non linear dynamic analysis of anisotropic cylindrical shells containing a flowing fluid abstract an analytical model is presented to predict the influence of non linearities associated with fluid flow on the dynamic behaviour of a structure consisting of shells and a surrounding fluid medium the model requires the use of two linear operators to control the equilibrium of the shell and the velocity potential a linear boundary condition of impermeability and a non linear dynamic boundary condition the method is based on thin shell theory and the non rotational flow of non viscous fluids in combination with finite element analysis it is applicable to non uniform thin anisotropic cylinders subjected to different boundary conditions the displacement functions for the wall and liquid column are derived from sanders equations and from the velocity field associated with the column respectively the set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration the coupled equations are solved for the non flow problem for cases of fluid flow certain analytical modifications are proposed to restore the situation to conventional modal analysis the non linear equations of motion are solved by the fourth order runge kutta numerical method the frequency variations are then determined with respect to the amplitude of the motion the trends of the non linearities are of a softening type

nonlinear stability of cylindrical shells subjected to axial flow theory and experiments abstract this paper is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow in particular it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid the theoretical model employs the donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure the clamped beam eigenfunctions are used to describe the axial variations of the shell deformation automatically satisfying the boundary conditions and the circumferential continuity condition exactly the fluid is assumed to be incompressible and inviscid and the fluid structure interaction is described by linear potential flow theory the partial differential equation of motion is discretized using the galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo arclength continuation and collocation techniques and the gear backward differentiation formula a theoretical model for shells with simply supported ends is presented as well experiments are also described for i elastomer shells subjected to annular external air flow and ii aluminium and plastic shells with internal water flow the experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour finally theory and experiments are compared showing good qualitative and reasonable quantitative agreement

the cauchy integral analytic capacity and uniform rectifiability several explanations concerning notation terminology and background are in order first notation by 7hi we have denoted the one dimensional hausdorff measure i e length and a z r stands for the closed disc with center z and radius r a curve f is called ad regular that is ahlfors david regular if it satisfies 1 2 with e f since the lower bound is automatic for curves this means that hl r n a z r 0 general sets satisfying 1 2 are called ad regular it is simplest to define the l2 boundedness of the cauchy singular integral operator via the truncated integrals we say that ce is bounded in l2 e without really defining the operator ce itself if there is m ox such that

calderon zygmund kernels and rectifiability in the plane abstract let e c be a borel set with finite length that is 0 h 1 e by a theorem of david and leger the l 2 h 1 e boundedness of the singular integral associated to the cauchy kernel or even to one of its coordinate parts x z 2 y z 2 z x y c implies that e is rectifiable we extend this result to any kernel of the form x 2 n 1 z 2 n z x y c n n we thus provide the first non trivial examples of operators not directly related with the cauchy transform whose l 2 boundedness implies rectifiability

nonlinear vibrations of circular cylindrical shells with different boundary conditions large amplitude geometrically nonlinear vibrations of circular cylindrical shells with different boundary conditions and subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated in particular simply supported shells with allowed and constrained axial displacements at the edges are studied in both cases the radial and circumferential displacements at the shell edges are constrained elastic rotational constraints are assumed they allow simulating any condition from simply supported to perfectly clamped by varying the stiffness of this elastic constraint two different nonlinear thin shell theories namely donnell s and novozhilov s theories are used to calculate the elastic strain energy the formulation is also valid for orthotropic and symmetric cross ply laminated composite shells geometric imperfections are taken into account comparison of calculations to experimental and numerical results available in the literature is performed both empty and fluid filled shells are investigated by using a potential fluid model the nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis

a hydroelastic investigation of circular cylindrical shells containing flowing fluid with different end conditions abstract this paper presents the effects of different end conditions on the response behavior of thin circular cylindrical shell structures fully in contact with flowing fluid the investigated end conditions are as follows simply supported clamped clamped clamped simply supported and clamped free cantilever shell ends additionally the dynamic responses of a tapered cylindrical shell conveying flowing fluid and simply supported at its ends were investigated the method employed in this study is a hybrid method a boundary integral equation method for the calculation of the fluid structure interaction effects and a finite element method for the structural analysis in this study the mathematical model presented before b ugurlu a ergin a hydroelasticity method for vibrating structures containing and or submerged in flowing fluid journal of sound and vibration 290 2006 572 596 is extended by applying the direct boundary integral equation method and by using a higher order panel method linear distribution it should also be said that the method used in this study could be applied to any shape of cylindrical structure in contact with internal and or external flowing fluid in contrast to the studies found in the literature in the analysis of the linear fluid structure system it is assumed that the fluid is ideal i e inviscid incompressible and its motion is irrotational it is assumed that the flexible structure vibrates in its in vacuo modes when it is in contact with flowing fluid and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure the in vacuo dynamic properties of the dry structure are obtained by using a standard finite element software in the wet part of the analysis the wetted surface is idealized by using appropriate boundary elements referred to as hydrodynamic panels the fluid structure interaction forces are calculated in terms of the generalized added mass coefficients generalized coriolis fluid force coefficients and generalized centrifugal fluid force coefficients to demonstrate the applicability of the method and assess the influences of the flowing fluid and end support conditions on the dynamic response behavior of the shell structures the non dimensional eigenfrequencies and associated eigenmodes are presented as a function of the non dimensional axial flow velocity and they compare well with the analytical solutions found in the literature

nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow abstract the high imperfection sensitivity of cylindrical shells under static compressive axial loads is a well known phenomenon in structural stability on the other hand less is known of the influence of imperfections on the nonlinear vibrations of these shells under harmonic axial loads the aim of this work is to study the simultaneous influence of geometric imperfections and an axial fluid flow on the nonlinear vibrations and instabilities of simply supported circular cylindrical shells under axial load the fluid is assumed to be non viscous and incompressible and the flow to be isentropic and irrotational the behavior of the thin walled shell is modeled by donnell s nonlinear shallow shell equations it is subjected to a static uniform compressive axial pre load plus a harmonic axial load a low dimensional modal expansion which satisfies the relevant boundary and continuity conditions and takes into account all relevant nonlinear modal interactions observed in the past in the nonlinear vibrations of cylindrical shells with and without flow is used together with the galerkin method to derive a set of eight coupled nonlinear ordinary differential equations of motion which are in turn solved by the runge kutta method the shell is considered to be initially at rest in a position corresponding to a pre buckling configuration then a harmonic excitation is applied and conditions for parametric instability and dynamic snap through are sought the results clarify the marked influence of geometric imperfections and fluid flow on the dynamic stability boundaries bifurcations and basins of attraction

dynamic instability and chaos of empty and fluid filled circular cylindrical shells under periodic axial loads abstract in the present paper the dynamic stability of circular cylindrical shells subjected to static and dynamic axial loads is investigated both donnell s nonlinear shallow shell and sanders koiter shell theories have been applied to model finite amplitude static and dynamic deformations results are compared in order to evaluate the accuracy of these theories in predicting instability onset and post critical nonlinear response the effect of a contained fluid on the stability and the post critical behaviour is analyzed in detail geometric imperfections are considered and their influence on the dynamic instability and post critical behaviour is investigated chaotic dynamics of pre compressed shells is investigated by means of nonlinear time series techniques extracting correlation dimension and lyapunov exponents

uniform rectifiability calderon zygmund operators with odd kernel and quasiorthogonality in this paper we study some questions in connection with uniform rectifiability and the l boundedness of calderon zygmund operators we show that uniform rectifiability can be characterized in terms of some new adimensional coefficients which are related to the jones numbers we also use these new coefficients to prove that n dimensional calderonzygmund operators with odd kernel of type c2 are bounded in l if is an n dimensional uniformly rectifiable measure

polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions abstract large amplitude geometrically nonlinear forced vibrations of circular cylindrical shells with different boundary conditions are investigated the sanders koiter nonlinear shell theory which includes in plane inertia is used to calculate the elastic strain energy the shell displacements longitudinal circumferential and radial are expanded by means of a double mixed series harmonic functions for the circumferential variable and three different formulations for the longitudinal variable these three different formulations are a chebyshev orthogonal polynomials b power polynomials and c trigonometric functions the same formulation is applied to study different boundary conditions results are presented for simply supported and clamped shells the analysis is performed in two steps first a liner analysis is performed to identify natural modes which are then used in the nonlinear analysis as generalized coordinates the lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations different expansions involving from 14 to 34 generalized coordinates associated with natural modes of both simply supported and clamped clamped shells are used to study the convergence of the solution the nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis numerical responses obtained in the spectral neighborhood of the lowest natural frequency are compared with results available in literature

position feedback global tracking control of el systems a state transformation approach the contribution of this paper is a dynamic position feedback global tracking controller for fully actuated euler lagrange el systems the properties we show for the closed loop system are uniform stability and exponential convergence global in the initial tracking errors and semiglobal in the initial estimation errors the novelty of our approach is that our observer and control design are based on a new model for el systems which is linear in the immeasurable velocities this model is shown to fit robot manipulators we also provide some simulation results

nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow abstract in the present study the geometrically nonlinear vibrations of circular cylindrical shells subjected to internal fluid flow and to a radial harmonic excitation in the spectral neighbourhood of one of the lowest frequency modes are investigated for different flow velocities the shell is modelled by donnell s nonlinear shell theory retaining in plane inertia and geometric imperfections the fluid is modelled as a potential flow with the addition of unsteady viscous terms obtained by using the time averaged navier stokes equations a harmonic concentrated force is applied at mid length of the shell acting in the radial direction the shell is considered to be immersed in an external confined quiescent liquid and to contain a fluid flow in order to reproduce conditions in previous water tunnel experiments for the same reason complex boundary conditions are applied at the shell ends simulating conditions intermediate between clamped and simply supported ends numerical results obtained by using pseudo arclength continuation methods and bifurcation analysis show the nonlinear response at different flow velocities for i a fixed excitation amplitude and variable excitation frequency and ii fixed excitation frequency by varying the excitation amplitude bifurcation diagrams of poincare maps obtained from direct time integration are presented as well as the maximum lyapunov exponent in order to classify the system dynamics in particular periodic quasi periodic sub harmonic and chaotic responses have been detected the full spectrum of the lyapunov exponents and the lyapunov dimension have been calculated for the chaotic response they reveal the occurrence of large dimension hyperchaos

nonlinear dynamics and stability of cantilevered circular cylindrical shells conveying fluid abstract in this paper the nonlinear dynamics of thin circular cylindrical shells with clamped free boundary conditions subjected to axial internal flow is theoretically analyzed for the first time the nonlinearity is geometric and is related to the large deformation of the structure the nonlinear model of the shell is based on the flugge shell theory in this model in plane inertia terms and all the nonlinear terms due to the mid surface stretching are retained the fluid is considered to be inviscid and incompressible and its modelling is based on linearized potential flow theory the fluid behaviour beyond the free end of the shell is described by an outflow model which characterizes the fluid boundary condition at the free end of the shell at the clamped end however it is assumed that the fluid remains unperturbed the fourier transform method is used to solve the governing equations for the fluid and to obtain the hydrodynamic forces the extended hamilton principle is utilized to formulate the coupled fluid structure system and a direct approach is employed to discretize the space domain of the problem the resulting coupled nonlinear odes are integrated numerically and bifurcation analyses are performed using the auto software results indicate that the shell loses stability through a supercritical hopf bifurcation giving rise to a stable periodic motion limit cycle the amplitude of this oscillation grows with flow velocity until it loses stability to nonperiodic oscillatory motion namely quasiperiodic and chaotic oscillation the values of the critical flow velocities for various length to radius ratios obtained by nonlinear theory agree well with available experimental data

non linear dynamics and stability of circular cylindrical shells containing flowing fluid part i stability abstract the study presented is an investigation of the non linear dynamics and stability of simply supported circular cylindrical shells containing inviscid incompressible fluid flow non linearities due to large amplitude shell motion are considered by using the non linear donnell s shallow shell theory with account taken of the effect of viscous structural damping linear potential flow theory is applied to describe the fluid structure interaction the system is discretiszd by galerkin s method and is investigated by using a model involving seven degrees of freedom allowing for travelling wave response of the shell and shell axisymmetric contraction two different boundary conditions are applied to the fluid flow beyond the shell corresponding to i infinite baffles rigid extensions of the shell and ii connection with a flexible wall of infinite extent in the longitudinal direction permitting solution by separation of variables they give two different kinds of dynamical behaviour of the system as a consequence of the fact that axisymmetric contraction responsible for the softening non linear dynamical behaviour of shells is not allowed if the fluid flow beyond the shell is constrained by rigid baffles results show that the system loses stability by divergence

hidden symmetry concepts in the elastic buckling of axially loaded cylinders abstract the recognized harmonic buckling modes for the elastic axially loaded cylinder are by nature symmetric equal and opposite amplitudes giving equal energy levels on the other hand in combination they account for considerable asymmetry inwards deflection being fundamentally different from outwards this asymmetry is also apparent in the underlying differential equations and in the final large deflection yoshimura pattern taking the view that underlying symmetries are closely linked to the form of bifurcation experienced on buckling and hence to the gross instability of the phenomenon the paper thus explores a classic problem in a new light the wellknown donnell equations are first employed the analysis being neatly written in terms of the two variables radial displacement w and stress function an extension is then presented derived from the full strain displacement equations appropriate to genuinely large deflections this makes use of a suite of computer programs written for a small micro which handle the required manipulations of multiplication and integration of harmonic functions in algebraic rather than numerical fashion

square functions and uniform rectifiability speakers 1 vasilis chousionis university of helsinki finland square functions and uniform rectifiability 2 leonardo colzani universita degli studi di milano italy localization and convergence of fourier series and integrals 3 javier duoandikoetxea universidad del pais vasco euskal herriko unibertsitatea spain a comparison of the characterizations of a 4 bruno franchi universita degli studi di bologna italy differential forms in heisenberg groups and div curl systems 5 gustavo garrigos universidad de murcia spain maximal functions weights and convergence to initial data of certain poisson equations 6 jose ma ia martell icmat universidad autonoma de madrid spain the dirichlet problem for elliptic systems in the upper half space 7 alessio martini christian albrechts universitat zu kiel germany hypoelliptic operators and sharp multiplier theorems 8 joan mateu universitat autonoma de barcelona spain euler equation and vortex patches 9 carlos perez universidad de sevilla spain around a conjecture of e sawyer for the hilbert transform and weights 10 ezequiel rela universidad de sevilla spain optimality of weighted estimates without examples

a study on the dynamic stability of a cylindrical shell conveying a pulsatile flow of hot fluid abstract the flow of hot fluid having a harmonic component superposed on the mean flow velocity is considered flowing through an insulated cylindrical shell the cylindrical shell will be subjected to thermal load due to the flow of hot fluid the semi analytical finite element forms the basis for modelling the structural continuum under the influence of temperature and the flowing fluid the fluid flowing through the cylindrical shell is incompressible and linear potential flow theory is used to formulate the fluid domain bernoulli s principle and impermeability conditions of the fluid are the basis for a coupled fluid structure interaction analysis model reduction technique in conjunction with the fourth order runge kutta method using gill s coefficient is adopted to compute the state transition matrix which provides the stability information of the periodic system the results of the theoretical studies are presented related to instability regions due to a pulsatile flow of hot fluid through a cylindrical shell hot fluid at various magnitude of constant temperature limited by the critical thermal buckling temperature is considered in the study the effect of fluid temperature and excitation parameter on the behavior of dynamic instability of the system is examined

nonlinear supersonic flutter of circular cylindrical shells the aeroelastic stability of simply supported circular cylindrical shells in supersonic flow is investigated nonlinearities caused by large amplitude shell motion are considered by using the donnell nonlinear shallow shell theory and the effect of viscous structural damping is taken into account two different in plane constraints are applied to the shell edges zero axial force and zero axial displacement the other boundary conditions are those for simply supported shells linear piston theory is applied to describe the fluid structure interaction by using two different formulations taking into account or neglecting the curvature correction term the system is discretized by galerkin projections and is investigated by using a model involving seven degrees of freedom allowing for traveling wave flutter of the shell and shell axisymmetric contraction results show that the system loses stability by standing wave flutter through supercritical bifurcation however traveling wave flutter appears with a very small increment of the freestream static pressure that is used as the bifurcation parameter a very good agreement between theoretical and existing experimental data has been found for flutter amplitudes the influence of internal static pressure has also been studied

low dimensional models for the nonlinear vibration analysis of cylindrical shells based on a perturbation procedure and proper orthogonal decomposition in formulating mathematical models for dynamical systems obtaining a high degree of qualitative correctness i e predictive capability may not be the only objective the model must be useful for its intended application and models of reduced complexity are attractive in many cases where time consuming numerical procedures are required this paper discusses the derivation of discrete low dimensional models for the nonlinear vibration analysis of thin cylindrical shells in order to understand the peculiarities inherent to this class of structural problems the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed this choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads geometric nonlinearities due to finite amplitude shell motions are considered by using donnell s nonlinear shallow shell theory a perturbation procedure validated in previous studies is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the galerkin method using modal expansions for the displacements that

chaotic vibrations of circular cylindrical shells galerkin versus reduced order models via the proper orthogonal decomposition method abstract the geometric nonlinear response of a water filled simply supported circular cylindrical shell to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency is investigated the response is investigated for a fixed excitation frequency by using the excitation amplitude as bifurcation parameter for a wide range of variation bifurcation diagrams of poincare maps obtained from direct time integration and calculation of the lyapunov exponents and lyapunov dimension have been used to study the system by increasing the excitation amplitude the response undergoes i a period doubling bifurcation ii subharmonic response iii quasi periodic response and iv chaotic behaviour with up to 16 positive lyapunov exponents hyperchaos the model is based on donnell s nonlinear shallow shell theory and the reference solution is obtained by the galerkin method the proper orthogonal decomposition pod method is used to extract proper orthogonal modes that describe the system behaviour from time series response data these time series have been obtained via the conventional galerkin approach using normal modes as a projection basis with an accurate model involving 16 degrees of freedom dofs validated in previous studies the pod method in conjunction with the galerkin approach permits to build a lower dimensional model as compared to those obtainable via the conventional galerkin approach periodic and quasi periodic response around the fundamental resonance for fixed excitation amplitude can be very successfully simulated with a 3 dof reduced order model however in the case of large variation of the excitation even a 5 dof reduced order model is not fully accurate results show that the pod methodology is not as robust as the galerkin method

stability and vibration of empty and fluid filled circular cylindrical shells under static and periodic axial loads abstract in the present study the dynamic stability of simply supported circular cylindrical shells subjected to dynamic axial loads is analysed geometric nonlinearities due to finite amplitude shell motion are considered by using the donnell s nonlinear shallow shell theory the effect of structural damping is taken into account a discretization method based on a series expansion involving a relatively large number of linear modes including axisymmetric and asymmetric modes and on the galerkin procedure is developed axisymmetric modes are included indeed they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position and in describing the axisymmetric deflection due to axial loads a finite length simply supported shell is considered the boundary conditions are satisfied including the contribution of external axial loads acting at the shell edges the effect of a contained liquid is investigated the linear dynamic stability and nonlinear response are analysed by using continuation techniques and direct simulations

a hydroelasticity method for vibrating structures containing and or submerged in flowing fluid this paper presents a method for investigating the dynamics of elastic structures containing and or submerged in flowing fluid the method presented is based on a boundary integral equation method in conjunction with the method of images in order to impose appropriate boundary condition on the fluid s free surface the method of analysis can be applied to any shape of cylindrical structure partially in contact with flowing fluid in the analysis of the linear fluid structure system it is assumed that the fluid is ideal i e inviscid incompressible and its motion is irrotational it is assumed that the flexible structure vibrates in its in vacuo eigenmodes when it is in contact with flowing fluid and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure the in vacuo dynamic properties of the dry structure are obtained by using a standard finite element software in the wet part of the analysis the wetted surface is idealized by using appropriate boundary elements referred to as hydrodynamic panels the fluid structure interaction effects are calculated in terms of the generalized added mass coefficients generalized coriolis fluid force coefficients and generalized centrifugal fluid force coefficients in order to demonstrate the applicability of the proposed method a circular cylindrical shell simply supported at both ends was adopted for the calculations the cylindrical shell was considered separately with rigid and flexible extensions at its ends to assess the influence of flowing fluid on the dynamic behavior of the shell structure the non dimensional eigenfrequencies and associated eigenmodes are presented as a function of the non dimensional fluid velocity the predictions compare well with available analytical calculations found in the literature

free boundary regularity for harmonic measures and poisson kernels one of the basic aims of this paper is to study the relationship between the geometry of hypersurface like subsets of euclidean space and the properties of the measures they support in this context we show that certain doubling properties of a measure determine the geometry of its support a radon measure is said to be doubling with constant c if c times the measure of the ball of radius r centered on the support is greater than the measure of the ball of radius 2r and the same center we prove that if the doubling constant of a measure on r n 1 is close to the doubling constant of the ndimensional lebesgue measure then its support is well approximated by ndimensional a ne spaces provided that the support is relatively at to start with primarily we consider sets which are boundaries of domains in r n 1 the n dimensional hausdorfi measure may not be deflned on the boundary of a domain in r n 1 thus we turn our attention to the harmonic measure which is well behaved under minor assumptions see section 3 we obtain a new characterization of locally at domains in terms of the doubling properties of their harmonic measure see section 3 along these lines we investigate how the weak regularity of the poisson kernel of a domain determines the geometry of its boundary sections 5 and 6 pursue this goal as in alt and cafiarelli s work see ac c1 c2 and also jerison s j in both cases the goal is to prove that under the appropriate technical conditions at at points of the boundary the oscillation of the poisson kernel controls the oscillation of the unit normal vector the difierence between our work and the work in ac is that we measure the oscillation in an integral sense bmo estimates

wasserstein distance and the rectifiability of doubling measures part i let mu be a doubling measure in mathbb r n we investigate quantitative relations between the rectifiability of mu and its distance to flat measures more precisely for x in the support sigma of mu and r 0 we introduce a number alpha x r in 0 1 that measures in terms of a variant of the l 1 wasserstein distance the minimal distance between the restriction of mu to b x r and a multiple of the lebesgue measure on an affine subspace that meets b x r 2 we show that the set of points of sigma where int 0 1 alpha x r dr over r infty can be decomposed into rectifiable pieces of various dimensions we obtain additional control on the pieces and the size of mu when we assume that some carleson measure estimates hold

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

rectifiable sets and the traveling salesman problem let k c c be a bounded set in this paper we shall give a simple necessary and sufficient condit ion for k to lie in a rectifiable curve we say that a set is a rectifiable curve if it is the image of a finite interval under a lipschitz mapping recall that for a connected set f c c f is a rectifiable curve not necessarily simple if and only if l f where l denotes one dimensional hausdorff measure this classical result follows from the fact that on any finite graph there is a tour which covers the entire graph and which crosses each edge but not necessarily each vertex at most twice if k is a finite set then we are essentially reduced to the classical traveling salesman problem tsp compute the length of the shortest hami l ton ian cycle which hits all points of k this is the same up to a constant multiple as asking for the inf imum of l f where f is a curve k c f such a f is called a spanning tree in tsp theory for infinite sets k we cannot hope in general to have k be a subset of a jordan curve what we should therefore look at is connected sets which conta in k let fmi n be the shortest minimal spanning tree then we cannot possibly solve our problem for sets k of infinite cardinality if we cannot find f i f c o fmin for any finite set k here and throughout the paper c co c1 c o etc denote various universal constants while there are several algorithms for computing l fml these algorithms work for finite graphs satisfying the triangle inequality and do not use the euclidean properties of k see 13 for an excellent discussion of some of these algorithms therefore these methods cannot solve our problem for general infinite k we present a method which is a minor modification of a well known algorithm farthest insert ion see 13 which yields a f with i f c o l fmi the farthest insert ion algorithm has been extensively studied with large numerical calculations on computers and is experimentally good in the sense that the f produced satisfy i f c o l f i for all examples which have

theory and experiments for large amplitude vibrations of empty and fluid filled circular cylindrical shells with imperfections abstract the large amplitude response of perfect and imperfect simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated donnell s non linear shallow shell theory is used and the solution is obtained by the galerkin method several expansions involving 16 or more natural modes of the shell are used the boundary conditions on the radial displacement and the continuity of circumferential displacement are exactly satisfied the effect of internal quiescent incompressible and inviscid fluid is investigated the non linear equations of motion are studied by using a code based on the arclength continuation method a series of accurate experiments on forced vibrations of an empty and water filled stainless steel shell have been performed several modes have been intensively investigated for different vibration amplitudes a closed loop control of the force excitation has been used the actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model several interesting non linear phenomena have been experimentally observed and numerically reproduced such as softening type non linearity different types of travelling wave response in the proximity of resonances interaction among modes with different numbers of circumferential waves and amplitude modulated response for all the modes investigated the theoretical and experimental results are in strong agreement

nonlinear vibrations of clamped free circular cylindrical shells abstract only experimental studies are available on large amplitude vibrations of clamped free shells in the present study large amplitude nonlinear vibrations of clamped free circular cylindrical shell are numerically investigated for the first time shells with perfect and imperfect shape are studied the sanders koiter nonlinear shell theory is used to calculate the elastic strain energy shell displacement fields longitudinal circumferential and radial are expanded by means of a double mixed series i e harmonic functions for the circumferential variable and chebyshev polynomials for the longitudinal variable all boundary conditions are satisfied the system is discretized by using natural modes of the shell and lagrange equations by an energy approach retaining damping through rayleigh s dissipation function different expansions involving from 18 to 52 generalized coordinates are used to study the convergence of the solution the nonlinear equations of motion are numerically studied by using arclength continuation method and bifurcation analysis numerical responses to harmonic radial excitation in the spectral neighborhood of the lowest natural frequency are compared with experimental results available in literature the effect of geometric imperfections and excitation amplitude are numerically investigated and fully explained

technical communique global output feedback tracking control for a class of lagrangian systems the problem of global tracking control without velocity measurement of the so called euler lagrange systems has been paid a lot of attention for the past several years in this note a nice property of one degree of freedom euler lagrange systems is highlighted which in particular allows us to obtain a new solution to the problem of tracking control for this class of systems the solution is under the form of a linear like observer based controller which gives fairly good results as illustrated in the simulation the method can be generalized to any system having the same property

a comparison of shell theories for large amplitude vibrations of circular cylindrical shells lagrangian approach abstract large amplitude geometrically non linear vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated the lagrange equations of motion are obtained by an energy approach retaining damping through rayleigh s dissipation function four different non linear thin shell theories namely donnell s sanders koiter flugge lur e byrne and novozhilov s theories which neglect rotary inertia and shear deformation are used to calculate the elastic strain energy the formulation is also valid for orthotropic and symmetric cross ply laminated composite shells the large amplitude response of perfect and imperfect simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories numerical responses obtained by using these four non linear shell theories are also compared to results obtained by using the donnell s non linear shallow shell equation of motion a validation of calculations by comparison with experimental results is also performed both empty and fluid filled shells are investigated by using a potential fluid model the effects of radial pressure and axial load are also studied boundary conditions for simply supported shells are exactly satisfied different expansions involving from 14 to 48 generalized co ordinates associated with natural modes of simply supported shells are used the non linear equations of motion are studied by using a code based on an arclength continuation method allowing bifurcation analysis

non linear vibration analysis of fluid filled cylindrical shells abstract a theoretical analysis is presented for determining the elastic non linear vibrations of a prestressed thin walled cylindrical shell filled with an ideal fluid for the vibrations of the shell itself the dynamic version of the sanders non linear equations for the case of moderately small rotations is employed modal expansions are used for the displacements of the shell middle surface that are required to satisfy the classical simply supported boundary conditions and the circumferential periodicity condition the fluid is taken as non viscous and incompressible and the coupling between the deformable shell and this medium is taken into account the velocity potential is expanded in terms of harmonic functions which satisfy the laplace equation term by term the galerkin method is used to reduce the problem to a system of coupled algebraic non linear equations for the modal amplitudes solutions are presented to show the effects of fluid and shell parameters on the non linear vibrations of the shell

semi analytical shape functions in the finite element analysis of rectangular plates this paper presents a method for the dynamic analysis of a thin elastic isotropic rectangular plate the method is a hybrid of finite element theory and classical thin plate theory the displacement functions are derived from sanders thin shell equations and are expanded in power series expressions for mass and stiffness are determined by precise analytical integration the free vibrations of rectangular plates with various boundary conditions are studied by following this method the results obtained reveal that the frequencies calculated in this way are in good agreement with those obtained by others

a class of globally convergent velocity observers for robotic manipulators we present a method for global estimation of joint velocities in rigid manipulators a class of velocity observers with smooth dynamics are introduced whose structure depend on freely selectable functions and gains giving the flexibility of achieving multiple design objectives at the same time unlike most methods no a priori knowledge of an upper bound for velocity magnitude is used an adaptive version of the observer is also presented to handle a class of structured uncertainties in manipulator model simulation example illustrates low noise sensitivity of the globally convergent observer in comparison with semi globally convergent observers

non linear dynamics and stability of circular cylindrical shells containing flowing fluid part ii large amplitude vibrations without flow abstract the non linear response of empty and fluid filled circular cylindrical shells to harmonic excitations is investigated both modal and point excitations have been considered the model is suitable to study simply supported shells with and without axial constraints donnell s non linear shallow shell theory is used the boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied the radial deflection of the shell is expanded by using a basis of seven linear modes the effect of internal quiescent incompressible and inviscid fluid is investigated the equations of motion obtained in part i of this study are studied by using a code based on the collocation method the validation of the present model is obtained by comparison with other authoritative results the effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated clarifying questions open for a long time the results show the occurrence of travelling wave response in the proximity of the resonance frequency the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half wave and limit cycle responses modes with two longitudinal half waves are also investigated

non linear dynamic analysis of orthotropic open cylindrical shells subjected to a flowing fluid abstract a theory is presented to predict the influence of non linearities associated with the wall of the shell and with the fluid flow on the dynamics of elastic thin orthotropic and non uniform open cylindrical shells submerged and subjected simultaneously to an internal and external fluid the open shells are assumed to be freely simply supported along their curved edges and to have arbitrary straight edge boundary conditions the method developed is a hybrid of thin shell theory fluid theory and the finite element method the solution is divided into four parts in part one the displacement functions are obtained from sander s linear shell theory and the mass and linear stiffness matrices for the empty shell are obtained by the finite element procedure in part two the modal coefficients derived from the sanders koiter non linear theory of thin shells are obtained for these displacement functions expressions for the second and third order non linear stiffness matrices of the empty shell are then determined through the finite element method in part three a fluid finite element is developed the model requires the use of a linear operator for the velocity potential and a linear boundary condition of impermeability with the non linear dynamic pressure we develop in the fourth part three non linear matrices for the fluid the non linear equation of motion is then solved by the fourth order runge kutta numerical method the linear and non linear natural frequency variations are determined as a function of shell amplitudes for different cases

on the uniform rectifiability of ad regular measures with bounded riesz transform operator the case of codimension 1 we prove that if is a d dimensional ahlfors david regular measure in mathbb r d 1 then the boundedness of the d dimensional riesz transform in l2 implies that the non baup david semmes cells form a carleson family combined with earlier results of david and semmes this yields the uniform rectifiability of

new class of control laws for robotic manipulators part 1 non adaptive case a new class of exponentially stabilizing control laws for joint level control of robot arms is introduced it has recently been recognized that the non linear dynamics associated with robotic manip

natural vibrations and stability of shells of revolution interacting with an internal fluid flow abstract a finite element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory the fluid behavior is described using the perturbed velocity potential the shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized bernoulli equation for calculation of hydrodynamic pressure acting on the shell the problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements for cylindrical shells the results of numerical simulations are compared with recently published experimental analytical and numerical data the paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential the investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type