periodic impact behavior of a class of hamiltonian oscillators with obstacles abstract in this paper we study the existence of harmonic and subharmonic solutions of a class of non smooth hamiltonian systems then apply its results to the vibration problems x q x x 2 g t x f t x t 0 x t 0 x t 0 if x t 0 0 infinitely many harmonic and subharmonic bouncing solutions are always obtained if q x satisfies some coercive conditions

periodic solutions for p laplacian lienard equation with a deviating argument abstract by employing mawhin s continuation theorem the existence of periodic solutions of the p laplacian lienard equation with a deviating argument p x t f x t x t g x t t e t under various assumptions are obtained

existence of multiple nontrivial solutions for semilinear elliptic problems the aim of this paper is to prove the existence of multiple nontrivial solutions to a semilinear elliptic problem at resonance the proofs used here are based on combining the morse theory and the minimax methods

periodic solutions of the lienard equation with one sided growth restrictions in this article we are concerned with the problem of the existence of periodic solutions to the periodically forced scalar lienard equation x f x x g x e t d dt 1 where f g e r r are continuous functions and e is periodic we are looking for solutions of 1 having the same period of the forcing term e throughout the paper we assume without loss of generality see e g 22 36 p 693 that

discrete time hybrid control in borel spaces average cost optimality criterion abstract this paper addresses an optimal hybrid control problem in discrete time with borel state and action spaces by hybrid we mean that the evolution of the state of the system may undergo deep changes according to structural modifications of the dynamic such modifications occur either by the position of the state or by means of the controller s actions the optimality criterion is of a long run ratio average or ratio ergodic type we provide the existence of optimal average policies for this hybrid control problem by analyzing an associated dynamic programming equation we also show that this problem can be translated into a standard or non hybrid optimal control problem with cost constraints besides we show that our model includes some special and important families of control problems such as those with an impulsive or switching mode finally to illustrate our results we provide an example on a pollution accumulation problem

periodic solutions of a second order ordinary differential equation a necessary and sufficient condition for nonresonance the nonlinearity g in 1 1 is a continuous function from r to r and the forcing term h is taken in l o 27r nonresonance means that 1 1 admits at least one solution x for any given h integrating eq 1 1 over a period one immediately sees that a necessary condition for nonresonance is that the function g be unbounded from above and from below on r it will appear later cf 1 6 that this unboundedness can be looked at as a condition relating the behaviour at infinity of the nonlinearity g with respect to the first eigenvalue 1 0 of the associated linear problem xf ax in 0 27r x 0 x 27r x 0 x1 271 1 2

nonresonance conditions for asymptotically positively homogeneous differential systems the fucik spectrum and its generalization in this article we propose how to define the fucik spectra for differential systems in rnwith jumping nonlinearities the propertyp a generalization of the non fucik spectra to positively homogeneous nonautonomous differential systems is also defined in the most general setting a quantitative estimate result concerning the parameterized completely continuous positively homogeneous perturbations of the identity in banach spaces is given in this article such a result is a generalization of one property in the spectrum theory for completely continuous linear operators using this estimate result we will give some significantly improved nonresonance results from the fucik spectra and propertypfor asymptotically positively homogeneous differential systems

an algebraically partitioned feti method for parallel structural analysis algorithm description an algebraically partitioned feti method for the solution of structural engineering problems on parallel computers is presented the present algorithm consists of three attributes an explicit generation of the orthogonal null space matrix associated with the interface nodal forces the floating subdomain rigid body modes computed from the subdomain static equilibrium equation of the classical force method and the identification of redundant interface force constraint operator that emanates when the interface force computations are localized comparisons of the present method with the previously developed differentially partitioned feti method are offered in terms of the saddle point formulations at the end of the paper a companion paper reports implementation details and numerical performance of the proposed algorithm 1997 john wiley sons ltd

periodic solutions for p laplacian rayleigh equations abstract by employing mawhin s continuation theorem the existence of the p laplacian delay rayleigh equation p x t f x t g x t t e t under various assumptions is obtained

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

estimation of reciprocal residual flexibility from experimental modal data a technique is presented for estimating the residual flexibility between nonexcited structural degrees of freedom from experimental structural vibration data using this method one can include the residual flexibility estimated from modal measurements in the computation of measured flexibility for experiments with incomplete reciprocity i e when the response and excitation measurement sensors are not fully collocated the method can also be used to estimate the unknown entries in the residual flexibility matrix for experimental component mode synthesis when excitations are not provided at all interface degrees of freedom a general solution is presented that contains an unknown positive semidefinite contribution the general solution satisfies modal orthogonality in the limit that all of the structural degrees of freedom are instrumented and when the positive semidefinite contribution lies in a nullspace defined by the stiffness matrix and the modal flexibility with a limited number of measurements modal orthogonality is shown to be satisfied to the extent that the measured modes are preserved by static condensation a rank deficient solution is presented that allows the residual to be used in the computation of the flexibility matrix without further modeling assumptions numerical and experimental results that demonstrate the application of the method to both flexibility matrix convergence and experimental component mode synthesis are presented

periodic solutions of a second order nonlinear system abstract we discuss the existence of periodic solutions of the system x t d dt grad f x t g t x t e t under various asymptotic behaviours of g

structural damage assessment using a generalized minimum rank perturbation theory recently the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties the algorithms make use of a finite element model and a subset of measured eigenvalues and eigenvectors the developed theories approach the damage location and extent problem in a decoupled fashion first a theory is developed to determine the location of structural damage with location determined a damage extent theory is then developed the damage extent algorithm is a minimum rank perturbation which is consistent with the effects of many classes of structural damage on a finite element model in this work the concept of the minimum rank perturbation theory mrpt is adopted to determine the damage extent on the mass properties of an undamped structure in addition the mrpt is extended to the case of proportionall y damped structures for proportionally damped structures the mrpt is used to find the damage extent in any two of the three structural property matrices mass damping or stiffness finally illustrative case studies using both numerical and actual experimental data are presented he advent of the space shuttle has prompted considerable attention to the design and control of large space structures due to the large size and complexity of envisioned structures as well as the use of advanced materials to reduce structural weight it may become necessary to develop a structural health monitoring system to detect and locate structural damage as it occurs from experience gained in the machinery health monitoring field one would expect the vibration signature of the structure either frequency response functions and or modal parameters to provide useful information in determining the location and extent of structural damage assume that a refined finite element model fem of the structure has been developed before damage has occurred by refined we mean that the measured and analytical modal properties are in agreement next assume that at a later date some form of structural damage has occurred if significant the damage will result in a change in the structures modal parameters the question is can the discrepancy between the original fem modal properties and postdamage modal properties be used to ascertain structural damage most prior work in damage detection has used the general framework of fem refinement system identification in the development of damage assessment algorithms the motivation behind the development of fem refinement techniques is based on the need to validate engineering fems before their acceptance as the basis for final design analysis the standard problem has been to seek a refined fem that is as close to the original fem and whose modal properties are in agreement with those that are measured subject to various constraints such as symmetry and sparsity preservation a considerable amount of work in this area has been

eigenstructure assignment approach for structural damage detection in this work a methodology for incorporating measured modal data into an existing refined finite element model is examined with the objective of detecting and locating structural damage the algorithm is based on the partial inverse problem in that only partial spectral information is required the technique utilizes a symmetric eigenstructure assignment algorithm to perform the partial spectral assignment algorithms to enhance mode shape assignability and to preserve sparsity in the damaged fem are developed the sparsity preservation is of particular importance when considering damage detection in trusslike structures several examples are presented to highlight the key points made within the paper

periodic solutions for duffing equations with a p laplacian like operator in this paper sufficient conditions are established to guarantee the existence of at least one periodic solution to a second order duffing equation with a p laplacian like operator generalized polar coordinates are applied in our proof

existence and uniqueness of periodic solution for a class of differential systems in this paper sufficient conditions are obtained for the existence of a unique periodic solution for a class of differential systems

updating finite element dynamic models using an element by element sensitivity methodology a sensitivity based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented the proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors the updating algorithm is derived from the unconstrained minimization of the squared 2 norms of the modal dynamic residuals via an iterative two step staggered procedure at each iteration the measured mode shapes are first expanded assuming that the model is error free then the model parameters are corrected assuming that the expanded mode shapes are exact the numerical algorithm is implemented in an element by element fashion and is capable of zooming on the detected error locations several simulation examples which demonstrate the potential of the proposed methodology are discussed i introduction e ven though the field of finite element analysis of structural dynamic problems has witnessed tremendous progress in the last two decades greater confidence is still placed in experimental data therefore the finite element model of a given structure is often updated to reflect the results of a particular experiment usually the computed eigenmodes are compared with the measured frequencies and mode shapes if both sets are not in agreement the finite element model is refined via a two step updating procedure which 1 locates the errors and 2 corrects them clearly the first step is the most challenging of the two once the location of the errors is known it is relatively easy to correct them especially if the error sources can be identified however locating and identifying these errors can be a difficult task for the following reasons in general only a few experimental modes are available and these may be contaminated with random and systematic measuring errors moreover only a subset of the degrees of freedom dof in the finite element model can be monitored and as for practical and economical reasons only a few sensors can be utilized

method for determining minimum order mass and stiffness matrices from modal test data a new method for determining mass and stiffness matrices from modal test data is presented the method builds on the identified modes and the mass normalized mode shapes at the sensor locations and is not limited by either the number of driving points or measurement points and so it is applicable to most general test settings a mixed coordinate basis is defined for the mass and stiffness matrices which is analogous to the craig bampton component mode synthesis method for finite element models the resultant mass and stiffness are of minimal order necessary to span the measured modes and the resulting generalized coordinates provide an objective basis for the test derived matrices to be used as if they are component mode synthesized finite element matrices inclusion of rigid body modes and the relationship of the new method to traditional physical parameter computations based on mobility curves is considered examples of the method as applied to numerical and experimental data are provided

metrics for labelled markov processes the notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions thus a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent this instability is due to the quantitative nature of probabilistic processes in a situation where the process behavior has a quantitative aspect there should be a more robust approach to process equivalence this paper studies a metric between labelled markov processes this metric has the property that processes are at zero distance if and only if they are bisimilar the metric is inspired by earlier work on logics for characterizing bisimulation and is related in spirit to the hutchinson metric

semilinear duffing equations crossing resonance points abstract in this paper using a generalized form of the poincare birkhoff theorem and a fixed point theorem we prove under weaker conditions two theorems for the equation x g x p t p t p t 2 of which one shows the existence of a harmonic solution the other that the equation may have an infinite number of harmonic solutions in the resonance case this is an enhancement of the results already obtained

resonance and rotation numbers for planar hamiltonian systems multiplicity results via the poincare birkhoff theorem abstract in the general setting of a planar first order system 0 1 u g t u u r 2 with g 0 t r 2 r 2 we study the relationships between some classical nonresonance conditions including the landesman lazer one at infinity and in the unforced case i e g t 0 0 at zero and the rotation numbers of large and small solutions of 0 1 respectively such estimates are then used to establish via the poincare birkhoff fixed point theorem new multiplicity results for t periodic solutions of unforced planar hamiltonian systems j u u h t u and unforced undamped scalar second order equations x g t x 0 in particular by means of the landesman lazer condition we obtain sharp conclusions when the system is resonant at infinity

on finite state approximants for probabilistic computation tree logic we generalize the familiar semantics for probabilistic computation tree logic from finite state to infinite state labelled markov chains such that formulas are interpreted as measurable sets then we show how to synthesize finite state abstractions which are sound for full probabilistic computation tree logic and in which measures are approximated by monotone set functions this synthesis of sound finite state approximants also applies to finite state systems and is a probabilistic analogue of predicate abstraction sufficient and always realizable conditions are identified for obtaining optimal such abstractions for probabilistic propositional modal logic

extraction of substructural flexibility from global frequencies and mode shapes a computational procedure for extracting substructure by substructure flexibility properties from global modal parameters is presented the present procedure consists of two key features an element based direct flexibility method which uniquely determines the global flexibility without resorting to case dependent redundancy selections and the projection of cinematically inadmissible modes that are contained in the iterated substructural matrices the direct flexibility method is used as the basis of an inverse problem whose goal is to determine substructural flexibilities given the global flexibility geometrically determined substructural rigid body modes and the local to global assembly operators the resulting procedure given accurate global flexibility extracts the exact element by element substructural flexibilities for determinate structures for indeterminate structures the accuracy depends on the iteration tolerance limits the procedure is illustrated using both simple and complex numerical examples and appears to be effective for structural applications such as damage localization and finite element model reconciliation

nonresonance to the right of the first eigenvalue for the one dimensional p laplacian a quasilinear two point boundary value problem was considered this problem is given by the equation

periodic solutions of rayleigh equations via time maps abstract in this paper we study the existence of periodic solutions of rayleigh equations x f t x g x e t where f r 2 r is continuous and t periodic with respect to the first variable g e r r are continuous and e is t periodic we prove that the given equation possesses at least one t periodic solution provided that either lim sup c c lim inf c c t or lim inf c c lim sup c c t is satisfied where is the time map defined in section 1

on the peroidic bvp for the forced duffing equation with jumping nonlinearity on etudie le probleme suivant u cu f t u e t p p sur 0 t u t u 0 0 u t u 0 0 c est une fonction arbitraire dans l 1 0 t r c r et l application non lineaire f est a saut

a continuation lemma and its applications to periodic solutions of rayleigh differential equations with subquadratic potential conditions in this paper we study the existence of periodic solutions of rayleigh equations x f t x g x e t where f g e are continuous functions and f is t periodic with the first variable e is t periodic by developing a continuation lemma for rayleigh equations we prove that the given equation has at least one t periodic solution provided that f t y is sublinear with respect to the variable y and g x 0xg u du satisfies some subquadratic conditions

multiplicity of periodic solutions of semilinear duffing s equation at resonance in this paper we prove an infinity of periodic solutions to the periodically forced nonlinear duffing equation under new conditions

periodic solutions of lienard equations with singular forces of repulsive type in this paper we will use the coincidence degree to give an existence result of periodic solutions for the scalar lienard equations with singular forces of repulsive type the main result of this paper clearly describes what balance conditions between the singular force at the singularity and at the infinity should be imposed if the equation has a periodic solution as an application we will improve the results of ding ye and wang for the brillouin electron beam focusing system

a direct flexibility method we present a direct flexibility method dfm for the solution of finite element equations this method is based on a decomposition of the finite element model into substructures which may reduce to individual elements substructures are preprocessed by the direct stiffness method dsm to generate free free flexibility matrices for floating substructures the interface problem is solved for the interface forces and the solution recovered over substructure interiors the dfm shares with the dsm the advantages of being automatic maintaining locality and sparseness efficiently handling continuum elements and requiring only the availability of element stiffness libraries the new method appears to be advantageous for specific applications these include massively parallel processing inverse problems treatment of rigid members and inclusions and use of underintegrated elements without spurious mode stabilization

existence and multiplicity results for periodic solutions of semilinear duffing equations we obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear duffing s equation x g x p t in the semi linear case 0 a g x x b for x large we introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x x and show by some nonlinear counterexamples that the results are sharp

periodic solutions for p laplacian neutral functional differential equation with deviating arguments by using the theory of coincidence degree we study a kind of periodic solutions to p laplacian neutral functional differential equation with multiple deviating arguments a new result on the existence of periodic solutions is obtained

nonresonance below the first eigenvalue for a semilinear elliptic problem let be a bounded open subset in hbox i r n with smooth boundary and let f x s be a real valued caratheodory function on upomega times hbox i r we consider the semilinear dirichlet problem

second order structural identification procedure via state space based system identification a theory is presented for transforming the system theory based realization models into the corresponding physical coordinate based structural models the theory has been implemented into a computational procedure and applied to several example problems the results show that the present transformation theory yields an objective model basis possessing a unique set of structural parameters from an infinite set of equivalent system realization models for proportionally damped systems the transformation directly and systematically yields the normal modes and modal damping when nonproportional damping is present the relative magnitude and phase of the damped mode shapes are separately characterized and a corrective transformation is then employed to capture the undamped normal modes and nondiagonal modal damping matrix namics equations has hampered the application and acceptance of the system theory based structural identification techniques and can eventually curtail the progress of hybrid experimental analyti cal modeling and design efforts the present paper offers a theory for transforming the system theory based realization models into the corresponding physical coordinate based structural models since a key idea employed in the development of the present theory is an objective common basis normalization it is designated as a common basis normal ized structural identification cbsi procedure the resultant model is unique for a given sequence of markov parameters which in turn are uniquely determined for a linear structure with given inputs and outputs therefore the realized model after transformation has a one to one correspondence with the physical parameters of the system and can either yield data for finite ele ment model correlation or alternatively for direct calculation of mass stiffness and damping matrices of the original structure specifically we begin with the so called mcmillan transformation employed by longman and juang9 and show that the mcmillan transformation does not in general yield the desired structural nor mal modes to arrive at an objective transformation basis of gener alized coordinates we invoke two invariance properties the first is the output invariance property viz the outputs are invariant with respect to any choice of generalized coordinates the second is the normal mode identity viz for proportionally damped cases the mode shapes for the displacement velocity and acceleration vectors are the same there are several byproducts that the present theory provides primarily due to the common basis normalization employed in the theory first the present transformation theory allows the integra tion of different realized models with varying actuator and sensor locations if they arise from the same structure second each sensor and actuator or groups of sensors and actuators can be processed in parallel and combined concurrently or sequentially for the con struction of a global model third it can facilitate a decentralized real time control implementation from a structural dynamics point of view the transformation to an objective basis provides a state space model coinciding with the canonical form of the second order equations of motion thus extracting the classical real valued parameters of interest to modal testing mass normalized normal modes and the general modal damping matrix while maintaining the system equivalence properties of the state space form

periodic solutions of duffing s equations with superquadratic potential abstract this paper is devoted to the study of harmonic and subharmonic solutions for the second order scalar nonlinear duffing s equation x g x p t x x where g and p are continuous functions with p bounded and periodic in the first variable and g satisfying the assumption g x sign x as x among other results we prove the existence of infinitely many harmonic and subharmonic solutions of any order p p t and if the potential g x of g x satisfies certain conditions of superquadratic growth at the new existence results can be applied to situations in which the more classical superlinear growth condition g x x as x is not satisfied in this manner various preceding theorems are improved and sharpened see the introduction for more details proofs are based on a generalized version of the poincare birkhoff twist theorem due to w ding

model update using modal contribution to static flexibility error a new technique for the parametric correction of full order analytical stiffness matrices from reduced order modal measurements is presented the proposed algorithm corrects model parameters by minimizing a matrix residual formed at measurement degrees of freedom only the residual is the difference between the measured modal contribution to the static flexibility matrix and the corresponding analytical modal contribution to the static flexibility matrix analytical expressions are developed for the flexibility matrix error residual gradient in terms of modal sensitivities found via nelson s method by utilizing a flexibility based matrix error residual the effect of poorly modeled inertia properties on stiffness parameter estimates is greatly reduced unlike technlques that utilize only static data this technique is suitable for use on unconstrained structures in addition the method avoids the problems of mode selection determining modal correspondence and eigenvector expansion or model reduction numerical simulation results are presented for kabe s model as well as a finite element model of a welded frame structure

a relationship between the periodic and the dirichlet bvps of singular differential equations in this paper a relationship between the periodic and the dirichlet boundary value problems for second order ordinary differential equations with singularities is established this relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations using this relationship we give in this paper an existence result of positive periodic solutions to singular differential equations when the singular forces satisfy some strong force condition at the singularity 0 and some linear growth condition at infinity

half eigenvalues of periodic sturm liouville problems we consider the nonlinear sturm liouville problem 1 pu qu au bu u in 0 2 2 u 0 u 2 pu 0 pu 2 where 1 p q l1 0 2 with p 0 a e on 0 2 a b l1 0 2 is a real parameter and u t max u t 0 for t 0 2 values of for which 1 2 has a non trivial solution u will be called half eigenvalues while the corresponding solutions u will be called half eigenfunctions the set of half eigenvalues will be denoted by h we show that a sequence of half eigenvalues exists the corresponding half eigenfunctions having certain nodal properties and we obtain certain spectral and degree theoretic properties associated with h these properties yield results on the existence and non existence of solutions of the problem 3 pu qu f t u h in 0 2 together with 2 where h l1 0 2 f 0 2 r r is a caratheodory function and the limits a t lim f t b t lim f t exist for a e t 0 2 when the functions a and b are constant the set h is closely related to the fucik spectrum of the problem and equivalent solvability results are obtained using the two approaches however when a and b are not constant the half eigenvalue approach yields stronger results

periodic solutions for a kind of lienard equation with a deviating argument abstract by means of continuation theorem of coincidence degree theory we study a kind of lienard equation with a deviating argument as follows x t f x t x t g x t t x t e t some new results on the existence of periodic solutions are obtained

verification of discrete time stochastic hybrid systems a stochastic reach avoid decision problem we present a dynamic programming based solution to a probabilistic reach avoid problem for a controlled discrete time stochastic hybrid system we address two distinct interpretations of the reach avoid problem via stochastic optimal control in the first case a sum multiplicative cost function is introduced along with a corresponding dynamic recursion which quantifies the probability of hitting a target set at some point during a finite time horizon while avoiding an unsafe set during each time step preceding the target hitting time in the second case we introduce a multiplicative cost function and a dynamic recursion which quantifies the probability of hitting a target set at the terminal time while avoiding an unsafe set during the preceding time steps in each case optimal reach while avoid control policies are derived as the solution to an optimal control problem via dynamic programming computational examples motivated by two practical problems in the management of fisheries and finance are provided

periodic solutions for second order equations with time dependent potential via time map in this paper the approach via time map is used to investigate the existence of periodic solutions for second order equation with time dependent potential our theorem generalized the results obtained by ding habets omari and zanolin which are for time independent potential and relate the behavior of the primitive of the nonlinearity with respect to the fucik spectrum of the periodic problem

upper and lower solutions and topological degree this paper deals with second order nonlinear boundary value problems we suppose the existence of upper and lower solutions of the problems which are well ordered i e the lower solution is less than the upper one and we also consider the case of upper and lower solutions having the opposite ordering we prove the relation between the topological degree and strict upper and lower solutions in both cases and using this we get the existence and multiplicity results for the boundary value problems under consideration

method for structural model update using dynamically measured static flexibility matrices a new method is presented for parametric correction of full order analytical stiffness matrices from reduced order dynamically measured static flexibility matrices the measured static flexibility matrix is formed using modal data in conjunction with a residual flexibility estimate the algorithm corrects model parameters by minimizing a static flexibility matrix error residual constructed for measurement degrees of freedom only by utilizing a flexibility matrix residual instead of one derived using stiffness matrices numerical problems associated with inverting a rank deficient measured flexibility matrix are avoided posing the problem in terms of flexibility matrices also avoids the problems of modal correspondence mode selection and modal truncation in addition incorporating static reduction relationships into the error residual makes prior eigenvector expansion or model reduction unnecessary two formulations for the error residual are presented an explicit inverse formulation and one derived from a pseudoinverse relationship the second leads to an exact linear update problem when all of the model degrees of freedom are measured numerical simulation results demonstrate that both formulations are capable of localizing and quantifying local stiffness errors in a full order finite element model from reduced order measurements experimental results for a cantilever beam structure are also presented

a new fixed point theorem and periodic solutions of nonconservative weakly coupled systems abstract in this paper we prove a new fixed point theorem for the coupling of twist conditions and poincare bohl type conditions as its applications we prove the existence of periodic solutions for various nonconservative mixed type weakly coupled systems

periodic solutions of duffing equations with semi quadratic potential and singularity abstract in this paper we deal with the existence of periodic solutions of the second order differential equations x g x p t with singularity we prove that the given equation has at least one periodic solution when g x has singularity at origin g x 1 x g s d s satisfies n 2 4 lim inf x 2 g x x 2 lim sup x 2 g x x 2 n 1 2 4 for large positive x where n 0 is an integer and g x tends to positive infinity as x 0

periodic and unbounded motions in asymmetric oscillators at resonance abstract we consider the existence of periodic and unbounded solutions for the asymmetric oscillator x a x b x g x p t where x max x 0 x max x 0 a and b are two positive constants p t is a 2 periodic smooth function and g x satisfies lim x x 1 g x 0 we have proved previously that the boundedness of all the solutions and the existence of unbounded solutions have a close relation to the interaction of some well defined functions p and h in this paper we consider some critical cases and obtain some new sufficient conditions for the existence of 2 periodic and unbounded solutions in particular the obtained periodic solutions are new and cannot be deduced from landesman lazer s and fabry fonda s existence conditions in contrast with many existing results the function g x may be unbounded or oscillatory without asymptotic limits

periodic solutions for a kind of second order differential equation with multiple deviating arguments by means of continuation theorem of coincidence degree theory some new results on the existence and nonexistence of periodic solutions for a kind of second order functional differential equation with multiple deviating arguments are obtained

existence and localization of solution for second order elliptic bvp in presence of lower and upper solutions without any order abstract we prove an existence and localization result for a solution of a second order elliptic equations with dirichlet and regular oblique derivative boundary conditions the main result is obtained assuming the existence of a lower and an upper solution without particular order and a positively homogeneous asymptotic behaviour of the right hand member of the equation

a contact formulation based on localized lagrange multipliers formulation and application to two dimensional problems the non penetration condition in contact problems is traditionally based on the classical lagrange multiplier method this method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non matching to deal with this problem we introduce a novel element in the lagrange multiplier approach of contact modelling namely a contact frame placed in between contacting bodies it acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic the contact frame has its own independent freedoms which allows the formulation to pass contact patch tests by design copyright 2002 john wiley sons ltd

a nonresonance condition for radial solutions of a nonlinear neumann elliptic problem abstract we prove an existence result for radial solutions of a neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues to this aim we introduce an alternative nonresonance condition with respect to the second eigenvalue which in the scalar case generalizes the classical one in the spirit of fonda et al 1991 2 our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption

existence of periodic solutions for second order duffing equations with p laplacian like operators the existence of periodic solutions for second order duffing equations with p laplacian like operator is studied by applying a new generalization of polar coordinates

probabilistic reachability and safety for controlled discrete time stochastic hybrid systems in this work probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs a suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations leading to dual algorithms for reachability computations in particular the set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired safe region of the state space is characterized in terms of a value function and maximally safe markov policies are determined via dynamic programming these results are of interest not only for safety analysis and design but also for solving those regulation and stabilization problems that can be reinterpreted as safety problems the temperature regulation problem presented in the paper as a case study is one such case

on the existence of periodic solutions for a class of p laplacian system by using generalized borsuk theorem in coincidence degree theory some criteria to guarantee the existence of periodic solutions for a class of p laplacian system are derived

multiple solutions of the periodic boundary value problem for some forced pendulum type equations if f x c 0 and e is a constant t then integrating 0 1 over 0 272 after multiplication of both members of the equation by x shows that the only possible solutions are constant and hence satisfy a sin x c consequently if we exclude the trivial translation by a multiple of 275 0 1 will have no solution if dj a one solution if lp a and two solutions if lc l a in 0th er t erms the intersection of the range of the operator d2 dt2 c d dt f u sin acting on zn periodic functions of class g with the subspace of constant functions in the space c o 2711 of real continuous functions on 0 27r is the closed interval a a whose interior points are images of two distinct solutions and boundary points of one we try to obtain similar results for the case where e is no more constant and

solvability of the forced duffing equation at resonance some existence theorems are obtained for periodic solutions of the forced duffing equation at resonance by the minimax methods

on periodic solutions of nonlinear second order vector differential equations this paper considers existence of periodic solutions for vector lienard differential equations in our main result we write where q t x is a symmetric matrix and h t x is sublinear the key assumption relates the asymptotic behaviour as x of the eigenvalues of q t x to the spectrum of the linear operator d 2 dt 2 several choices for q t x are considered which lead to known theorems and extend others in the case of the duffing equation the assumptions are weakened our approach is based on leray schauder s degree theory and a priori estimates

direct least squares formulation of a stiffness adjustment method a direct least squares formulation of the stiffness matrix adjustment method known as the kma method kabe a m stiffness matrix adjustment using mode data aiaa journal vol 23 no 9 1985 pp 1431 1436 is presented the kma method belongs to a class of procedures that refine dynamic models using test measured modes and structural connectivity viewed as a constrained minimization problem most of these methods have applied lagrange multiplier techniques in their development it is shown that these two approaches result in linear systems of equations that are algebraically equivalent and therefore have identical solutions by virtue of this equivalence the direct least squares formulation of the kma method is shown to be equivalent to its original lagrange multiplier formulation the direct least squares versions of other model refinement methods that preserve structural connectivity are also discussed in this respect this approach provides a rigorous framework for unifying these optimal update procedures and indicates how their solutions should compare numerical results are presented that illustrate the equivalence between the two formulations and also the conditions under which the various methods yield identical solutions the results also indicate that because of improved numerical conditioning the direct least squares approach yields more accurate computational solutions and generally requires less computer storage than methods that were developed using lagrange multipliers

periodic solutions of lienard differential equations with subquadratic potential conditions abstract in this paper we study the second order forced lienard equation x f x x g x e t we obtain the existence of periodic solutions under some subquadratic conditions

an application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations abstract in this paper a class of systems of nonlinear differential equations at resonance is considered with the use of a global inversion theorem which is an extended form of a non variational version of a max min principle we prove that this class of equations possesses a unique 2 periodic solution under a rather weaker condition for existence and uniqueness than those given in papers j chen w li periodic solution for 2 k th boundary value problem with resonance j math anal appl 314 2006 661 671 f cong periodic solutions for 2 k th order ordinary differential equations with nonresonance nonlinear anal 32 1998 787 793 f cong periodic solutions for second order differential equations appl math lett 18 2005 957 961 w li periodic solutions for 2 k th order ordinary differential equations with resonance j math anal appl 259 2001 157 167 w li h li a min max theorem and its applications to nonconservative systems int j math math sci 17 2003 1101 1110 w li z shen a constructive proof of existence and uniqueness of 2 periodic solution to duffing equation nonlinear anal 42 2000 1209 1220 this result extends the results known so far

bisimilar linear systems the notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics and in particular reachability in this paper the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems given a discrete time or continuous time linear system and a finite observation map we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system interestingly the characterizations for discrete time systems are more restrictive than for continuous time systems due to the existence of an atomic time step we show that computing the coarsest bisimulation which results in maximum complexity reduction corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map these results establish strong connections between complexity reduction concepts in control theory and computer science

structural damage detection of space truss structures using best achievable eigenvectors a method is presented by which measured modes and frequencies from a modal test can be used to determine the location and magnitude of damage in a space truss structure the damage is located by computing the euclid ean distances between the measured mode shapes and the best achievable eigenvectors the best achievable eigenvectors are the projection of the measured mode shapes onto the subspace defined by the refined analytical model of the structure and the measured frequencies loss of both stiffness and mass properties can be located and quantified to examine the performance of the method when experimentally measured modes are employed various damage detection studies using a laboratory eight bay truss structure were conducted the method per forms well even though the measurement errors inevitably make the damage location more difficult uture structures in space will be orders of magnitude larger and more complex than their predecessors structures such as space station freedom will typically be built around a large flexi ble frame and consist of habitation and experiment modules flexi ble and articulating appendages and numerous utility trays and pay loads along with the need to design the spacecraft to be light weight strong and modular for ease of expansion repair and modification the complexity and size of these structures require that the integrity of the structures be monitored periodically several researchers have studied the possibility of detecting damage or structural anomalies to large space trusses and locating the site of this damage based on changes in the natural frequencies and mode shapes of the structures references 1 and 2 provide a comprehensive overview of many of the proposed methods in this respect and the issues involved with on orbit modal identification and structural verification there are several distinct classes of model improvement damage location methods each of these methods begins with an initial finite element representation of the structure in the case of model improvement the goal is to use test data of the actual structure to modify this initial finite element model so that it may serve as an accurate representation of the un damaged structure in the case of damage location the goal is to use test data from the damaged structure and the updated corre lated finite element model of the undamaged structure to deter mine changes to the stiffness and or mass matrices that would ac count for the observed differences in the measured modes and frequencies the class of update methods that has been explored most widely is known as optimal matrix modification the goal of the optimal matrix modification is to find an updated matrix stiffness and or mass that is as close as possible to the original matrix assumed to be almost correct that accurately produces the measured modes

characterization and computation of infinite horizon specifications over markov processes this work is devoted to the formal verification of specifications over general discrete time markov processes with an emphasis on infinite horizon properties these properties formulated in a modal logic known as pctl can be expressed through value functions defined over the state space of the process the main goal is to understand how structural features of the model primarily the presence of absorbing sets influence the uniqueness of the solutions of corresponding bellman equations furthermore this contribution shows that the investigation of these structural features leads to new computational techniques to calculate the specifications of interest the emphasis is to derive approximation techniques with associated explicit convergence rates and formal error bounds

resonant and nonresonant oscillations for some third order nonlinear ordinary differential equations on etudie l existence de solutions 2 periodiques des equations differentielles d ordre 3 x ax bx g t x p t x x x x ax bx t x x x x p t x x x x ax f x x g t x p t x x x

a small twist theorem and boundedness of solutions for semilinear duffing equations at resonance abstract we obtain a new variant of moser s small twist theorem and apply this new version to investigate the boundedness of solutions for the following semilinear duffing equation x n 2 x g x p t where p is a 2 periodic smooth function and lim x x 1 g x 0 we obtain some sharp sufficient conditions for the boundedness of all solutions to the above equation at resonance unlike many existing results in the literature where the function g is required to be a bounded function with asymptotic limits our main results here allow g be unbounded or oscillatory without asymptotic limits

existence of periodic solutions of duffing equations on considere le probleme aux valeurs limites periodiques de type duffing u t ku t g t u t f t t 0 2 u 0 u 2 u 0 u 2 on demontre un resultat d existence general qui montre que si la croissance de g t u a l infini appartient a un ensemble avec la propriete p alors pour tout f l 1 0 2 le probleme a au moins une solution

upper and lower solutions and multiplicity results we consider the second order nonlinear differential equation with an unbounded right hand side and two point or nonlinear boundary conditions on a compact interval using the method of a priori estimates and the relation between the topological degree of the operators associated to the above boundary value problems and the strict lower and upper solutions we get the multiplicity results for the problems