calculating the forced response of two dimensional homogeneous media using the wave and finite element method abstract the forced response of two dimensional infinite homogenous media subjected to time harmonic loading is treated the approach starts with the wave and the finite element wfe method where a small segment of a homogeneous medium is modelled using commercial or in house finite element fe packages the approach is equally applicable to periodic structures with a periodic cell being modelled this relatively small model is then used along with periodicity conditions to formulate an eigenvalue problem whose solution yields the wave characteristics of the whole medium the eigenvalue problem involves the excitation frequency and the wavenumbers or propagation constants in the two directions the wave characteristics of the medium are then used to obtain the response of the medium to a convected harmonic pressure chp since the fourier transform of a general two dimensional excitation is a linear combination of chps the response to a general excitation is a linear combination of the responses to chps thus the response of a two dimensional medium to a general excitation can be obtained by evaluating an inverse fourier transform this is a double integral one of which is evaluated analytically using contour integration and the residue theorem the other integral can be evaluated numerically hence the approach presented herein enables the response of an infinite two dimensional or periodic medium to an arbitrary load to be computed via a modelling a small segment of the medium using standard fe methods and post processing its model to obtain the wave characteristics b formulating the fourier transform of the response to a general loading and c computing the inverse of the fourier transform semi analytically via contour integration and the residue theorem followed by a numerical integration to find the response at any point in the medium numerical examples are presented to illustrate the approach

solitary shock waves and other travelling waves in a general compressible hyperelastic rod in the literature it has been conjectured that solitary shock waves can arise in incompressible hyperelastic rods recently it has been shown that this conjecture is true one might guess that when compressibility is taken into account such a wave which is both a solitary wave and a shock wave can still arise one of the aims of this paper is to show the existence of this interesting type of wave in general compressible hyperelastic rods and provide an analytical description it is difficult to directly tackle the fully nonlinear rod equations here by using a non dimensionalization process and the reductive perturbation technique we derive a new type of nonlinear dispersive equation as the model equation we then focus on the travelling wave solutions of this new equation as a result we obtain a system of ordinary differential equations an important feature of this system is that there is a vertical singular line in the phase plane which leads to the appearance of shock waves by considering the equilibrium points and their relative positions to the singular line we are able to determine all qualitatively different phase planes those paths in phase planes which represent physically acceptable solutions are discussed one by one it turns out that there is a variety of travelling waves including solitary shock waves solitary waves periodic shock waves etc analytical expressions for all these waves are obtained a new phenomenon is also found a solitary wave can suddenly change into a periodic wave with finite period in dynamical systems this represents a homoclinic orbit suddenly changing into a closed orbit to the authors9 knowledge such a bifurcation has not been found in any other dynamical systems

vibroacoustics of the piano soundboard non linearity and modal properties in the low and mid frequency ranges abstract the piano soundboard transforms the string vibration into sound and therefore its vibrations are of primary importance for the sound characteristics of the instrument an original vibro acoustical method is presented to isolate the soundboard nonlinearity from that of the exciting device here a loudspeaker and to measure it the nonlinear part of the soundboard response to an external excitation is quantitatively estimated for the first time at 40 db below the linear part at the ff nuance given this essentially linear response a modal identification is performed up to 3 khz by means of a novel high resolution modal analysis technique k ege x boutillon b david high resolution modal analysis journal of sound and vibration 325 4 5 2009 852 869 modal dampings which so far were unknown for the piano in this frequency range are determined in the mid frequency domain where fft based methods fail to evaluate them with an acceptable precision they turn out to be close to those imposed by wood a finite element modelling of the soundboard is also presented the low order modal shapes and the comparison between the corresponding experimental and numerical modal frequencies suggest that the boundary conditions can be considered as blocked except at very low frequencies the frequency dependency of the estimated modal densities and the observation of modal shapes reveal two well separated regimes below 1 khz the soundboard vibrates more or less like a homogeneous plate above that limit the structural waves are confined by ribs as already noticed by several authors and localised in restricted areas one or a few inter rib spaces presumably due to a slightly irregular spacing of the ribs across the soundboard

dynamic analysis of space frames the method of reverberation ray matrix and the orthogonality of normal modes the formulation of reverberation ray matrix analysis has been proposed to study wave propagation in planar frames it is applied here to modal analysis of complex three dimensional framed structures optionally with lumped masses and or elastic supports furthermore by means of betti s reciprocity theorem orthogonal conditions are established for different natural modes and hence transient response analysis based on mode superposition is developed both the reverberation ray matrix analysis for free vibration and the mode superposition method for transient response are illustrated by numerical examples

on the lp formulation in measure spaces of optimal control problems for jump diffusions abstract in this short note we formulate a infinite horizon stochastic optimal control problem for jump diffusions of ito levy type as a lp problem in a measure space and prove that the optimal value functions of both problems coincide the main tools are the dual formulation of the lp primal problem which is strongly connected to the notion of sub solution of the partial integro differential equation of hamilton jacobi bellman type associated with the optimal control problem and the krylov regularization method for viscosity solutions

the treatment of forces in bloch analysis abstract in periodic lattice structures wave propagation on the infinite domain can be greatly simplified by invoking the floquet bloch theorem the theorem allows a system s degrees of freedom to be reduced to a small subset contained in a repeating unit cell the equations of motion governing this subset contain internal force terms which must be eliminated before establishing the eigenvalue problem for the dispersion relationships there are subtle issues with regard to the elimination of these forces which we address in this paper we demonstrate that for any two or three dimensional periodic lattice the internal forces vanish when acted upon by the linear transformation engendered by the degree of freedom reduction

minimizing infinite time horizon discounted cost with mean variance and bounded variation controls we consider an infinite time horizon discounted cost minimization problem for a class of ito processes the available controls are drift and diffusion coefficients and the added bounded variation process we show that the value function is twice continuously differentiable and derive an optimal policy which has feedback type drift and diffusion coefficients when the absolute value of the optimal drift grows faster than the running cost function the optimal bounded variation process is identically zero when it grows weaker than the running cost function optimal bounded variation process is a local time type process in this case we relate the control problem with an optimal stopping problem we also establish the abelian limit relations between the value functions of the discounted cost problem and the stationary problem

coupled tension torsion vibration of repetitive beam like structures equivalent continuum stiffness properties derived from the eigenanalysis of a single cell of a planar beam like repetitive structure have previously been employed within well known dynamic theories such as euler bernoulli and timoshenko for flexural vibration suitably modified to predict natural frequencies of vibration here the approach is applied to two structure types that exhibit tension torsion coupling the first is modelled on a nasa deployable structure with a cross section of equilateral triangular form but with asymmetric triangulation on the faces the second is a related more symmetric structure but with pre twist the simplest tension torsion dynamic theory due to di prima is employed and this is extended to more general end conditions this combined periodic structure substitute continuum approach provides excellent agreement with predictions from the finite element method especially for the lower modes of vibration typically agreement is within 1 for the lowest 8 10 natural frequencies for the longer 30 cell structures considered here the majority of these being torsional modes and within 1 for the lowest 4 5 modes for the shorter ten cell structures this level of accuracy is attainable so long as a single wavelength spans 2 3 cells of the repetitive structure

free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements this paper presents a formulation of an approximate spectral element for uniform and tapered rotating euler bernoulli beams the formulation takes into account the varying centrifugal force mass and bending stiffness the dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain where two different interpolating functions for the transverse displacement are used for the element formulation both free vibration and wave propagation analysis is performed using the formulated elements the studies show that the formulated element predicts results that compare well with the solution available in the literature at a fraction of the computational effort in addition for wave propagation analysis the element shows superior convergence

nonlinear optimal control via occupation measures and lmi relaxations we consider the class of nonlinear optimal control problems ocps with polynomial data i e the differential equation state and control constraints and cost are all described by polynomials and more generally for ocps with smooth data in addition state constraints as well as state and or action constraints are allowed we provide a simple hierarchy of lmi linear matrix inequality relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value under some convexity assumptions the sequence converges to the optimal value of the ocp preliminary results show that good approximations are obtained with few moments

an lp approach to dynamic programming principles for stochastic control problems with state constraints abstract we study a class of nonlinear stochastic control problems with semicontinuous cost and state constraints using a linear programming lp approach first we provide a primal linearized problem stated on an appropriate space of probability measures with support contained in the set of constraints this space is completely characterized by the coefficients of the control system second we prove a semigroup property for this set of probability measures appearing in the definition of the primal value function this leads to dynamic programming principles for control problems under state constraints with general bounded costs a further linearized dpp is obtained for lower semicontinuous costs

computing moments of the exit time distribution for markov processes by linear programming we provide a new approach to the numerical computation of moments of the exit time distribution of markov processes the method relies on a linear programming formulation of a process exiting from a bounded domain the lp formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments the conditions the moments have to satisfy are derived directly from the generator of the markov process and are not based on some approximation of the process excellent software is readily available because the computations involve finite dimensional linear programs

a bounded variation control problem for diffusion processes we consider an infinite horizon discounted cost minimization problem for a one dimensional stochastic differential equation model the available control is an added bounded variation process the cost structure involves a running cost function and a proportional cost for the use of the control process the running cost function is not necessarily convex we obtain sufficient conditions to guarantee the optimality of the zero control also for unbounded cost functions we provide sufficient conditions which make our optimal state process a reflecting diffusion on a compact interval in both cases the value function is a c2 function for bounded cost functions under additional assumptions we obtain a complex optimal strategy which turned out to be a mixture of jumps and local time type processes in this case we show that the value function is only a c1 function and that it fails to be a c2 function we also discuss a related variance control problem

repetitive beam like structures distributed loading and intermediate support theory is developed for the elastostatic transfer matrix analysis of a repetitive beam like structure subject to point wise distributed loading with and without an intermediate support this complements previous work in which loading is applied at one end only and reacted at the other state vectors are expressed in terms of participation coefficients of the eigen and principal vectors leading to the simplest description of the evolution of nodal displacement and force components as one moves along the structure in terms of powers of the jordan canonical form inaccuracy due to ill conditioning is explained in terms of powers of greater than unity eigenvalues

a separation principle for partially observed control of singular stochastic processes abstract the analysis of partially observed stochastic control problems often replaces the unknown state process with its conditional distribution given the observations this technique rewrites the dynamics in terms of knowable processes whose costs coincide with the original processes this paper considers stochastic processes having singular behavior and presents an approach which separates the determination of the optimal control from the task of estimating the conditional distribution of the unknown process it involves using a martingale problem characterization for the dynamics followed by a further characterization using occupation measures this final characterization forms the basis for an equivalent linear programming formulation of the problem over the space of occupation measures

transfer matrix analysis of the elastostatics of one dimensional repetitive structures transfer matrices are used widely for the dynamic analysis of engineering structures increasingly so for static analysis and are particularly useful in the treatment of repetitive structures for which in general the behaviour of a complete structure can be determined through the analysis of a single repeating cell together with boundary conditions if the structure is not of infinite extent for elastostatic analyses non unity eigenvalues of the transfer matrix of a repeating cell are the rates of decay of selfequilibrated loading as anticipated by saint venant s principle multiple unity eigenvalues pertain to the transmission of load e g tension or bending moment and equivalent homogenized continuum properties such as cross sectional area second moment of area and poisson s ratio can be determined from the associated eigen and principal vectors various disparate results the majority new others drawn from diverse sources are presented these include calculation of principal vectors using the moore penrose inverse bi and symplectic orthogonality and relationship with the reciprocal theorem restrictions on complex unity eigenvalues effect of cell left to right symmetry on both the stiffness and transfer matrices eigenvalue veering in the absence of translational symmetry and limitations on possible jordan canonical forms it is shown that only a repeating unity eigenvalue can lead to a non trivial jordan block form so degenerate decay modes cannot exist the present elastostatic analysis complements langley s langley 1996 proc r soc a 452 1631 1648 transfer matrix analysis of wave motion energetics

wave propagation in continuous periodic structures research contributions from southampton 1964 1995 abstract after brief reference to some early studies by other investigators this paper focuses mainly on methods developed at the university of southampton since 1964 to analyze and predict the free and forced wave motion in continuous periodic engineering structures beginning with receptance methods which have been applied to periodic beams and rib skin structures it continues with a method of direct solution of the wave equation this uses floquet s principle and has been applied to beams and quasi one dimensional periodic plates and cylindrical shells sample curves of the propagation and attenuation constants pertaining to these structures are presented a limited discussion of the transfer matrix then follows after which the method of space harmonics is introduced as the method best suited to the prediction of sound radiated from a vibrating periodic structure reviewed next are some theorems and variational principles relating to periodic structures which have been developed at southampton and which form a basis for finding natural frequencies of finite structures or for computing free and forced wave notion by energy methods this has led to the finite element method in its standard and hierarchical forms being used to study wave motion in genuine two dimensional and three dimensional structures examples of this work are shown the method of phased array receptance functions is then introduced as possibly the easiest way of setting up exact equations for the propagation constants of uniform quasi one dimensional periodic structures a summary is finally presented of the limited and early work performed at southampton on simple disordered periodic structures

dynamic response and wave propagation in plane trusses and frames the dynamics of planar frames and trusses is analyzed in terms of the propagation of axial longitudinal and flexural transverse stress waves being structural members the waves are multiscattered at the joints and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint the complex multireflected waves within the structure are evaluated in the frequency domain by a newly developed reverberation matrix which is formulated from scattering coefficients and propagating phase factors transient waves are then analyzed by fourier synthesis and evaluated by a fast fourier transform algorithm transient responses for the axial and bending strains in all structural members are calculated over a long duration for a model truss with rigid joints comparison to experimental data of the model truss under a step loading shows good agreement for the early as well as considerably long time responses

resonant frequency primitive waveforms and star waves in lattices for square and triangular lattices we have found a new line localized primitive waveform lpw existing at a resonant frequency in two dimensional 2d case the lpw represents a line of oscillating particles while the lattice outside this line remains at rest we show that a a single lpw does not conduct energy however a band consisting of two or more neighboring lpws is a conductor with the phase shift dependent energy flux velocity b any canonical sinusoidal wave consists of lpws in turn the lpw can be represented by a superposition of the sinusoidal waves these two types of waves are connected by the discrete fourier transform c there are two three lpw orientations for the square triangular lattice and this is why the sinusoidal wave group velocity orientation is piecewise constant at this frequency it coincides with the nearest lpw orientation d lpw can also exist at a lower frequency being localized at the lattice halfplane boundary further for 3d lattices plane localized waveforms are found to exist in a frequency region finally for the point harmonic excitation of 2d lattices we show that starlike waves develop with the rays in the lpw directions

passive vibration suppression of flexible space structures via optimal geometric redesign acomputationalframework is presented for the design of large flexible space structures with nonperiodicgeometries to achieve passive vibration suppression the present system combines an approximationmodel management framework ammf developed for evolutionary optimization algorithms eas with reduced basis approximate dynamic reanalysis techniques a coevolutionary genetic search strategy is employed to ensure that design changes during the optimization iterations lead to low rank perturbations of the structural system matrices for which thereduced basis methods give high quality approximations the k means algorithm is employed for cluster analysis of the population of designs to determine design points at which exact analysis should be carried out the fitness of the designs in an ea generation is then approximated using reduced basis models constructed around the points where exact analysis is carried out results are presented for the optimal design of a two dimensional cantilevered space structure to achieve passive vibration suppression it is shown that significant vibration isolation of the order of 50 db over a 100 hz bandwidth can be achieved further it is demonstrated that the ammf can potentially arrive at a better design compared to conventional approaches when a constraint is imposed on the computational budget available for optimization

asymptotic bifurcation solutions for compressions of a clamped nonlinearly elastic rectangle transition region and barrelling to a corner like profile in the two experiments by beatty and his coauthors on the compressions of elastic rectangles bars it was found that there is a transition region of the aspect ratio which separates buckling from b

eigenanalysis and continuum modelling of pre twisted repetitive beam like structures a repetitive pin jointed pre twisted structure is analysed using a state variable transfer matrix technique within a global coordinate system the transfer matrix is periodic but introduction of a local coordinate system rotating with nodal cross sections results in an autonomous transfer matrix for this floquet system eigenanalysis reveals four real unity eigenvalues indicating tension torsion coupling and equivalent continuum properties such as poisson s ratio cross sectional area torsion constant and the tension torsion coupling coefficient are determined a variety of real and complex near diagonal jordan decompositions are possible for the multiple eight complex unity eigenvalues and these are discussed in some detail analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment together with shear deformation in the perpendicular plane but no bending bending coupling the choice of a structure having an equilateral triangular cross section is thought responsible for this unexpected behaviour as the equivalent continuum second moments of area are equal about all cross sectional axes in addition an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling and possible causes are discussed

a geometrical characterization of multidimensional hausdorff polytopes with applications to exit time problems we present a formula for the corner points of the multidimensional hausdorff polytopes and show how this result can be used to improve linear programming models for computing e g moments of exit time distributions of diffusion processes specifically we compute the mean exit time of two dimensional brownian motion from the unit square as well as higher moments of the exit time of time space brownian motion i e the two dimensional process composed of a one dimensional wiener process and the time component from a rectangle the corner point formula is complemented by a convergence result which provides the analytical underpinning of the numerical method that we use

an abelian limit approach to a singular ergodic control problem we consider an ergodic stochastic control problem for a class of one dimensional ito processes where the available control is an added bounded variation process the corresponding infinite horizon discounted control problem was solved in a weerasinghe siam j control optim 44 2005 pp 389 417 here we show that as the discount factor approaches zero the optimal strategies derived in a weerasinghe siam j control optim 44 2005 pp 389 417 converge to an optimal strategy for the ergodic control problem under different assumptions two types of optimal strategies were derived also the abelian limit relationships among the ergodic control problem the infinite horizon discounted control problem and the finite time horizon control problem are established here a solution to a constrained optimization problem is obtained as an application

on sets of occupational measures generated by a deterministic control system on an infinite time horizon abstract we give a representation for the closed convex hull of the set of discounted occupational measures generated by control state trajectories of a deterministic control system we also investigate the limit behavior of the latter when the discount factor tends to zero and compare it with the limit behavior of the long run time average occupational measures set the novelty of our results is in that we allow the control set dependence on the state variables that make the results to be applicable to differential inclusions

an ergodic control problem for constrained diffusion processes existence of optimal markov control an ergodic control problem for a class of constrained diffusion processes is considered the goal is the almost sure minimization of long term cost per unit time the main result of the paper is that there exists an optimal markov control for the considered problem it is shown that under the assumption of regularity of the skorohod map and the assumption that the drift vector field takes values in a certain cone of stability the class of controlled diffusion processes considered have strong uniform in control stability properties the role of the boundary is critical in obtaining the stability and ergodic control results for the class of controlled constrained diffusion processes considered in this work since the domains are unbounded and the corresponding unconstrained diffusions are typically transient these stability properties are key in obtaining appropriate tightness estimates once these estimates are available the remaining work lies in identifying weak limits of a certain family of occupation measures in this regard an extension to the echeverria weiss kurtz characterization of invariant measures of markov processes to the case of constrained controlled processes considered in this paper is proved this characterization result is also crucially used in proving the compactness of the family of invariant measures of markov processes corresponding to all possible markov controls

linear programming formulation for optimal stopping problems optimal stopping problems for continuous time markov processes are shown to be equivalent to infinite dimensional linear programs over a space of pairs of measures under very general conditions the measures involved represent the joint distribution of the stopping time and stopping location and the occupation measure of the process until it is stopped these measures satisfy an identity for each function in the domain of the generator which is sufficient to characterize the stochastic process finite dimensional linear programs obtained using markov chain approximations are solved in two examples to illustrate the numerical accuracy of the linear programming formulation

bifurcation to a corner like formation in a slender nonlinearly elastic cylinder asymptotic solution and mechanism in this paper we study the corner like formation in a slender nonlinearly elastic cylinder due to compression mathematically this is a very challenging problem one needs to study the bifurcation of the nonlinear field equations complicated nonlinear partial differential equations and show that there is a bifurcation leading to a solution with a corner like profile we also aim to obtain the asymptotic expression for this post bifurcation solution as far as we know there is no available analytical method to obtain the post bifurcation solution of nonlinear partial differential equation s here we use a novel approach to tackle the present problem through a method of coupled series asymptotic expansions we manage to derive the normal form equation of the original nonlinear field equations which can be written as a singular ordinary differential equation ode system the vector field has a singularity at one point with welding end conditions the problem is reduced to study the boundary value problem of a singular ode system it seems that such a boundary value problem of a singular ode system was not formulated or studied before in the context of the present problem with the help of phase planes we manage to solve such a boundary value problem it turns out that there is a vertical singular line in phase planes which causes the bifurcation to a corner like solution the expression for this post bifurcation solution is also obtained from the analytical results obtained we reveal that the coupling effect of the material nonlinearity and geometrical size is the physical mechanism that causes the formation of a corner like profile

long term optimal investment strategies in the presence of adjustment costs we consider the problem of determining in a dynamical way the optimal capacity level of an investment project that operates within a random economic environment in particular we consider an investment project that yields payoff at a rate that depends on its installed capacity level and on a random economic indicator such as the price of the project s output commodity we model this economic indicator by means of a general one dimensional ergodic diffusion at any time the project s capacity level can be increased or decreased at given proportional costs the aim is to maximize an ergodic performance criterion that reflects the long term average payoff resulting from the project s management we solve this genuinely two dimensional stochastic control problem by constructing an explicit solution to an appropriate hamilton jacobi bellman equation and by fully characterizing an optimal investment strategy

higher order effective modeling of periodic heterogeneous beams ii derivation of the proper boundary conditions for the interior asymptotic solution abstract this paper constitutes the second part of a study devoted to the 1d modeling of beam like structures of arbitrary cross section with periodic properties along the axis in the first part the asymptotic expansion method has been described and the equations involving the successive terms of the outer solution have been given in particular it has been shown that neither the leading term nor the full outer solution are able to satisfy arbitrary prescribed edge data a specific study is thus necessary and it is presented in this paper the method used is the decay analysis initially proposed for homogeneous plates by gregory and wan j elast 14 1984 27 this approach consists in deriving the appropriate set of boundary conditions for the outer expansion solution for any arbitrary edge data stress displacement or mixed data these boundary conditions are obtained from the solution of canonical beam problems without computing any inner solution the method is illustrated through numerical examples on a lattice structure the results obtained prove the importance of a correct treatment of the edge effects in order that the inclusion of higher order terms in the beam model serves actually to increase the accuracy of the outer expansion solution

dynamics of complex truss type space structures a laboratory test was conducted to validate experimentally and to help establish the limits of the mbct approach the results show that the mbct method is a vital alternate technique for ground testing large flexible structures a three dimensional mast type truss structure has been successfully simulated

survey paper a partial history of the early development of continuous time nonlinear stochastic systems theory this article is a survey of the early development of selected areas in nonlinear continuous time stochastic control key developments in optimal control and the dynamic programming principle existence of optimal controls under complete and partial observations nonlinear filtering stochastic stability the stochastic maximum principle and ergodic control are discussed issues concerning wide bandwidth noise for stability modeling filtering and ergodic control are dealt with the focus is on the earlier work but many important topics are omitted for lack of space

on saint venant s principle in pin jointed frameworks numerical experiments performed by hoff 50 years ago on the application of saint venant s principle to frameworks are extended and his conclusions qualified guided by these results a general treatment is formulated employing a state variable approach this leads directly to an eigenvalue problem in which the decay rates are the eigenvalues of the cell transfer matrix unity eigenvalues correspond to the transmitting modes of rigid body displacement and the stress resultants of tension bending moment shearing force and twisting moment consideration of the associated eigenvectors and principal vectors gives exact values for the equivalent continuum beam properties of the framework such as equivalent cross sectional area poisson s ratio second moment of area shear coefficient and torsion constant

the torsion extension coupling in pretwisted elastic beams abstract an explicit asymptotic formula is derived for the untwist of a pretwisted elastic beam subjected to homogeneous extension or equivalently for the longitudinal contraction produced by a torsional moment it is based on an asymptotic expansion of the three dimensional equations of linear elasticity the general result consists of two terms one due to lengthwise variation of the warping of the cross sections and another due to local rotations from bending when the elastic center is not on the axis of pretwist the result supports some recent approximate theories for pretwisted elastic beams

pathwise stochastic optimal control this paper approaches optimal control problems for discrete time controlled markov processes by representing the value of the problem in a dual lagrangian form the value is expressed as an infimum over a family of lagrangian martingales of an expectation of a pathwise supremum of the objective adjusted by the lagrangian martingale term this representation opens up the possibility of numerical methods based on monte carlo simulation which may be advantageous in high dimensional problems or in problems with complicated constraints

natural frequencies of axial torsional coupled motion in springs and composite bars the natural frequencies corresponding to axial torsional extension twist coupled motion of a helical spring or the corresponding motion induced through material coupling in a composite bar are considered using an equivalent continuum approach closed form solution of the governing differential equations leads either to an exact dynamic stiffness matrix or to a number of exact relationships between the natural frequencies corresponding to coupled and uncoupled motion the latter relationships both guarantee that the wittrick williams root finding algorithm can still be used to converge on any required natural frequency despite any lack of reciprocity arising from differential coupling and for the case of symmetric material coupling coefficients enable their value to be determined precisely from experimental results a number of examples are then given to confirm the accuracy of the proposed theory and to indicate its range of application

existence of markov controls and characterization of optimal markov controls given a solution of a controlled martingale problem it is shown under general conditions that there exists a solution having markov controls which has the same cost as the original solution this result is then used to show that the original stochastic control problem is equivalent to a linear program over a space of measures under a variety of optimality criteria existence and characterization of optimal markov controls then follows an extension of echeverria s theorem characterizing stationary distributions for uncontrolled markov processes is obtained as a corollary in particular this extension covers diffusion processes with discontinuous drift and diffusion coefficients

the saint venant problem and principle in elasticity abstract the traditional semi inverse solution method of the saint venant problem and the saint venant principle which were described in the euclidian space under the lagrange system formulation are updated to be solved in the symplectic space under the conservative hamiltonian system thus the saint venant problem and the saint venant principle have been unified by the direct method it is proved in the present paper that all the saint venant solutions can be obtained directly via the zero eigenvalue solutions and all their jordan normal forms of the corresponding hamiltonian operator matrix and the saint venant principle corresponds to neglect of all the non zero eigenvalue solutions in which the non zero eigenvalue gives the decay rate

two armed restless bandits with imperfect information stochastic control and indexability we present a two armed bandit model of decision making under uncertainty where the expected return to investing in the risky arm increases when choosing that arm and decreases when choosing the safe arm these dynamics are natural in applications such as human capital development job search and occupational choice using new insights from stochastic control along with a monotonicity condition on the payoff dynamics we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with gittins index our result implies the indexability of a new class of restless bandit models

dynamic response analysis of truss type structural networks a wave propagation approach abstract a typical space structure is composed of piece wise periodic arrays of connected truss units these arrays can intersect each other and form multiple closed loops in this paper a detailed step by step numerical procedure is provided for computing the response of such a structure to external excitations the basic idea is to treat an array of connected truss units as a multi channel waveguide capable of transmitting several types of wave motions each waveguide or each junction where several waveguides intersect can be characterized by a wave scattering matrix which is composed of the transmission and reflection submatrices a reflection submatrix reverses the direction of incoming waves whereas a transmission submatrix permits the incoming waves to enter or to be directed to other waveguides by use of wave scattering matrices in the formulation the numerical computation always follows the directions of propagation of various waves thus numerical stability is assured since the amplitude of wave motion decays as it propagates along a path due to structural damping the numerical procedure described herein represents an extension of the author s previous works by 1 describing for the first time the dynamics of individual truss arrays in terms of scattering matrices 2 adopting a new bookkeeping system to accommodate more complicated configurations of structural networks and 3 developing an efficient procedure to eliminate step by step superfluous unknowns thus simplifying the calculation combination of the three advances makes it possible to treat for the first time such complicated configurations as multiple closed loops since the actual truss type construction is retained when obtaining the wave scattering matrices the procedure is considered more accurate than those based on substitution for truss construction of timoshenko beam elements application of the procedure is illustrated by an example

linear programming approach to deterministic infinite horizon optimal control problems with discounting we investigate relationships between the deterministic infinite time horizon optimal control problem with discounting in which the state trajectories remain in a given compact set y and a certain infinite dimensional linear programming idlp problem we introduce the problem dual with respect to this idlp problem and obtain some duality results we construct necessary and sufficient optimality conditions for the optimal control problem under consideration and we give a characterization of the viability kernel of y we also indicate how one can use finite dimensional approximations of the idlp problem and its dual for construction of near optimal feedback controls the construction is illustrated with a numerical example

duality in linear programming problems related to deterministic long run average problems of optimal control it has been established recently that under mild conditions deterministic long run average problems of optimal control are asymptotically equivalent to infinite dimensional linear programming problems lpps and that these lpps can be approximated by finite dimensional lpps in this paper we introduce the corresponding infinite and finite dimensional dual problems and study duality relationships we also investigate the possibility of using solutions of finite dimensional lpps and their duals for numerical construction of the optimal controls in periodic optimization problems the construction is illustrated with a numerical example

propagation of decaying waves in periodic and piecewise periodic structures of finite length abstract a new method is described for the analysis of long and complicated structures which are composed of spatially periodic units or sections of spatially periodic units the response of such a structure to external excitations is treated as a superposition of wave motions with account taken of the effects of wave reflection due to change in the construction pattern along the structure and boundary conditions since damping usually exists in a real structure a wave motion always decays as it propagates along the structure however this can cause numerical difficulties if the structure is rather long because a decaying wave appears as a growing wave in the opposite direction and since propagations in both directions must be accounted for in the analysis computational errors associated with the apparent growing waves also grow and the numerical results become meaningless in the proposed new scheme use is made of wave reflection and transmission matrices making it possible for all computations to proceed in the direction of wave propagation so that the results are always stable numerically furthermore the required computing time is greatly reduced in comparison with that of an all encompassing finite element analysis for the entire structure application of the new method is illustrated by examples

on the direct solution of wave propagation for repetitive structures abstract the direct method of solving the wave constants for a repetitive structure with given frequency is developed in this paper the analogy between structural mechanics and optimal control theory is applied the dynamic stiffness matrix approach is used to solve for the eigensolutions of wave propagation the weighted adjoint symplectic orthonormality relationship and the eigenvector expansion theorem are also established for this approach the symplectic eigenproblem is derived for skew symmetric matrices a cell triangular decomposition for skew symmetric matrices is introduced to reduce the generalized eigenproblem and the symplectic householder transformation is introduced to cell tri diagonalize the skew symmetric matrix to solve the eigenequation the problem of a wave impinging on the boundary is considered by the eigenvector expansion method which could also be applied to a wave scattering when passing over an abnormal part numerical examples show that resonance will occur for the localized vibration case

approximation of infinite dimensional linear programming problems which arise in stochastic control we study a general approximation scheme for infinite dimensional linear programming lp problems which arise naturally in stochastic control we prove that the optimal value of the approximating problems converges to the value of the original lp problem for the controls we show that if the approximating optimal controls converge the limiting control is an optimal control for the original lp problem as an application of this theory we present numerical approximations to the lp formulation of stochastic control problems in continuous time we study long term average and discounted control problems for the example for which the theoretical solution is known our approximation results are very accurate

on wave propagation in repetitive structures two forms of transfer matrix abstract two forms of dynamic transfer matrix are derived for a one dimensional beam like repetitive pin jointed structure with point masses located at nodal cross sections the displacement force transfer matrix g and the displacement displacement transfer matrix h similarity matrices are introduced to relate g and h together with their respective metrics symplectic orthogonality relationships for the eigenvectors of both g and h are derived together with relationships between their respective sets of eigenvectors new expressions for the group velocity are derived for repetitive structures of finite length natural frequency equations are derived employing both g and h including phase closure and the direct application of boundary end conditions besides an exposition of the theory some familiar but much new the focus of the present paper is on the relationships between the two forms of transfer matrix including their respective dis advantages numerical results together with further theory necessary for interpretation are presented in companion papers

phase transitions in a slender cylinder composed of an incompressible elastic material i asymptotic model equation we present reasons both experimental and mathematical for why it is important to consider the radial deformation thus the lateral traction free boundary conditions as well for phase transitions in a slender elastic cylinder one of the main purposes of this paper is to derive an asymptotic model equation which takes into account the radial deformation and satisfies the traction free boundary conditions up to the right order this is achieved from the three dimensional field equations through a novel approach that combines a series expansion and an asymptotic expansion an alternative approach based on whitham s approach well used in fluids is also given then we present some interesting analytic solutions for an infinite cylinder including those that seem to describe the structure of a phase boundary the nucleation process and the merge of two phase boundaries in particular by considering the energy distribution based on the nucleation solution it is revealed that the nucleation process is one of energy localizations concentrations and separation

work conjugacy between rotation dependent moments and finite rotations in this paper we investigate the work conjugacy between rotation dependent moments and finite rotation measures the methodology adopted consists of writing all the relevant quantities in terms of the rotation vector using expressions that remain exact in the finite rotation range through this procedure we show how i to identify work conjugate rotation dependent moments and rotation measures ii to derive a necessary condition for moment conservativeness and iii to obtain the general form of an isotropic conservative rotation dependent moment several moment and finite rotation definitions that have been used in the past are investigated and in particular it is shown that the various existing definitions for the so called semi tangential moments are distinct in the finite rotation range and that not all of them are conservative the tangent operator symmetry is discussed in the context of finite element analysis of conservative systems with rotational degrees of freedom adopting either an additive or a multiplicative update