achievable performance limitations for siso plants with pole location constraints in this paper performance limitations in the linear control of general linear discrete time scalar systems are considered the performance is measured with the 2 norm of an error function which at the same time ensures that the closed loop poles lie in a prescribed region the deleterious effect of this constraint on a classical performance measurement is also quantified in such a way that the interplay between the size of the desired region and structural features of the plant is revealed

inclusion principle for the rayleigh ritz based substructure synthesis according to this substructure synthesis the motion of every substructure is modeled in terms of quasicomparison functions which are linear combinations of admissible functions capable of satisfying all the boundary conditions

reduction of substructural interface degrees of freedom in flexibility based component mode synthesis a flexibility based component mode synthesis cms is proposed for reduced order modelling of dynamic behaviour of large structures the approach employs partitioning via the localized lagrange multiplier method the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes the flexibility based cms method has shown significant advantages over the classical craig bampton method a key feature of the method is its substructural mode selection criterion that is independent of loading conditions unlike the majority of available cms approaches where one retains the full dimension of partition boundary degrees of freedom dofs the flexibility based method allows to reduce significantly the interface dofs the reduction of interface dofs represents the major contribution of the present communication the efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3d structure both partitioned into several substructures copyright 2006 john wiley sons ltd

rayleigh ritz based substructure synthesis for flexible multibody systems this paper is concerned with the modeling of flexible multibody systems by a rayleigh ritz based substructure synthesis method so that certain advantages can be accrued by using the variational approach to derive the eigenvalue problem as with the classical rayleigh ritz method if the admissible functions used to represent the motion of the substructures are not chosen properly convergence can suffer this paper presents a new substructure synthesis method with superior convergence characteristics achieved by representing the motion by means of a recently developed class of functions namely the class of quasi compari son functions this improved convergence is shown to be related to improved approximation of both the differential equations and the natural boundary conditions the theory is demonstrated by means of a numerical example i introduction t his investigation is concerned with the modeling of flexible multibody systems many structures such as fixedwing aircraft helicopters flexible spacecraft flexible robots etc can be modeled as assemblages of interacting flexible bodies a method proposed by hurty1 2 in the early 1960s and known as component mode synthesis consists of modeling the motion of the individual substructures referred to as components by means of component modes he uses three types of modes to represent the motion of a substructure rigid body modes constraint modes and normal modes to define constraint modes hurty divides the constraints into two classes statically determinate and redundant the constraint modes are equal in number to the number of redundant constraints and are defined by producing a unit displacement on each redundant constraint in turn with all other constraints fixed the normal modes represent the modes of vibration of the components with all constraints fixed an approach by craig and hampton3 differs from that of hurty 1 2 mainly in the selection of the component modes indeed craig and hampton suggest two types of component modes boundary modes providing for displacements and rotations at points along the substructure boundaries and related to the constraint modes of hurty and substructure modes corresponding to completely restrained boundaries the substructures modeled individually in refs 1 3 are made to act together as a single structure by eliminating the redundant generalized coordinates arising from the fact that displacements at points common to two adjacent substructures are included twice in the overall problem formulation once for each substructure the elimination process is based on the use of constraint equations resulting from the enforcement of compatibility conditions which amounts to saying that the displacement of a boundary point shared by two substructures is the same in another approach to the problem proposed by

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

mimo interaction measure and controller structure selection in this paper a mimo interaction measure is described and its use in structure selection of multivariable controllers is discussed the proposal is built upon a gramian based measure of interaction in multivariable plants and the results in this paper apply to stable processes this measure provides support for decentralized input output pairing as well as for a richer controller architecture selection in continuous and discrete time time frameworks including triangular block diagonal and sparse structures

novel partitioned time integration methods for dae systems based on l stable linearly implicit algorithms real time applications based on the principle of dynamic substructuring require integration methods that can deal with constraints without exceeding an a priori fixed number of steps for these applications first we introduce novel partitioned algorithms able to solve daes arising from transient structural dynamics in particular the spatial domain is partitioned into a set of disconnected subdomains and continuity conditions of acceleration at the interface are modeled using a dual schur formulation interface equations along with subdomain equations lead to a system of daes for which both staggered and parallel procedures are developed moreover under the framework of projection methods also a parallel partitioned method is conceived the proposed partitioned algorithms enable a rosenbrock based linearly implicit lsrt2 method to be strongly coupled with different time steps in each subdomain thus user defined algorithmic damping and subcycling strategies are allowed secondly the paper presents the convergence analysis of the novel schemes for linear single degree of freedom dof systems the algorithms are generally a stable and preserve the accuracy order as the original monolithic method successively these results are validated via simulations on single and three dofs systems finally the insight gained from previous analyses is confirmed by means of numerical experiments on a coupled spring pendulum system copyright 2011 john wiley sons ltd

a general procedure for improving substructures representation in dynamic synthesis in the general substructure synthesis method for the dynamic analysis of complex flexible structures developed earlier by the authors the motion of each substructure is represented by a given number of substructure admissible functions and the otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of weighted residuals in this paper a general procedure for improving the admissible functions representing each substructure in the synthesis is developed the procedure is an iterative one and it leads to an improved eigensolution for the intermediate structure i e a fictitious structure defined by the approximate compatibility conditions where the improved eigensolution is obtained while always using the same number of degrees of freedom to represent a given substructure in any iteration the computations associated with each substructure are independent of those for all other substructures and they can be performed in parallel by increasing the number of iterations the eigensolution for the intermediate structure is approached the procedure is applicable to assembled structures that are either positive definite or positive semidefinite moreover the procedure represents an extension of the concept of subspace iteration to structures composed of substructures

eigenvalue convergence in the finite element method in static force deflection applications of the finite element method convergence rates for the p version in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed are superior to those for the h version in which the element degree remains fixed while the mesh is refined so that element size approaches zero in structural dynamics applications one does not seek to approximate a single solution as in static applications but seeks estimates for a number of the lower system eigenvalues this paper identifies factors responsible for poorer accuracy in higher computed eigenvalues in addition it explains why the p version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h version numerical examples demonstrate the superiority of the p version over the h version they also show the effects of various mechanisms limiting eigenvalue convergence

a numerical scheme to couple subdomains with different time steps for predominantly linear transient analysis abstract this paper generalizes the explicit implicit time integration algorithms pioneered by belytschko hughes and their respective co workers and the feti domain decomposition methods introduced by farhat and his co workers to the case where the same newmark scheme but different and coefficients and different time steps are specified in each subdomain building upon the work of farhat crivelli and geradin it considers various interface boundary constraints and performs a stability analysis of the proposed time integration algorithms

a general dynamic synthesis for structures with discrete substructures abstract this paper presents a substructure synthesis method for the dynamic simulation of complex structures where the structures consist of an assemblage of discrete substructures an analogy between distributed and discrete structures is extensively invoked to stimulate the motion of discrete substructures the concept of admissible vectors is introduced where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures the individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures a numerical example illustrating the method is presented

on a new iterative approach of component mode synthesis a wholly new concept of intermediate structure is developed in this paper based on this a new component mode iteration cmi or subdomain subspace iteration method is proposed in the new cmi method the ordinarily required step of ensuring interface compatibility is eliminated an outstanding achievement of this method is that it retains the merit of the standard subspace iteration ssi technique concerning the number of vectors required in computation in the present method iteraton is carried out at subdomain levels on machines capable of parallel processing this work can be performed simultaneously numerical examples clearly demonstrate the excellence of this new method

arlequin framework for multi model multi time scale and heterogeneous time integrators for structural transient dynamics this paper presents a general framework for performing spatio temporal multi scale multi model coupling based on displacement continuity this approach guarantees a global energy balance of the system in the context of the arlequin method it introduces specific interpolation of the lagrange multipliers and parameters of time integration operators in the overlapping zone a dual schur implementation is then used to illustrate the efficiency and robustness of the method convergence analysis with numerical experiments is performed finally 1d 1d and 2d 1d coupling applications are presented in which each subdomain is integrated in time using different time steps and different schemes this approach gives the user more ways of controlling computational behaviour via newmark parameters time steps and sizing the overlapping zones

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

a feti based multi time step coupling method for newmark schemes in structural dynamics we present an efficient and accurate multi time step coupling method using feti domain decomposition for structural dynamics using this method one can divide a large structural mesh into a number of smaller subdomains solve the individual subdomains separately and couple the solutions together to obtain the solution to the original problem the various subdomains can be integrated in time using different time steps and or different newmark schemes this approach will be most effective for very large scale simulations on complex geometries our coupling method builds upon a method previously proposed by gravouil and combescure gc method we show that for the simplest case when the same time step is used in all subdomains of the mesh our method reduces to the gc method and is unconditionally stable and energy preserving in addition we show that our method possesses these desirable properties for general multi time step cases too unlike the gc method which is dissipative greater computational efficiency is also achieved through our method by limiting the computation of interface forces to the largest time step as opposed to the smallest time step in the gc method copyright 2004 john wiley sons ltd

linear non linear dynamic substructures the dynamic substructure method is extended to linear and non linear coupling systems only those master co ordinates with non linear nature non linear co ordinates are retained other slave co ordinates relating to the linear part linear co ordinates are eliminated by the dynamic substructure method the dynamic flexibility matrix associated with the linear co ordinates is first expanded in terms of the fixed interface natural modes the condensed dynamic stiffness matrix associated with the non linear co ordinates is formed subsequently the convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and taylor series expansion to find the steady state solutions the non linear responses are expanded into a fourier series responses of the linear co ordinates are related to the non linear co ordinates analytically to solve for the unknown fourier coefficients the harmonic balance method gives a set of non linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients a newtonian algorithm is adopted to solve for the unknown fourier coefficients iteratively the computational cost of a non linear analysis depends heavily on the number of degrees of freedom encountered in the method the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced

eigensolution of augmented graph products using shifted inverse iteration method two important matrices associated with graphs are adjacency and laplacian matrices in this paper efficient methods are presented for eigensolution of graph products augmented by other graphs for augmentations that do not destroy the symmetry of the graph products a method is proposed for decomposition of matrices resulting in considerable simplification of their eigensolution for graphs composed of two non overlapping graph products joined through a small number of link members a method based on shifted inverse iteration is proposed which utilizes all eigenvalues and eigenvectors of each individual graph products owing to the availability of fast methods for eigensolution of graph products this method simplifies the eigensolution of a variety of graph models and proves to be very efficient in determining the few smallest eigenpairs of these models with high levels of accuracy

damped dynamic substructures the dynamic substructure method is extended to lightly or heavily damped systems both internal and external dampings are considered the damped dynamic flexibility associated with the slave co ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co ordinates is formed subsequently the convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices since the dynamic stiffness method is equivalent to the modal synthesis method the component mode method and kron s method the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

interaction measures for control configuration selection based on interval type 2 takagi sugeno fuzzy model interaction measure determines decentralized and sparse control configurations for a multivariable process control this paper investigates interval type 2 takagi sugeno fuzzy it2tsf model based interaction measures using two different criteria one is controllability and observability gramians the other is relative normalized gain array rnga the main contributions are first a data driven it2tsf modeling method is introduced second explicit formulas to execute the two measures based on it2tsf models are given third two interaction indexes are defined from rnga to select sparse control configuration fourth the calculations to derive sensitivities of the two measures with respect to parametric variations in the it2tsf models are developed and fifth the discussion to compare the two measures is presented three multivariable processes are used as examples to show that the results calculated from it2tsf models are more accurate than that from their type 1 counterparts and compared to gramian based measure rnga selects more reasonable control configurations and is more robust to the parametric uncertainties

gibbs phenomenon in structural mechanics the concepts of complementary boundary condition and interior condition are discussed guidelines are developed to eliminate the gibbs effect when selecting trial functions for the series expansion

partitioned component mode synthesis via a flexibility approach a new flexibility based component mode synthesis method is presented which is derived by approximating the partitioned equations of motion that employ a localized method of lagrange multipliers the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes hence the resulting interface flexibility matrices are uniquely determined and well suited for the present method development an attractive feature of the present method is its substructural mode selection criterion that is independent of loading conditions numerical experiments show that the present modal selection criterion is reliable and that the proposed flexibility based component mode synthesis method performs well relative to the classical craig bampton method in terms of accuracy and of its ability to include dominant substructural modes for simple plates and a relatively complex solid ring

on multi time step monolithic coupling algorithms for elastodynamics we present a way of constructing multi time step monolithic coupling methods for elastodynamics the governing equations for constrained multiple subdomains are written in dual schur form and the continuity of velocities is enforced at system time levels the resulting equations will be in the form of differential algebraic equations to crystallize the ideas we shall employ newmark family of time stepping schemes the proposed method can handle multiple subdomains and allows different time steps as well as different time stepping schemes from the newmark family in different subdomains we shall use the energy method to assess the numerical stability and quantify the influence of perturbations under the proposed coupling method two different notions of energy preservation are introduced and employed to assess the performance of the proposed method several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method we shall also compare the proposed multi time step coupling method with some other methods available in the literature

substructure synthesis and its iterative improvement for large nonconservative vibratory systems a general synthesis method is developed for the dynamic analysis of nonconservati ve vibratory systems composed of substructures the idea of the synthesis is to represent each substructure by a reduced order model and to couple the substructure models together to act as the whole system for general nonconservative systems a state space formulation is adopted for each substructure reduced order substructure models are obtained by approximating each state vector as a linear combination of a small number of real trial vectors the accuracy with which the synthesized model represents the whole system depends on the choices of trial vectors and the number of vectors used a procedure is developed for increasing the accuracy by iteratively generating improved substructure trial state vectors

domain decomposition methods for eigenvalue problems abstract this paper proposes several domain decomposition methods to compute the smallest eigenvalue of linear self adjoint partial differential operators let us be given a partial differential operator on a domain which consists of two nonoverlapping subdomains suppose a fast eigenvalue solver is available for each of these subdomains but not for the union of them the first proposed method is a scheme which determines an appropriate boundary condition at the interface separating the two regions this boundary condition can be derived from the zero of a nonlinear operator which plays the same role for the eigenvalue problem as the steklov poincare operator for the linear equation an iterative method can be used to solve this nonlinear equation yielding the exact boundary condition at the interface this enables the determination of the eigenpair on the whole domain the same concept can be applied to a schwarz alternating method for the eigenvalue problem in case the subdomains overlap a nonoverlapping scheme in the spirit of schur complement will also be discussed these ideas are also applicable to a domain imbedding algorithm

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

component mode iteration for frequency calculations this paper presents component mode iteration a new method for carrying out a form of subspace iteration on the substructure level for structures composed of substructures in component mode iteration substructure displacement is in terms of component modes with the interface displacements as coefficients component modes are chosen such that exact compatibility is assured throughout the structure the reduced structure eigenvalue problem is assembled and solved for lower mode approximations the resulting estimates of lower mode interface motion are used to refine the component modes by approximating the dynamic response of substructures to interface motion with a vector iteration process for this step the substructures are independent and can be processed in parallel reassembly and solution of the reduced structure problem yields improved lower mode estimates further iterations of refinement and reassembly are performed until convergence takes place the initial component modes are generated automatically and at negligible expense and numerical examples show that convergence with these is excellent yielding very accurate results after only one iteration indeed convergence is shown to be significantly faster than in the standard subspace iteration method

dynamic analysis using a reduced basis of exact modes and ritz vectors the problem of obtaining an approximate solution for the response of a structure under dynamic forces is addressed the structure is modeled using mass and stiffness matrices and has n degrees of freedom an dimensional approximation is sought in a subspace defined by an arbitrary m orthogonal array a residual vector which is smaller in magnitude the more accurate the approximation is derived the residual contains two terms one is the error involved representing the force vector in the subspace the other is smaller the better the array leads to m approximate solutions of the exact eigenproblem numerical experiments are performed using arrays that are combinations of exact eigenvectors and of ritz vectors in one case when 11 different 10 dimensional bases are used to approximate the solution of a 60 degree of freedom problem it is found that a root mean square measure of relative error is smallest for the basis formed using the 6 lowest exact eigenvectors plus 4 ritz vectors generated from the spatial distribution of the loading

a procedure for improving discrete substructure representation in dynamic synthesis n important problem in the dynamic analysis for flexible structures is that of determining the natural frequencies and associated natural modes of vibration particularly the lower ones complex structures are often represented by mathematical models such as finite element models possessing a very large number of degrees of freedom where the number can reach into the tens of thousands because of the large number of degrees of freedom a direct iterative method for obtaining a partial eigensolution know as subspace iteration was developed the subspace iteration method has a long history an extensive bibliography is given in ref 1 and the current status of the method is discussed in refs 2 4 in the context of structural dynamics even the subspace iteration method however can be overwhelmed by the large number of degrees of freedom in the mathematical model so that a method for prior reduction of the number of degrees of freedom is desirable complex structures are often modeled by breaking the structure into a number of simpler components or substructures the substructure models are then coupled together to form the whole structure model the technique is known as substructure synthesis and its origin can be found in refs 5 and 6 the idea of refs 5 and 6 is to represent the motion of each substructure by a set of substructure normal modes obtained by solving an eigenvalue problem for each substructure then each substructure is represented in the synthesis process by a reduced number of lower substructure modes the synthesis leads to an eigenvalue problem for the assembled structure of a substantially smaller order than that of the original formulation the price paid in reducing the order of the eigenvalue problem is that its solution is only an approximation of the actual eigensolution of the original structure

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

two feti based heterogeneous time step coupling methods for newmark and α schemes derived from the energy method abstract the purpose of this paper is to describe a general methodology to obtain multi time step coupling methods for different time integration schemes newmark hht wbz ch on the basis of energetic considerations the general framework of the feti method is considered for building the heterogeneous time step coupling methods by ensuring the gluing of subdomains with lagrange multipliers the proposed methods for coupling subdomains with different time integration schemes and time steps fine and large time steps are based on the pseudo energy measure as introduced by hughes in the so called energy method employed for proving the stability of implicit explicit algorithms assuming a given variation of the lagrange multipliers over the large time step kinematic conditions are derived by ensuring the zero pseudo energy at the interface two methods will be derived in this paper the first new method for which the interface problem involving the lagrange multipliers is solved at the large time scale can handle the popular dissipative schemes hht wbz ch in the particular case of the newmark schemes the new method matches with the ph method proposed by prakash and hjelmstad the second new method is based at the micro time scale it can be viewed as an extension of the method proposed by gravouil and combescure gc method for the coupling of the schemes nonetheless like the gc method the new micro time based method turns out to be dissipative when non dissipative second order accurate schemes are involved and looses one order of accuracy

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

a scalable lagrange multiplier based domain decomposition method for time dependent problems we present a new efficient and scalable domain decomposition method for solving implicitly linear and non linear time dependent problems in computational mechanics the method is derived by adding a coarse problem to the recently proposed transient feti substructuring algorithm in order to propagate the error globally and accelerate convergence it is proved that in the limit for large time steps the new method converges toward the feti algorithm for time independent problems computational results confirm that the optimal convergence properties of the time independent feti method are preserved in the time dependent case we employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors and demonstrate the effective scalability of the new transient feti method with the large scale finite element dynamic analysis on the paragon xp s and ibm sp2 systems of several diffraction grating finite element structural models we also show that this new domain decomposition method outperforms the popular direct skyline solver the coarse problem presented herein is applicable and beneficial to a large class of lagrange multiplier based substructuring algorithms for time dependent problems including the fictitious domain decomposition method

on the substructure synthesis method substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures the motion of each of the substructures is represented by a series of admissible functions vectors and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures because the series of admissible functions vectors represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions the computed eigensolution is only an approximation of the actual one convergence of computed eigenvalues to actual eigenvalues requires two limiting processes one in which the number of admissible functions vectors is increased and the other in which the number of geometric compatibility conditions is increased

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

technical communique fixed modes in multivariable systems using constrained controllers a general expression is derived relating an arbitrary output feedback controller to the resulting closed loop characteristic polynomial in terms of suitably defined zero polynomials of the system this expression is then used to characterize the fixed modes of a multivariable system with respect to controllers of any desired structure

kron s method for symmetric eigenvalue problems kron s method has been used successfully by engineers for over 30 years to find eigenvalues of large symmetric matrices these matrices arise from domain decomposition of nonoverlapping domains of self adjoint partial differential operators this paper discusses some theoretical aspects of kron s method specifically the poles and zeroes of eigenvalues of the kron matrix and their relationships with the eigenvalues of the original matrix are given

a reduction method for nonlinear structural dynamic analysis abstract a computational algorithm for predicting the nonlinear dynamic response of a structure is presented the nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a rayleigh ritz analysis the basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing only a few basis updatings are required during the whole time integration the truncation error introduced at every change of basis is pointed out as the cause for a divergence type behaviour and some means for eliminating it are discussed results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations

on three modal synthesis variants abstract a unified formulation of fixed free and loaded interface variants of modal synthesis is presented a formal proof of the exactness of all three variants in the absence of modal truncation is established the sensitivity of the truncation error to the different interface conditions is studied

novel generalized α methods for interfield parallel integration of heterogeneous structural dynamic systems a novel partitioned algorithm able to solve odes arising from transient structural dynamics is presented the spatial domain is partitioned into a set of disconnected subdomains owing to computational or physical considerations and continuity conditions of velocity at the interface are modelled using a dual schur formulation where lagrange multipliers represent reaction forces interface equations along with subdomain equations lead to a system of daes for which an interfield parallel procedure is developed the algorithm solves interface lagrange multipliers which are subsequently used to advance the solution in subdomains the proposed coupling algorithm that enables arbitrary email protected schemes to be coupled with different time steps in each subdomain is an extension of a method originally proposed by pegon and magonette thus subcycling permitting to deal also with stiff and nonstiff subsystems is allowed in detail the paper presents the convergence analysis of the novel interfield parallel scheme for linear single and two degrees of freedom systems because a multi degrees of freedom system is too difficult for a mathematical treatment however the insight gained from the analysis of these coupled problems and the consequent conclusions are confirmed by means of numerical experiments on a four degrees of freedom system

approximate eigensolution of laplacian matrices for locally modified graph products laplacian matrices and their spectrum are of great importance in algebraic graph theory there exist efficient formulations for eigensolutions of the laplacian matrices associated with a special class of graphs called product graphs in this paper the problem of determining a few approximate smallest eigenvalues and eigenvectors of large scale product graphs modified through the addition or deletion of some nodes and or members is investigated the eigenproblem associated with a modified graph model is reduced using the set of master eigenvectors and linear approximated slave eigenvectors from the original model implicitly restarted lanczos method is employed to obtain the required eigenpairs of the reduced problem examples of large scale models are included to demonstrate the efficiency of the proposed method compared to the direct application of the irl method

another look at admissible functions abstract problems associated with using global admissible functions in boundary value problems are discussed it is shown that if care is not taken it is possible to construct sets of trial functions that yield inaccurate results which take too long to converge the concept of complementary boundary conditions is introduced and their existence is established complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries it is shown that trial functions that yield incorrect or very slowly converging results are those that violate the complementary boundary conditions a revision for the definition of admissible and comparison functions is proposed that takes the complementary boundary conditions into consideration

gain tuning of fuzzy pid controllers for mimo systems a performance driven approach a new methodology for tuning the scaling factors or gains of fuzzy proportional integral derivative controllers by taking explicitly into account the closed loop system performance is proposed in this study the solution is obtained by solving a nonlinear constrained optimization problem considering a set of constraints on the scaling factors of the mamdani type fuzzy system and on the plant s inputs and outputs two distinct approaches are presented which are associated with the optimization being carried out offline or in real time the offline tuning scheme assumes the system dynamics described by a nonlinear model while for the real time implementation the plant s dynamics is locally approximated by a linear model with the underlying parameters recursively updated in order to cope with rather stringent sampling time requirements the constrained online optimization problem is implemented based on the grid computing paradigm given the adaptive nature of the real time scheme time varying dynamics and unknown disturbances can be accommodated in such a way that the closed loop performance is effectively maximized while avoiding wind up phenomena induced by the integrator term the proposed tuning methodologies are assessed on a benchmark three tank system and compared against a conventional based tuning approach results from experiments illustrate the feasibility of the proposed approaches and also all the relevance in optimal control systems based on mamdani type fuzzy controllers

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

direct component modal synthesis technique for system dynamic analysis a method for substructure modal synthesis to determine the modal parameters of a structure is investigated the order of the solution matrix does not depend on the number of substructure modes used instead it depends only on the number of connections between substructures the eigensolution determined by this method is exact since the system dynamic matrix equation is not needed in this method numerical computations required for the solution are drastically reduced the eigensolutions of the system in any frequency range can be obtained independently computation is reduced because lower or higher eigensolutions outside the interested frequency range are not required to be calculated the results obtained by this technique and the analytical method are compared and they are identical

control configuration selection for bilinear systems via generalised hankel interaction index array decentralised and partially decentralised control strategies are very popular in practice to come up with a suitable decentralised or partially decentralised control structure it is important to select the appropriate input and output pairs for control design this procedure is called control configuration selection it is well known that a suitable control configuration selection is an important prerequisite for a successful industrial control in this paper the problem of control configuration selection for multiple input and multiple output mimo bilinear processes is addressed first the concept of the cross gramian is developed for bilinear systems the conditions for the existence of generalised cross gramian are derived it is shown that if the cross gramian exists it is the solution to the generalised sylvester equation to obtain the cross gramian in a more computationally efficient way an iterative method for solving the generalised sylvester equation is proposed the generalised cross gram

convergence analysis of a parallel interfield method for heterogeneous simulations with dynamic substructuring summary in order to predict the dynamic response of a complex system decomposed by computational or physical considerations partitioned procedures of coupled dynamical systems are needed this paper presents the convergence analysis of a novel parallel interfield procedure for time integrating heterogeneous numerical physical subsystems typical of hardware in the loop and pseudo dynamic tests the partitioned method is an extension of the method originally proposed by gravouil and combescure which utilizes a domain decomposition enforcing the continuity of the velocity at interfaces in particular the merits of the new method which can couple arbitrary newmark schemes with different time steps in different subdomains and advance all the substructure states simultaneously are analysed in terms of accuracy and stability all theoretical results are derived for single and two degrees of freedom systems as a multi degree of freedom system is too difficult to analyse mathematically however the insight gained from the analysis of these coupled problems and the conclusions drawn are confirmed by means of the numerical simulation on a four degrees of freedom system copyright q 2008 john wiley sons ltd