random response of symmetric cross ply composite beams with arbitrary boundary conditions a generalized modal approach is presented to solve the equations of motion of a laminated composite beam obtained with a third order shear deformation theory the biorthonormal eigenfunctions of the differential equations expressed in the state form are used to decouple the equations to obtain these eigenfunctions for beams with any arbitrary beam boundary conditions a method is presented the solution obtained by this approach is used to calculate the beam response for spatially and temporally correlated random loads several sets of numerical results are presented to demonstrate the importance of shear deformations in the dynamic analysis of composite beams

weak stability of ricci expanders with positive curvature operator we prove the l infty stability of expanding gradient ricci solitons with positive curvature operator and quadratic curvature decay at infinity

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

in plane vibration of slightly curved laminated composite beams abstract a complete set of equations for the free and forced vibration analysis of laminated composite beams of shallow curvature is presented the beam is assumed to be vibrating in its plane these equations are shown to be consistent by variational derivation natural frequencies for simply supported curved beams are obtained by exact solutions the ritz method with algebraic polynomials is used to obtain approximate solutions for arbitrary boundary conditions natural frequencies for completely free and cantilevered curved beams are presented as examples extension bending coupling due to lamination is distinguished from that due to curvature effects of curvature material orthotropy and lamination sequence on the natural frequencies are studied

dynamical stability and instability of ricci flat metrics in this short article we improve the dynamical stability and instability results for ricci flat metrics under ricci flow proved by sesum duke math j 133 1 26 2006 and haslhofer calc var partial differ equ 45 481 504 2012 getting rid of the integrability assumption

on the ornstein uhlenbeck operator in spaces of continuous functions we study the realization of the ornstein uhlenbeck operator a in the space of the uniformly continuous and bounded functions in rn we prove that it generates a semigroup which is neither strongly continuous nor analytic but enjoys nice smoothing properties such properties are used to prove a schauder type theorem for the elliptic equation u au f

laplace s method for the laws of heat processes on loop spaces abstract in this paper we will consider laplace s method for a class of heat processes on loop spaces we will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the hessian at the point is non degenerate this kind of process was first introduced by p malliavin in 1990 for the loop group case and then gradually generalized by various authors our tool is the rough path theory of t lyons this technique was pioneered by s aida for finite dimensional processes in his unpublished paper

expanding solitons with non negative curvature operator coming out of cones we consider ricci flow of complete riemannian manifolds which have bounded non negative curvature operator non zero asymptotic volume ratio and no boundary we prove scale invariant estimates for these solutions using these estimates we show that there is a limit solution obtained by scaling down this solution at a fixed point in space this limit solution is an expanding soliton coming out of the asymptotic cone at infinity

semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space abstract we study a semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space key results are semiboundedness theorem of the schrodinger operator laplace type asymptotic formula and ims localization formula we also make a remark on the semiclassical problem of a schrodinger operator on a path space over a riemannian manifold

linear and dynamical stability of ricci flat metrics we can talk about two kinds of stability of the ricci flow at ricci flat metrics one of them is a linear stability defined with respect to perelman s functional f see 1 page 5 the other one is a dynamical stability and it refers to a convergence of a ricci flow starting at any metric in a neighborhood of a considered ricci flat metric we show that dynamical stability implies linear stability we also show that a linear stability together with the integrability assumption implies dynamical stability as a corollary we get a stability result for k3 surfaces part of which has been done in 11 corollary 4 15 theorem 4 16 our stability result applies to calabi yau manifolds as well

on uniqueness of tangent cones for einstein manifolds we show that for any ricci flat manifold with euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross section similarly for any noncollapsing limit of einstein manifolds with uniformly bounded einstein constants we show that local tangent cones are unique if one tangent cone has a smooth cross section

well posedness for the navier stokes equations where u is the velocity and p is the pressure it is well known that the navierstokes equations are locally well posed for smooth enough initial data as long as one imposes appropriate boundary conditions on the pressure at for instance it is easy to see see 9 for much more general results that if s n 2 then for any h initial data there exists a unique c 0 t h r local solution with a pressure p c 0 t h r in the sequel we consider solutions for less regular initial data this has to be understood in the sense that the map from the initial data to the solution extends continuously to rougher function spaces the question we are interested in is the global well posedness for small data and local well posedness for large data with respect to a certain space of

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

vibration and buckling of multilayered composite beams according to higher order deformation theories natural frequencies and buckling stresses of laminated composite beams are analyzed by taking into account the complete effects of transverse shear and normal stresses and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for laminated composite beams subjected to axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported laminated composite beam in order to ensure the accuracy of the present theory convergence properties of the first seven natural frequencies are examined in detail numerical results are compared with those of the published existing theories and fem solutions the modal displacement and stress distributions in the depth direction are obtained and plotted in figures the present global higher order approximate theories can predict the natural frequencies buckling stresses and interlaminar stresses of multilayered composite beams as accurately as three dimensional elasticity solutions

dynamic stiffness matrix of thin walled composite i beam with symmetric and arbitrary laminations abstract for the spatially coupled free vibration analysis of thin walled composite i beam with symmetric and arbitrary laminations the exact dynamic stiffness matrix based on the solution of the simultaneous ordinary differential equations is presented for this a general theory for the vibration analysis of composite beam with arbitrary lamination including the restrained warping torsion is developed by introducing vlasov s assumption next the equations of motion and force displacement relationships are derived from the energy principle and the first order of transformed simultaneous differential equations are constructed by using the displacement state vector consisting of 14 displacement parameters then explicit expressions for displacement parameters are derived and the exact dynamic stiffness matrix is determined using force displacement relationships in addition the finite element fe procedure based on hermitian interpolation polynomials is developed to verify the validity and the accuracy of this study the numerical solutions are presented and compared with analytical solutions the results from available references and the fe analysis using the thin walled hermitian beam elements particular emphasis is given in showing the phenomenon of vibrational mode change the effects of increase of the modulus and the bending twisting coupling stiffness for beams with various boundary conditions

precise asymptotics of certain wiener functionals abstract in this article we present a method for developing certain wiener integrals in an asymptotic expansion as the variance of the wiener goes to 0 the basic ideas are a combination of methods borrowed from the theory of large deviations together with techniques from the calculus of wiener space

equilibrium and modal analyses of rotating multibeam structures employing multiple reference frames a single reference frame is frequently employed to derive equations of motion in structural dynamic analysis for simple structures like a single beam and a single plate the method of employing a single reference frame usually provides well converged and accurate results for equilibrium and modal analyses however for structures having more general configurations such as multibeam structures use of a single reference frame often results in slow convergence and even erroneous analysis results in the present study a modeling method employing multiple reference frames for dynamic equilibrium and modal analyses of rotating structures is presented the superiority of the proposed modeling method over the single reference frame modeling method is verified with numerical examples

asymptotic expansions for the laplace approximations for ito functionals of brownian rough paths abstract in this paper we establish asymptotic expansions for the laplace approximations for ito functionals of brownian rough paths under the condition that the phase function has finitely many non degenerate minima our main tool is the banach space valued rough path theory of t lyons we use a large deviation principle and the stochastic taylor expansion with respect to the topology of the space of geometric rough paths this is a continuation of a series of papers by inahama y inahama laplace s method for the laws of heat processes on loop spaces j funct anal 232 2006 148 194 and by inahama and kawabi y inahama h kawabi large deviations for heat kernel measures on loop spaces via rough paths j london math soc 73 3 2006 797 816 y inahama h kawabi on asymptotics of certain banach space valued ito functionals of brownian rough paths in proceedings of the abel symposium 2005 stochastic analysis and applications a symposium in honor of kiyosi ito springer berlin in press available at http www abelprisen no no abelprisen deltagere 2005 html

vibration and buckling of deep beam columns on two parameter elastic foundations natural frequencies and buckling stresses of a deep beam column on two parameter elastic foundations are analyzed by taking into account the effect of shear deformation depth change the transverse displacement w can vary in the depth direction of beam columns and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for thin rectangular beam columns subjected to axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported deep elastic beam column in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling stress are examined in detail it is noted that the present approximate theories can predict the natural frequencies and buckling stress of deep beam columns on elastic foundations accurately compared with the timoshenko beam theory and the classical beam theory

thermo mechanical vibration of fgm sandwich beam under variable elastic foundations using differential quadrature method thermo mechanical vibration analysis of functionally graded fg beams and functionally graded sandwich fgsw beams are presented the functionally graded material fgm beams are considered to be resting on variable i winkler foundation and ii two parameter elastic foundation the material properties of these beams are assumed to be varying in the thickness direction the governing differential equations for beam vibration are being solved using the modified differential quadrature method mdqm the applied kinematic boundary conditions are implemented using the modified weighting coefficient matrix mwcm the weighting coefficients are generated from the chebyshev basis function present results for the vibration of isotropic beam with variable winkler foundation are in good agreement with those reported in the literature parametric study on the vibration response of fg beams and fgsw beams are being investigated these parameters include i temperature distributions ii power law index iii variable winkler foundation modulus iv two parameter elastic foundation modulus and v normalized core thickness of fgsw beams

free vibration and stability of laminated composite circular arches subjected to initial axial stress natural frequencies and buckling stresses of laminated composite circular arches subjected to initial axial stress are analyzed by taking into account the complete effects of transverse shear and normal stresses and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for laminated composite circular arches subjected to initial axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported circular arch in order to assure the accuracy of the present theory convergence properties of the first four natural frequencies are examined in detail numerical results are compared with those of the published existing theories the present global higher order approximate theories can predict the natural frequencies and buckling stresses of multilayered circular arches accurately with a small number of unknowns

on the shape of the ground state eigenvalue density of a random hill s equation consider the hill s operator q d2 dx2 q x in which q x 0 x 1 is a white noise denote by f the probability density function of 0 q the negative of the ground state eigenvalue at we prove the detailed asymptotics as this result is based on a precise laplace analysis of a functional integral representation for f established by s cambronero and h p mckean in 5 2005 wiley periodicals inc

exact and approximate solutions and variational principles for stochastic shear beams under deterministic loading probabilistic response of shear beams with stochastic flexibility and subjected to deterministic static loads is studied in this paper the differential equations governing the probabilistic responses as well as the variational principles for the probabilistic responses are formulated apparently for the first time new exact solutions are also derived for specific cases stochastic versions of galerkin and rayleigh ritz method are then applied to obtain approximate solutions when exact solution is unfeasible to derive both the exact and the approximate solutions possess a unique characteristic they are applicable to any value of the coefficient of variation previous investigations were unable to capture this remarkable characteristic

free vibration and stability of thin elastic beams subjected to axial forces abstract natural frequencies and buckling loads of a simply supported beam with small length to depth ratio and sufficiently thin rectangular cross sections subjected to initial axial tensile and or compressive forces are analyzed by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimentional higher order beam theory for thin rectangular beams is derived through hamilton s principle several sets of truncated approximate theories which can take into account the effects of both shear deformations with depth changes and rotary inertia are applied to solve the eigenvalue problem of a thin elastic beam the navier solution procedure is used to satisfy the boundary conditions of a simply supported thin rectangular beam in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling load for the axial and bending problems of thin beams are examined in detail it is noticed that the present approximate theories can predict the natural frequencies and buckling loads of thin beams with small length to depth ratio more accurately than other refined higher order theories and the classical beam theory

deforming the metric on complete riemannian manifolds soit m g ij x une variete de riemann a n dimensions complete non compacte de tenseur de complexe riemannien r ijkl satisfaisant r ijkl 2 k 0 sur m ou 0 0 dependant seulement de n et de k 0 telle que l equation d evolution g ij x t t 2r ij x t sur m g ij x o g ij x x m ait une solution lisse g ij x t 0 pour un temps court 0 t t u k 0 et satisfait l estimation suivante pour un entier m 0 il existe des constantes c m 0 dependant seulement de n m et k 0 telles que sup x m v m r ijkl x t 2 c m t m 0 t t u k 0

bending vibration and buckling of simply supported thick multilayered orthotropic plates an evaluation of a new displacement model abstract based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously the non linear in the von karman sense equations of motion for thick multilayered orthotropic plates are developed successively the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates in order to assess the accuracy of the proposed theory the sample problem of the bending free undamped vibration and buckling of a three layered symmetric cross ply square plate simply supported on all edges is investigated for purposes of comparison numerical results from the exact elasticity theory the classical lamination kirchhoff theory and the shear deformation theory timoshenko and mindlin with three different values of the shear correction factor are also presented it is found that the proposed approach is very efficient in predicting the global responses deflection natural frequencies and buckling loads of thick multilayered plates and models effects such as the distortion of the deformed normals not attainable from the classical lamination theory as well as the shear deformation theory