalous diffusion modeling the characteristics of the new models in contrast to constant order fractional diffusion models change with time space concentration or other independent quantities we introduced a classification of variable order fractional diffusion models based on the possible physical origins which prompt the variable order some potential applications of the variable order fractional diffusion models are also discussed

adaptive discretization of fractional order viscoelasticity using sparse time history an efficient numerical method to integrate the constitutive response of fractional order viscoelasticity is developed the method can handle variable time steps to overcome the problem of the growing amount of data that has to be stored and used in each time step we introduce sparse quadrature we use an internal variable formulation of the viscoelastic equations where the internal variable is of stress type the rate equation that governs the evolution of the internal variable involves a fractional integral and can be identified as a volterra integral equation of the second kind with a weakly singular kernel for the numerical integration of the rate equation we adopt the finite element method in time in particular the discontinuous galerkin method with piecewise constant basis functions is used a priori and a posteriori error estimates are proved an adaptive strategy based on the a posteriori error estimate is developed finally the precision and effectiveness of the method are demonstrated by comparing the numerical solutions with analytical solutions

frames induced by the action of continuous powers of an operator abstract we investigate systems of the form a t g g g t 0 l where a b h is a normal operator in a separable hilbert space h g h is a countable set and l is a positive real number although the main goal of this work is to study the frame properties of a t g g g t 0 l as intermediate steps we explore the completeness and bessel properties of such systems from a theoretical perspective which are of interest by themselves beside the theoretical appeal of investigating such systems their connections to dynamical and mobile sampling make them fundamental for understanding and solving several major problems in engineering and science

power law damping parameter identification abstract the parameter estimation of a nonlinear power damping system is studied the parameter identification method used here assumes a priori the equation of motion describing the system dynamics the method which is based on the measured data acceleration was applied to the free and forced vibrations the identification procedure was found to be robust on the guessed value of parameters at the numerical experimentation the parameter values were estimated with a good accuracy for both modes of system operation free and forced if only the measured time history was sampled at a high enough rate for the noise level contained within it was shown that the steady state of the harmonically excited system is not the best region for the parameter identification with this method during the experimentation the method was applied to the free vibrations in different media air and water the results obtained by the parameter identification method were compared to the ones obtained by separate tests and good agreement was found the identification procedure was found to work fine for all models under consideration and the models responses correspond well to the measured acceleration time histories

control of damping oscillations by fractional differential operator with time dependent order abstract the aim of the present paper is application of a differential operator of variable order in constitutive relations for viscoelastic materials this operator is used for studying the vibrations of a one degree of freedom oscillator in which the viscoelastic deformation is governed by a servo order function a method for numerical determination of the eigenfrequency of the fractional differential equation is proposed

time domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations numerical procedures for the time integration of the spatially discretized finite element equations for viscoelastic structures governed by a constitutive equation involving fractional calculus operators are presented to avoid difficulties concerning fractional order initial conditions a form of the fractlonal calculus model of viscoelasticity involving a convolution integral with a singular memory kernel of mittag lefler type is used the constitutive equation is generalized to three dimensional states for isotropic materials a simplification of the fractional derivative of the memory kernel is used in connection with grunwald s definition of fractional differentiation and a backward euler rule for the time evolution of the convolution term a desirable feature of this process is that no actual evaluation of the memory kernel is needed this together with the newmark method for time integration enables the direct calculation of the time evolution of the nodal degrees of freedom to illustrate the ability of the numerical procedure a few numerical examples are presented in one example the numerically obtained solution is compared with a time series expansion of the analytical solution

ground state spaces of frustration free hamiltonians we study the ground state space properties for frustration free hamiltonians we introduce a concept of reduced spaces to characterize local structures of ground state spaces for a many body system we characterize mathematical structures for the set k of all the k particle reduced spaces which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure the smallest nonzero elements in k called atoms are analogs of extreme points we study the properties of atoms in k and discuss its relationship with ground states of k local frustration free hamiltonians for spin 1 2 systems we show that all the atoms in 2 are unique ground states of some 2 local frustration free hamiltonians moreover we show that the elements in k may not be the join of atoms indicating a richer structure for k beyond the convex structure our study of k deepens the understanding of ground state space properties for frustration free hamiltonians from the new perspective of reduced spaces

calculation of eigensolution derivatives for nonviscously damped systems using nelson s method a method to calculate the derivatives of the eigenvalues and eigenvectors of multiple degree of freedom damped linear dynamic systems with respect to arbitrary design parameters is presented in contrast to the traditional viscous damping model a more general nonviscous damping model is considered the nonviscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over given kernel functions because of the general nature of the damping eigensolutions are generally complex valued and eigenvectors do not satisfy the classical orthogonality relationship the proposed method to calculate the eigenvector derivative depends only on the eigenvector concerned numerical examples are provided to illustrate the derived results nomenclature c j constant associated with the derivative of u j d s dynamic stiffness matrix d j constant associated with the derivative of v j g s laplace transform of g t g t nonviscous damping matrix k stiffness matrix l laplace transform of m mass matrix m total number of eigenvectors n number of degrees of freedom of the system n number of relaxation parameters p design parameter rank rank of a matrix s laplace domain parameter u j jth eigenvector t displacement vector v j jth adjoint left eigenvector x j vector associated with the derivative of u j yj vector associated with the derivative of v j j normalization constant for the jth eigenvector j jth eigenvalue k relaxation parameters subscripts t matrix transpose derivative with respect to s

stabilization of quasi integrable hamiltonian systems with fractional derivative damping by using fractional optimal control an innovative procedure for designing fractional optimal control to asymptotically stabilize with probability one quasi integrable hamiltonian systems with fractional derivative dampings is proposed it is proved that the systems indeed can be stabilized by using the proposed procedure an example is given to illustrate the procedure and its effectiveness

numerical solution of two sided space fractional wave equation using finite difference method in this paper a class of finite difference method for solving two sided space fractional wave equation is considered the stability and consistency of the method are discussed by means of gerschgorin theorem and using the stability matrix analysis numerical solutions of some wave fractional partial differential equation models are presented the results obtained are compared to exact solutions

dynamic stability of a viscoelastic beam with frequency dependent modulus abstract this study presents the dynamic stability of a simply supported viscoelastic beam subjected to an axially harmonic load the complex modulus of viscoelastic material is considered to depend on the frequency of parametric loading applying galerkin s method the governing equation of motion is simplified to the complex form of the mathieu equation with frequency dependent coefficients then the boundary of dynamic stability is determined by coupling the numerical binary search procedure and the complex incremental harmonic balance ihb method which are developed in this study this algorithm is easily simply and conveniently used to perform computer numerical analysis the results indicate that the loss factor presents the damping capacity of viscoelastic material the numerical results reveal that the frequency influences the dynamic stability

planar voronoi cells the violation of aboav s law explained in planar cellular systems mn denotes the average sidedness of a cell neighbouring an n sided cell aboav s empirical law states that nmn is linear in n a downward curvature is nevertheless observed in the numerical nmn data of the random voronoi froth the exact large n expansion of mn obtained in the present work namely explains this curvature its inverse square root dependence on n sets a new theoretical paradigm similar curved behaviour may be expected and must indeed be looked for in experimental data of sufficiently high resolution we argue that it occurs in particular in diffusion limited colloidal aggregation on the basis of recent simulation data due to fernandez toledano et al 2005 phys rev e 71 041401 and earlier experimental results by earnshaw and robinson 1994 phys rev lett 72 3682

fractional differential equations and related exact mechanical models the aim of the paper is the description of fractional order differential equations in terms of exact mechanical models this result will be archived in the paper for the case of linear multiphase fractional hereditariness involving linear combinations of power laws in relaxation creep functions the mechanical model corresponding to fractional order differential equations is the extension of a recently introduced exact mechanical representation di paola and zingales 2012 33 and di paola et al 2012 34 of fractional order integrals and derivatives some numerical applications have been reported in the paper to assess the capabilities of the model in terms of a peculiar arrangement of linear springs and dashpots

stability of viscoelastic control systems classical root locus plot analysis is adapted to some one dimensional controlled distributed viscoelastic structures the constitutive law that is used for the viscoelastic material may be modeled with fractional order derivatives provided the control law s involve similar derivatives two sample one dimensional structures and control systems are used to introduce the approach a partial differential equation representation of each structure is used as well as ritz approximation the effect of error due to approximation on stability conclusions is discussed in the context of this comparison

eigenvalues of linear viscoelastic systems the calculation of eigenvalues of single and multiple degree of freedom linear viscoelastic systems is considered the assumed viscoelastic forces depend on the past history of motion via convolution integrals over exponentially decaying kernel functions current methods to solve this type of problem normally use the state space approach involving additional internal variables such approaches often increase the size of the eigenvalue problem to be solved and can become computationally expensive for large systems here an approximate non state space based approach is proposed for this type of problem the proposed approximations are based on certain physical assumptions which simplify the underlying characteristic equation to be solved closed form approximate expressions of the complex and real eigenvalues of the system are derived these approximate expressions are obtained as functions of the elastic eigenvalues only this enables one to approximately calculate the eigenvalues of complex viscoelastic systems by simple post processing of the elastic undamped eigenvalues representative numerical examples are given to verify the accuracy of the derived expressions

on the quantification of damping model uncertainty abstract the characterization of uncertainty in the damping forces in a vibrating structure is of significant interest in structural dynamics the most common approach is to use a viscous damping matrix with uncertain coefficients the viscous damping is not the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model there are many functional forms which can be used as damping models in this paper two approaches are proposed to quantify such model form uncertainty associated with the use of the viscous damping model not only the model parameters the first approach is based on an ensemble of equivalent damping functions and the second approach is based on the random matrix theory the results obtained from the two methods are compared using numerical examples it was observed that the random matrix theory can be used to quantify damping model uncertainty in some cases

geometrical structure of disordered sphere packings the three dimensional structure of large packings of monosized spheres with volume fractions ranging between 0 58 and 0 64 has been studied with x ray computed tomography we search for signatures of organization classifying local arrangements and exploring the effects of local geometrical constrains on the global packing this study is the largest and the most accurate empirical analysis of disordered packings at the grain scale to date mapping over 380 000 sphere coordinates with precision within 0 1 of the sphere diameters we discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures some of the main results are 1 the observation that the average number of contacts increases with the volume fraction 2 the discovery that these systems have a very compact contact network 3 the finding that disordered packing can be locally more efficient than crystalline packings 4 the observation that the peaks of the radial distribution function follow power law divergences 5 the discovery that geometrical frustration plays no role in the formation of such amorphous packings

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

formulation and integration of the standard linear viscoelastic solid with fractional order rate laws abstract a physically sound three dimensional anisotropic formulation of the standard linear viscoelastic solid with integer or fractional order rate laws for a finite set of the pertinent internal variables is presented it is shown that the internal variables can be expressed in terms of the strain as convolution integrals with kernels of mittag leffler function type a time integration scheme based on the generalized midpoint rule together with the grunwald algorithm for numerical fractional differentiation for integration of the constitutive response is developed the predictive capability of the viscoelastic model for describing creep relaxation and damped dynamic responses is investigated both analytically and numerically the algorithm and the present general linear viscoelastic model are implemented into the general purpose finite element code abaqus the algorithm is then used together with an explicit difference scheme for integration of structural responses in numerical examples the quasi static and damped responses of a viscoelastic ballast material that is subjected to loads simulating the overrolling of a train are investigated

fractional integral formulation of constitutive equations of viscoelasticity a fractional integral viscoelasticity model is discussed the model has the same constitutive advantages as the fractional derivative viscoelasticity model both models need few parameters to model the weak frequency dependence of many engineering materials also both models represent a causal relation between excitation and response the fractional integral model however gives a unique relation between excitation and response whereas the fractional derivative model needs initial conditions to give a unique relation the fractional integral model is incorporated into structural equations of motion a time discretization scheme for the solution of these equations is outlined and some examples are given

stability approach to the fractional variational iteration method used for the dynamic analysis of viscoelastic beams abstract non integer derivatives are frequently used to describe the constitutive behavior of viscoelastic materials the dynamic analysis of a simply supported viscoelastic beam for a fractional zener model is performed with the help of a modified variational iteration method the structure is subjected to two loading scenarios a uniformly distributed transverse load and a periodic concentrated force at the center of the beam using the properties of convolution product in banach spaces l p r n and the fixed point theory the stability temporal intervals of a nonlinear operator for a given fractional order are determined the graphical representations present in the numerical examples show how the existence of fractional derivative in the selected rheological model influences the dynamic response of the structure compared to the classical zener model the results of this study prove that the presented algorithm is an efficient tool for solving the fractional integro differential equations

power law and fractional calculus model of viscoelasticity mathematical relationships between the power law model and the fractional calculus model of viscoelastic behavior are developed it is demonstrated that the two models have mathematically similar relaxation spectra this similarity is seen to produce an asymptotic equivalence of the models at long relaxation times and correspondingly low frequencies of motion in the lower transition and rubbery regions the divergent behavior of the models at higher frequencies in the transition and glassy regions is presented porposals to take advantage of the similarities between power law and fractional calculus models are discussed

closed form eigensolutions of nonviscously nonproportionally damped systems based on continuous damping sensitivity abstract in this paper nonviscous nonproportional vibrating structures are considered nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass stiffness and damping matrices viscoelasticity leads to a frequency dependence of this latter in this work a novel closed form expression to estimate complex eigenvalues is derived the key point is to consider the damping model as perturbed by a continuous fictitious parameter assuming then the eigensolutions as function of this parameter the computation of the eigenvalues sensitivity leads to an ordinary differential equation from whose solution arises the proposed analytical formula the resulting expression explicitly depends on the viscoelasticity frequency derivatives of the damping function the nonproportionality influence of the modal damping matrix off diagonal terms eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue the method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems

differential geometry of viscoelastic models with fractional order derivatives viscoelastic materials with memory effect are studied based on the fractional rheonomic geometry the geometric objects are regarded as basic quantities of fractional viscoelastic models i e the metric tensor and torsion tensor are interpreted as the strain and the fractional strain rate respectively the generalized viscoelastic equations are expressed by the geometric objects especially the basic constitutive equations such as voigt and maxwell models can be derived geometrically from the generalized equation this leads to the fact that various viscoelastic models can be unified into one geometric expression

shapes of quantum states the shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k 2 hence the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of points various correspondences between point configurations and quantum states such as linear superposition as well as unitary and stochastic evolution of shapes are illustrated in particular a complete characterization of shape eigenstates for an arbitrary number of points is given in terms of cyclotomic equations

comparative study of three numerical schemes for fractional integro differential equations this paper presents a comparative study of three numerical schemes such as linear quadratic and quadratic linear scheme for the fractional integro differential equations defined in terms of the caputo fractional derivatives the error estimates of the respective approximations are also established numerical tests of the discussed schemes show that all schemes work well and when the number of terms approximating the solution is increased the desired solution is achieved the accuracy of the numerical schemes with respect to the step size h is analysed and illustrated through various tables finally comparative performances of the schemes are discussed comparative study of three schemes such as linear quadratic and quadratic linear schemes is presented for the fractional integro differential equations the convergences of the schemes are also established the performances of the schemes are compared through the test examples

collocation method with convergence for generalized fractional integro differential equations abstract in this paper we study a numerical approach for some class of generalized fractional integro differential equations gfides defined in terms of the b operators presented recently we develop collocation method for linear and nonlinear forms of gfides the numerical approach uses the idea of collocation methods for solving integral equations legendre polynomials are used to approximate the solution in finite dimensional space with convergence analysis the obtained approximate solution recovers the solution of the fractional integro differential equation fide defined using caputo derivatives in a special case fides containing convolution type kernels appear in diverse area of science and engineering applications therefore some test examples varying the kernel in the b operator are considered to perform the numerical investigations the numerical results validate the presented scheme and provide good accuracy using few legendre basis functions

time domain formulation in computational dynamics for linear viscoelastic media with model uncertainties and stochastic excitation the paper is devoted to the computational time domain formulation of linear viscoelastic systems submitted to a nonstationary stochastic excitation and in the presence of model uncertainties which are modeled in the framework of the probability theory the objective is to introduce and to develop an adapted and complete formulation of such a problem in the context of computational mechanics a reduced order model in the time domain with stochastic excitation is derived from the computational model for the reduced order model the stochastic modeling of both computational model parameter uncertainties and modeling errors is carried out using the nonparametric probabilistic approach and the random matrix theory we present a new formulation of model uncertainties to construct the random operators for viscoelastic media we then obtained a linear stochastic integro differential equation side with random operators and with a stochastic nonhomogeneous part stochastic excitation a time discretization of this side is proposed in a first step the side is transformed to a linear ito stochastic differential equation isde with random operators then the isde is discretized using an extension of the stormer verlet scheme which is a particularly well adapted algorithm for long time good behavior of the numerical solution finally for the stochastic solver and statistical estimations of the random responses we propose to use the monte carlo simulation for gaussian and non gaussian excitations

wavelet approximation scheme for distributed order fractional differential equations abstract this paper is concerned with the study of wavelet approximation scheme based on legendre and chebyshev wavelets for finding the approximate solutions of distributed order linear differential equations the operational matrix for distributed order fractional differential operator is derived for legendre and chebyshev wavelets basis furthermore the obtained operational matrix along with gauss legendre quadrature formula and standard tau method are utilized to reduce the distributed order linear differential equations into the system of linear algebraic equations for the better understanding of the method numerical algorithms are also provided for the considered problems in order to verify the desired accuracy of the proposed method five test examples are included and numerical experiments confirm the theoretical results and illustrate applicability and efficiency of the proposed method also the convergence analysis error bounds error estimate and numerical stability of presented method via legendre and chebyshev wavelets are investigated moreover comparison of the numerical results obtained by the proposed approach is provided with the results of existing method

adaptive discretization of an integro differential equation with a weakly singular convolution kernel an integro differential equation involving a convolution integral with a weakly singular kernel is considered the kernel can be that of a fractional integral the integro differential equation is discretized using the discontinuous galerkin method with piecewise constant basis functions sparse quadrature is introduced for the convolution term to overcome the problem with the growing amount of data that has to be stored and used in each time step a priori and a posteriori error estimates are proved an adaptive strategy based on the a posteriori error estimate is developed finally the precision and effectiveness of the algorithm are demonstrated in the case that the convolution is a fractional integral this is done by comparing the numerical solutions with analytical solutions

sampling uniformly from the set of positive definite matrices with trace constraint we derive a parameterization of positive definite matrices using the cholesky decomposition in combination with hyperspherical coordinates based on the parameterization we develop a simple and efficient method to randomly generate positive definite matrices with constant or bounded trace according to a uniform distribution further we present an efficient implementation using the inversion method and either rejection sampling or transforming a beta distribution the matrix parameterization might be of independent interest whereas the random sampling algorithm finds applications in monte carlo simulations testing of algorithms and performance studies with the help of an abstract example we describe how the sampling method can be used to approximate the optimum in a difficult e g nonconvex optimization problem for which no solution or efficient global optimization algorithm is known in this paper we consider real as well as complex matrices

roughness and scaling in cellular patterns analysis of a simple model a foam can be decomposed into successive layers of cells at the same topological distance to an origin which is either an arbitrary cell or a basal plane the shape of these layers profile and thickening indicates the degree of randomness of the cellular pattern to support this idea we analyse the layer shapes in 2d rectangular models of foam as confirmed by numerical simulations the fluctuations in the direction normal to the layers are self affine on a significant range of scales with values of the exponents compatible with the kpz universality class 0 5 for the roughness exponent and z 1 5 for the dynamic exponent measuring the increase of the intralayer correlation length these fluctuations are not sufficient however to affect the dominant behaviour of the number of cells per layer found to saturate in cylindrical geometry and to increase linearly in concentric geometry

a finite element formulation for the coupled thermoviscoelastic response of solid fluid systems the coupled thermoviscoelastic response of a solid fluid system is computed by a finite element formulation which involves only temperature and displacement fields the laplace transform with respect to time is applied to the coupled equations this results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution also this formulation permits the use of fractional derivatives to model viscoelastic material behaviour

beyond fractional derivatives local approximation of other convolution integrals dynamic systems involving convolution integrals with decaying kernels of which fractionally damped systems form a special case are non local in time and hence infinite dimensional straightforward numerical solution of such systems up to time t needs o t 2 computations owing to the repeated evaluation of integrals over intervals that grow like t finite dimensional and local approximations are thus desirable we present here an approximation method which first rewrites the evolution equation as a coupled in finite dimensional system with no convolution and then uses galerkin approximation with finite elements to obtain linear finite dimensional constant coefficient approximations for the convolution this paper is a broad generalization based on a new insight of our prior work with fractional order derivatives singh chatterjee 2006 nonlinear dyn 45 183 206 in particular the decaying kernels we can address are now generalized to the laplace transforms of known functions of these the power law kernel of fractional order differentiation is a special case the approximation can be refined easily the local nature of the approximation allows numerical solution up to time t with o t computations examples with several different kernels show excellent performance a key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system as distinct from numerically approximating just the solution for the given initial values this allows non standard uses of the approximation e g in stability analyses

application of legendre wavelets for solving fractional differential equations in this paper we develop a framework to obtain approximate numerical solutions to ordinary differential equations odes involving fractional order derivatives using legendre wavelet approximations the properties of legendre wavelets are first presented these properties are then utilized to reduce the fractional ordinary differential equations fodes to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique results show that this technique can solve the linear and nonlinear fractional ordinary differential equations with negligible error compared to the exact solution

dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractionalderivatives frame structures with viscoelastic dampers mounted on them are considered in this paper viscoelastic ve dampers are modelled using two three parameter fractional rheological models the structures are treated as elastic linear systems the equation of motion of the whole system structure with dampers is written in terms of state space variables the resulting matrix equation of motion is the fractional differential equation the proposed state space formulation is new and does not require matrices with huge dimensions the paper is devoted to determine the dynamic properties of the considered structures the nonlinear eigenvalue problem is formulated from which the dynamic parameters of the system can be determined the continuation method is used to solve the nonlinear eigenvalue problem moreover results of typical calculations are presented

identifying time dependent damping and stiffness functions by a simple and yet accurate method the inverse vibration problem is a mathematical process to determine unknown mechanical parameters from measured vibration data in this study the data of displacement are chosen in order to identify a time dependent function of damping or stiffness however when both functions are to be identified we require both the data of displacement and velocity this is the first time that a closed form estimation method for the inverse vibration problems of estimating time dependent parameters has been constructed we are able to transform the inverse vibration problem into an identification problem governed by a parabolic type partial differential equation pde then a one step group preserving scheme gps for the semi discretization of pde is established which can be used to derive a closed form solution for estimating parameters the new lie group estimation method has three further advantages it does not require any prior information on the functional forms of unknown functions no initial guesses are required and no iterations are required numerical examples were examined to show that the present approach is highly accurate and efficient even for identifying discontinuous and oscillatory parameters against the noise is good when only one function is estimated however the present approach is slightly weak against the noise when both functions are identified

constrained geometries in soap froth dynamics abstract soap froths as archetypal disordered cellular structures exhibiting spatial and temporal evolution have been predominantly studied in terms of their topological properties recently constrained geometries in froth have attracted attention since these arise both from existing or natural structure or more usually can be artificially configured using a direct simulation method which retains detailed information on bubble cell mechanisms we have investigated dynamics in 2d froths with various initial structures corresponding to controlled disorder in particular we examine the special case of a defect ring surrounding a central inclusion in a uniform froth for different number of defects and ring radius this geometry permits comparison with shell theory as well as insight on dynamics of a virtual phase as defined for persistence and non equilibrium processes in general it appears that defect location and pattern of inclusion in the virtual phase cause considerable variation in the evolutionary behaviour leading to non universal exponents for the phase dynamics this is probably explained by the fact that the froth is still in the transient period over simulation time scales rather than achieving the final stage of persistence however distinctive patterns of response can be identified for the different froth regions despite system size limitations with topological and other properties indicating that a quasi equilibrium results

long range geometrical correlations in two dimensional foams the statistical properties of two dimensional space filling random cellular structures foams or their dual random triangulations in statistical equilibrium are obtained by maximum entropy inference and topological simulations we show by maximum entropy inference that for a broad class of foams shell structured including three sided cell inclusions all two cell topological correlators aj k n average number of pairs of k cell and n cell at a topological distance j are linear in n and k the numbers of neighbours of the cells this generalizes a correlation known for neighbouring cells j d 1 which implies the linearity of aboav s relation between the total number of neighbours of the cells adjacent to a n neighboured cell andn our results verified by simulations also build up gauss s theorem for cellular structures any additional restriction in exploring local cell configurations besides the constraints of filling space at random will manifest itself through a deviation from linearity of the correlators aj k n and the aboav relation notably foams made of feynman diagrams have additional context dependent restrictions and their aboav relation is slightly curved it is essential that the local random variablen denotes the number of neighbours of the cell and not that of its sides whenever the two are different

temporal second order difference schemes for the multi dimensional variable order time fractional sub diffusion equations abstract a special point on each time interval is found for the approximation of the variable order time caputo derivative which makes at least second order approximation accuracy be obtained on this basis two difference schemes are proposed for the multi dimensional variable order time fractional sub diffusion equations which have second order accuracy in time second order and fourth order accuracy in space respectively the obtained difference schemes are proved to be uniquely solvable the convergence and stability of the schemes in the discrete h 1 norm are analyzed by utilizing the energy method some numerical examples are presented to verify the theoretical results

a novel numerical method for the time variable fractional order mobile immobile advection dispersion model evolution equations containing fractional derivatives can provide suitable mathematical models for describing anomalous diffusion and transport dynamics in complex systems that cannot be modeled accurately by normal integer order equations recently researchers have found that many physical processes exhibit fractional order behavior that varies with time or space the continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable in this paper we consider the mobile immobile advection dispersion model with the coimbra variable time fractional derivative which is preferable for modeling dynamical systems and is more efficient from the numerical standpoint a novel implicit numerical method for the equation is proposed and the stability of the approximation is investigated as for the convergence of the numerical method we only consider a special case i e the time fractional derivative is independent of the time variable t the case where the time fractional derivative depends on both the time variable t and the space variable x will be considered in a future work finally numerical examples are provided to show that the implicit difference approximation is computationally efficient

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

numerical techniques for the variable order time fractional diffusion equation abstract in this paper we consider the variable order time fractional diffusion equation we adopt the coimbra variable order vo time fractional operator which defines a consistent method for vo differentiation of physical variables the coimbra variable order fractional operator also can be viewed as a caputo type definition although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature here an approximate scheme is first proposed the stability convergence and solvability of this numerical scheme are discussed via the technique of fourier analysis numerical examples are provided to show that the numerical method is computationally efficient

a note on cubic convolution interpolation we establish a link between classical osculatory interpolation and modern convolution based interpolation and use it to show that two well known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago we also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing

dynamic finite element analysis of viscoelastic composite plates in the time domain numerical procedures for analysing transient responses of anisotropic viscoeiastic composite plates have been developed in the time domain using variational principles and a direct time integration method recursion relationships have been formulated in order to reduce computer storage substantially the method developed herein requires only two previous lime solutions to evaluate the next time solution and the necessary storage is independent of the number of the time steps verification studies were conducted to evaluate the accuracy and convergence of the present numerical algorithm and they show that the numerical solutions agree well with analytical ones as examples dynamic transient responses of viscoeiastic composite plates subjected to unit step loads were calculated using the presently developed procedure

linking multiple relaxation power law attenuation and fractional wave equations the acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media e g biological tissue polymers rocks and rubber recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power law attenuation on the other hand a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by nachman et al j acoust soc am 88 1584 1595 1990 through assumption of a continuum of relaxation mechanisms each with an effective compressibility described by a distribution related to the mittag leffler function this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation this work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling

spectral representations of solutions of linear elliptic equations on exterior regions abstract this paper describes spectral representations and approximations of solutions of second order self adjoint linear elliptic boundary value problems on exterior regions u in r n for n 2 inhomogeneous dirichlet robin and neumann boundary conditions are treated some new trace results are proved and used to provide spectral characterizations of the boundary traces of functions in h 1 u orthonormal bases of these hilbert spaces are derived using a theory of steklov eigenproblems the steklov eigenfunctions of a regularized laplace operator on the exterior of a ball are explicitly determined when n 2 3

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

the existence of mild and classical solutions for a second order abstract fractional problem in this paper we consider a second order abstract problem involving derivatives of non integer order the existence and uniqueness of mild and classical solutions are established in appropriate spaces under weak assumptions

modal synthesis when modeling damping by use of fractional derivatives the fractional derivative damping model and some of its properties are discussed small problems involving fractional derivatives may be solved in the fourier domain here modal synthesis is used to solve the equatlons of motion in the time domain a state space vector containing fractional derivatives of the displacements is then introduced and the system of equations is expanded the resulting system of equations is decoupled by use of the complex eigenvectors of the system the solutions of the decoupled equations are superposed weighted by the eigenmodes to give the response of the structure the computational effort can be reduced by taking into account some of the properties of the system

deriving fractional acoustic wave equations from mechanical and thermal constitutive equations it is argued that fractional acoustic wave equations come in two kinds the first kind is constructed ad hoc to have loss operators that fit power law measurements the second kind is more fundamental as they in addition are based on underlying physical equations here that means constitutive equations these equations are the fractional kelvin voigt and the more general fractional zener stress strain relationships as well as a fractional version of the fourier heat law the properties of the wave equations are given in terms of attenuation and phase group velocities for low intermediate and high frequency regions in the most general case the attenuation exhibits power law behavior in all frequency ranges while the phase and group velocities increase sharply in the intermediate frequency range and converge to a constant finite value for high frequencies it is also shown that the fractional zener wave equation is equivalent to the multiple relaxation model for attenuation

solving non linear viscoelastic problems via a self adaptive precise algorithm in time domain this paper presents a new scheme of time stepping for solving non linear viscoelastic problems with a two level expanding technique by expanding variables at a discretized time interval a non linear coupled space time domain problem with initial and boundary values can be converted into a series of recursive linear boundary value problems the variations of variables can be described more precisely via a self adaptive computing procedure and the non linear iteration can be avoided fem is employed to solve recursive linear boundary value problems and numerical comparisons are made to validate the proposed algorithm

substructure synthesis method for frequency response of viscoelastic structures the method of substructure synthesis previously applicable to undamped and viscously damped systems has been extended to systems with viscoelastic damping in hereditary integral form differential operator form and steady state corm based on a variational principle for symmetric systems the corresponding substructure synthesis method is formulated in the frequency domain each substructure is represented by a set of admissible trial vectors in the rayleigh ritz method eigenvectors of the corresponding undamped substructure and ritz vectors obtained by spatial discretization of admissible functions are recommended as trial vectors the traditional state space formulation is avoided by the proposed substructure synthesis method so that the approach is independent of the form of viscoelastic models the effectiveness of the proposed method in terms of reducing the size of final equations is illustrated through numerical examples

nonlinear vibration of viscoelastic beams described using fractional order derivatives abstract the problem of non linear steady state vibration of beams harmonically excited by harmonic forces is investigated in the paper the viscoelastic material of the beams is described using the zener rheological model with fractional derivatives the constitutive equation which contains derivatives of both stress and strain significantly complicates the solution to the problem the von karman theory is applied to take into account geometric nonlinearities amplitude equations are obtained using the finite element method together with the harmonic balance method and solved using the continuation method the tangent matrix of the amplitude equations is determined in an explicit form the stability of the steady state solution is also examined a parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam s responses

simulation of fractionally damped mechanical systems by means of a newmark diffusive scheme a newmark diffusive scheme is presented for the time domain solution of dynamic systems containing fractional derivatives this scheme combines a classical newmark time integration method used to solve second order mechanical systems obtained for example after finite element discretization with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations which can be seen as internal memory variables the focus is given on the algorithm implementation into a finite element framework the strategies for choosing diffusive parameters and applications to beam structures with a fractional zener model

application of fractional operators to the analysis of damped vibrations of viscoelastic single mass systems free damped vibrations of an oscillator whose viscoelastic properties are described in terms of the fractional calculus kelvin voight model maxwell model and standard linear solid model are determined the problem is solved by the laplace transform method when passing from image to pre image one is led to find the roots of an algebraic equation with fractional exponents the method for solving such equations is proposed which allows one to investigate the roots behaviour in a wide range of single mass system parameters a comparison between the results obtained on the basis of the three models has been carried out it has been shown that for all models the characteristic equations do not possess real roots but have one pair of complex conjugates i e the test single mass systems subjected to the impulse excitation do not pass into an aperiodic regime in none of magnitudes of the relaxation and creep times main characteristics of vibratory motions of the single mass system as functions of the relaxation time or creep time which are equivalent to the temperature dependencies are constructed and analyzed for all three models

on the control of chaos via fractional delayed feedback method in this paper the problem of controlling unstable fixed points in discrete systems and periodic orbits in continuous system is investigated via a new scheme involving fractional derivatives this method is based on applying feedback of measured states and using the period of fixed points and periodic orbits in this method there is no need of information for fixed point and periodic orbits just the period is enough the effectiveness of this method is investigated via some demonstrative example

extensions of positive definite integral kernels on the heisenberg group abstract we consider positive definite extensions of functions and distributions which are defined on a cylindrical neighborhood and positive definite in the heisenberg group when rotational invariance is assumed we show existence of p d extensions we also give formulas of the classical bochner type for all such extensions they are expanded in terms of an integral transform associated to the sub laplacian we further show that the p d extension problem is closely related to the theory of extensions of hermitian infinitesimal representations in the sense considered earlier by powers and fuglede these are extensions to integrable representations in generally larger so called dilation hilbert spaces

iteration method for equation of viscoelastic motion with fractional differential operator of damping abstract mechanical properties of viscoelastic materials depend on the loading conditions and their history the work is devoted to the analysis of oscillation processes in viscoelastic media with loading prehistory taken into account by means of fractional derivative terms in the governing equations the paper suggests convergent procedure for numerical solution of this type of differential equations and their system for any combination of damping operator orders the order of the fractional derivative may be as constant so variable analysis of the amplitude frequency behavior of the oscillator versus the damping operator order is provided

new exact analytical solutions for stokes first problem of maxwell fluid with fractional derivative approach the unsteady flow of an incompressible maxwell fluid with fractional derivative induced by a sudden moved plate has been studied using fourier sine and laplace transforms the obtained solutions for the velocity field and shear stress written in terms of generalized g functions are presented as sum of the similar newtonian solutions and the corresponding non newtonian contributions the non newtonian contributions as expected tend to zero for l 0 furthermore the solutions for ordinary maxwell fluid performing the same motion are obtained as limiting cases of general solutions and verified by comparison with previously known results finally the influence of the material and the fractional parameters on the fluid motion as well as a comparison among fractional maxwell ordinary maxwell and newtonian fluids is also analyzed by graphical illustrations

nonprobabilistic convex theoretic modeling of scatter in material properties nonprobabilistic convex modeling of uncertain material properties for viscoelastic structures is developed in this paper in particular the problem of forced vibrations of viscoelastic beams is studied first the analytic solution by inman is generalized for a deterministic set of variables describing material properties next these variables are treated as varying in a solid ball in the four dimensional space thus modeling the scatter in material properties the least favorable response needed for the design of the structure is determined

von neumann indices and classes of positive definite functions with view to applications we establish a correspondence between two problems i the problem of finding continuous positive definite extensions of functions f which are defined on open bounded domains in r on the one hand and ii spectral theory for elliptic differential operators acting on constant coefficients a novelty in our approach is the use of a reproducing kernel hilbert space hf computed directly from f as well as algorithms for computing relevant orthonormal bases in hf

exponential stabilization of volterra integrodifferential equations in hilbert space we consider exponential stabilization of an abstract linear volterra integrodifferential equation in a hilbert space u e1au t e2 01k t s au s ds f t by a feedback control f t c0u t c1u t with bounded linear operators c0 and c1 of finite rank a is a positive semidefinite self adjoint unbounded operator k is nonnegative convex and decreasing with exponential decay k 0 being finite we introduce a concept of essential growth rate for resolvent operators similar to that for c0 semigroups and prove that the resolvent for the volterra equation has the same essential growth as the solution semigroup to u t e1au t e2k 0 e1u t f t stability can be checked by the location of poles and it is shown that exponential stabilization is possible with a decay rate of at most e2k 0 2e1 we apply our results to two problems concerning stabilization of motion of viscoelastic bodies

thermorheologically simple materials a bayesian framework for model calibration and validation abstract the dynamic properties of viscoelastic materials show highly frequency temperature dependency and numerical methods for structural systems containing this type of material require accurate mathematical models to describe their dynamical behaviour the material behaviour here is modelled using a constitutive equation based on fractional derivative operators and considering the temperature dependence of the material under the thermorheologically simple postulate the quest for information about the constitutive model parameters is phrased as a statistical inverse problem under the bayesian framework a markov chain monte carlo mcmc method is used to explore the posterior density of model parameters using measured data from dynamic tests at different temperatures the agreement between measured data and the predictive capabilities of sixteen models were quantitatively assessed using two validation metrics based on the validation metrics analysis it is possible to conclude that the range of temperature of the calibration data set is a key point into the implementation of the frequency temperature superposition principle ftsp this was verified defining some scenarios for assessing the agreement of model predictions and the set of available experimental data the results are quite compelling due to the fact that the proposed approach is easy handed furthermore this approach could be applied on any generic constitutive model using the ftsp

ring correlations in random networks we examine the correlations between rings in random network glasses in two dimensions as a function of their separation initially we use the topological separation measured by the number of intervening rings but this leads to pseudo long range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring this effect is associated with the noncircular nature of the shells it is therefore necessary to use the geometrical distance between ring centers hence we find a generalization of the aboav weaire law out to larger distances with the correlations between rings decaying away when two rings are more than about three rings apart

on the linear quadratic regulator problem in one dimensional linear fractional stochastic systems in this paper for one dimensional stochastic linear fractional systems in terms of the riemann liouville fractional derivative the optimal control is derived it is assumed that the state is completely observable and all the information regarding this is available the formulation leads to a set of stochastic fractional forward and backward equation in the riemann liouville sense the proposed method has been checked via some numerical simulations which show the effectiveness of the fractional stochastic optimal algorithm

damping described by fading memory analysis and application to fractional derivative models abstract some damping models where the actual stress does not depend on the actual strain but also on the entire strain history are studied basic requirements in the frequency and time domain significant for the choice of damping model are outlined a one dimensional linear constitutive viscoelastic equation is considered three different equivalent constitutive equations describing the viscoelastic model are presented the constitutive relation on the convolution integral form is studied in particular a closed form expression for the memory kernel corresponding to the fractional derivative model of viscoelasticity is given the memory kernel is examined with respect to its regularity and asymptotic behavior the memory kernels relation to the fractional derivative operator is discussed in particular and the fractional derivative of the convolution term is derived the fractional derivative model is also given by two coupled equations using an internal variable the inclusion of the fractional derivative constitutive equation in the equations of motion for a viscoelastic structure is discussed we suggest a formulation of the structural equations that involves the convolution integral description of the fractional derivative model of viscoelasticity this form is shown to possess several mathematical advantages compared to an often used formulation that involves a fractional derivative operator form of constitutive relation an efficient time discretization algorithm based on newmarks method for solving the structural equations is presented and some numerical examples are given a simplification of the fractional derivative of the memory kernel derived in the present study is then employed which avoids the actual evaluation of the memory kernel

an efficient numerical scheme to solve fractional diffusion wave and fractional klein gordon equations in fluid mechanics abstract the numerous applications of time fractional partial differential equations in different fields of science especially in fluid mechanics necessitate the presentation of an efficient numerical method to solve them in this paper galerkin method and operational matrix of fractional riemann liouville integration for shifted legendre polynomials has been applied to solve these equations some definitions for fractional calculus along with some basic properties of shifted legendre polynomials have also been put forth when approximations are substituted into the fractional partial differential equations a set of algebraic equations would be resulted the convergence of the suggested method was also depicted in the end the linear time fractional klein gordon equation dissipative klein gordon equations and diffusion wave equations were utilized as three examples so as to study the performance of the numerical scheme

five parameter fractional derivative model for polymeric damping materials fractional derivative models offer a powerful tool to describe the dynamic behaviour of real viscoelastic materials a version of the fractional derivative models characterized by five parameters is presented and investigated in this paper in order to describe asymmetrical loss factor peak and the high frequency behaviour of polymeric damping materials the speculative derivation of the model constitutive equation containing time derivatives of stress and strain of different orders is given the model behaviour is investigated in the frequency domain the physical meaning of the model parameters is defined and constraints on the parameter values are made it is shown that the asymmetry of loss peak and the high frequency behaviour of the model are governed by the difference between the order of time derivatives of stress and strain moreover it is shown that this difference is related to the high frequency limit value of the loss factor the model is fitted to experimental data on some polymeric damping materials to verify its behaviour

complex networks on hyperbolic surfaces abstract we explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties this method provides a new perspective to classify network complexity both on local and global scale we demonstrate by means of several examples that there is a strong relation between the network properties and the embedding surface

topology of slightly polydisperse real foams the topology of slightly polydisperse meta stable real foams was investigated by means of optical tomography associated with a numerical reconstruction procedure the values of the mean numbers of faces per bubble and edges per face were very close to matzke s data 1946 the real foams were essentially disordered and possessed a noncentered symmetry and ideal structures also could not be observed the disorder was quantified by the second moment of the edge per face and face per bubble distributions and also by a statistical correlation coefficient between the numbers of edges of adjacent faces it was found that the edge distributions of the internal bubbles and not of the external ones were significantly anticorrelated even during foam aging which provided a measure of the disorder in the foam no obvious relationship could be deduced between the isoperimetric quotient and the face combination in an individual bubble eventually it was shown that the physical boundaries of the foam sample had no influence on the foam topology beyond a single bubble layer

time domain modeling of damping using anelastic displacement fields and fractional calculus abstract a fractional derivative model of linear viscoelasticity based on the decomposition of the displacement field into an anelastic part and elastic part is developed the evolution equation for the anelastic part is then a differential equation of fractional order in time by using a fractional order evolution equation for the anelastic strain the present model becomes very flexible for describing the weak frequency dependence of damping characteristics to illustrate the modeling capability the model parameters are fit to available frequency domain data for a high damping polymer by studying the relaxation modulus and the relaxation spectrum the material parameters of the present viscoelastic model are given physical meaning the use of this viscoelastic model in structural modeling is discussed and the corresponding finite element equations are outlined including the treatment of boundary conditions the anelastic displacement field is mathematically coupled to the total displacement field through a convolution integral with a kernel of mittag leffler function type finally a time step algorithm for solving the finite element equations are developed and some numerical examples are presented

eigensolutions of nonviscously damped systems based on the fixed point iteration abstract in this paper nonviscous nonproportional symmetric vibrating structures are considered nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass stiffness and damping matrices this latter as dependent on frequency viscous damping can be considered as a particular case involving damping forces as function of the instantaneous velocity of the degrees of freedom in this work a new numerical procedure to compute eigensolutions is proposed the method is based on the construction of certain recursive functions which under a iterative scheme allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities eigenvalues can be read then as fixed points of those functions a deep analysis of the convergence is carried out focusing specially on relating the convergence conditions and error decay rate to the damping model features such as the nonproportionality and the viscoelasticity the method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper the convergence and the sequences behavior are in agreement with the results foreseen by the theory

analytical modeling of viscoelastic dampers for structural and vibration control different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared the standard mechanical model smm comprising linear springs and dashpots is shown to accurately describe the broad band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law the smm renders a prony series expression for the modulus and compliance functions in the time domain and the remarkable mathematical efficiency associated with the exponential basis functions of a prony series greatly facilitates model calibration and interconversion while cumbersome nonlinear regression is usually required for other models a simple collocation or least squares method can be used to fit the smm to available experimental data the model allows viscoelastic material functions to be readily determined either directly from the experimental data or through interconversion from a function established in another domain numerical examples on two common viscoelastic dampers demonstrate the advantages of the smm over fractional derivative and power law models detailed computational procedures for fitting and interconversion are discussed and illustrated published experimental data from a viscoelastic liquid damper and a viscoelastic solid damper are used in the examples

vibro acoustic study of a viscoelastic sandwich ring immersed in water abstract this work deals with the reduction of the system composed of a sandwich structure with a viscoelastic core coupled to fluids two reduction methods are proposed in this paper to solve this problem in the frequency domain the first one consists in developing added mass operators to take into account the fluid the second one is the use of iterative methods to calculate the coupled complex modes of the dissipative problem this numerical strategy is applied to the response of a bidimensional sandwich ring coupled to internal and external fluids

finite element analysis of vibrating linear systems with fractional derivative viscoelastic models abstract fractional derivative rheological models are known to be very effective in describing the viscoelastic behaviour of materials especially of polymers and when applied to dynamic problems the resulting equations of motion after a fractional state space expansion can still be studied in terms of modal analysis but the growth in matrix dimensions carried by this expansion is in general so fast to make the calculations exceedingly cumbersome this paper presents a method for reducing the computational effort due to finite element fe analysis of vibrating linear systems with a fractional derivative viscoelastic model namely the fractional kelvin voigt the proposed method may be applied also to problems involving other fractional derivative linear models and it takes under control the computational effort by reducing the main eigenproblem of large dimension to the solution of two standard related eigenproblems of lower size numerical examples are provided in order to validate both the accuracy and the efficiency of the proposed methodology