an element free galerkin approach for rigidflexible coupling dynamics in 2d state based on an improved element free galerkin efg method and the geometric nonlinear elastic theory an element free numerical approach for rigidflexible coupling dynamics of a rotating hubbeam system is implemented using the hamilton principle the coupled nonlinear integral differential governing equations are derived in which the dynamic stiffening effect is expressed by the longitudinal shrinking of the beam induced by the transverse displacement by the efg method where the global interpolating moving least squares imls and generalized moving least squares igmls were used for discretizing the longitudinal and transverse deformation variables respectively the spatially element free discretized dynamic equations of the system are obtained and the newmark scheme was selected as the time integration method for the numerical computation the superiority of the global interpolating property makes the ease for imposing both displacement and derivative boundary conditions the transverse bending vibration and structural dynamics of the flexible beam in non inertial system are analyzed in the numerical simulations and influence parameters of the efg method are also fully discussed simulation results verify the feasibility of the improved efg approach for rigidflexible coupling dynamics

flapwise bending vibration analysis of a rotating tapered cantilever bernoulli euler beam by differential transform method abstract this paper studies the vibration characteristics of a rotating tapered cantilever bernoulli euler beam with linearly varying rectangular cross section of area proportional to xn where n equals to 1 or 2 covers the most practical cases in this work the differential transform method dtm is used to find the nondimensional natural frequencies of the tapered beam numerical results are tabulated for different taper ratios nondimensional angular velocities and nondimensional hub radius the effects of the taper ratio nondimensional angular velocity and nondimensional hub radius are discussed the accuracy is assured from the convergence of the natural frequencies and from the comparisons made with the studies in the open literature it is shown that the natural frequencies of a rotating tapered cantilever bernoulli euler beam can be obtained with high accuracy by using dtm

network characterization of gul ko compact spaces and their relatives abstract in this paper we characterize the classes of gul ko and talagrand compact spaces through a network condition leading us to answer two questions posed by g gruenhage proc amer math soc 100 1987 371 376 on covering properties

non linear free vibrations of a rotating flexible arm abstract the non linear moderately large amplitude flexural free vibrations of an arm clamped with a setting angle to a rigid rotating hub are studied the shear deformation and rotary inertia effects are assumed to be negligible but account is taken of axial inertia non linear curvature and the inextensibility condition the lagrangian approach in conjunction with the assumed modes method assuming constant hub rotation speed is used in a consistent manner to obtain the third order non linear uni modal temporal problem because of the strength of the non linearities in the temporal problem which includes elastic and inertial geometric stiffening as well as inertial softening terms a time transformation method is employed to obtain an approximate solution to the frequency amplitude relation of arm free oscillation results in non dimensional form are presented graphically for the effect of hub rotation speed blade setting angle and hub radius on the variation of the natural frequency with vibration amplitude

hydrodynamical limit for a hamiltonian system with weak noise starting from a general hamiltonian system with superstable pairwise potential we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles we prolve that in the scaling limit the time conserved quantities energy momenta and density satisfy the euler equation of conservation laws up to a fixed timet provided that the euler equation has a smooth solution with a given initial data up to timet the strength of the noise term is chosen to be very small but nonvanishing so that it disappears in the scaling limit

homogenization of hamilton jacobi bellman equations with respect to time space shifts in a stationary ergodic medium we consider a family fu t x g 0 of solutions to the equation u t c u 2ch t x ru d0 with the terminal datau t x du x assuming that the dependence of the hamiltonian h t x p on time and space is realized through shifts in a stationary ergodic random medium and that h is convex inp and satisfies certain growth and regularity conditions we show the almost sure locally uniform convergence in time and space of u t x as 0 to the solution u t x of a deterministic averaged equation u t c h ru d 0 u t x d u x the effective hamiltonian h is given by a variational formula

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

multi scale analysis on nonlinear gyroscopic systems with multi degree of freedoms abstract a method of multiple scales is developed for n degree of freedom weakly nonlinear gyroscopic systems a general procedure is proposed to establish solvability conditions the conditions have n different versions whose equivalence cannot be mathematically demonstrated the procedure is applied to a 4 degree of freedom nonlinear gyroscopic system that is the 4 term galerkin truncation of the governing equation of a pipe conveying fluid flowing in the supercritical speed the investigation focuses on the primary external resonance in the first frequency 1 and the two to one internal resonance of the first two frequencies 1 and 2 the multi scale analysis shows that the amplitude frequency response curve in each of the first two modes has a peak bending to the left when 2 2 1 two peaks with the same height and the opposite bending directions when 2 2 1 and a peak bending to the right when 2

stability of an axially accelerating string subjected to frictional guiding forces abstract the dynamic response of an axially translating continuum subjected to the combined effects of a pair of spring supported frictional guides and axial acceleration is investigated such systems are both non conservative and gyroscopic the continuum is modeled as a tensioned string translating between two rigid supports with a time dependent velocity profile the equations of motion are derived with the extended hamilton s principle and discretized in the space domain with the finite element method the stability of the system is analyzed with the floquet theory for cases where the transport velocity is a periodic function of time direct time integration using an adaptive step runge kutta algorithm is used to verify the results of the floquet theory this approach can also be employed in the general case of arbitrary time varying velocity results are given in the form of time history diagrams and instability point grids for different sets of parameters such as the location of the stationary load the stiffness of the elastic support and the values of initial tension this work showed that presence of friction adversely affects stability but using non zero spring stiffness on the guiding force has a stabilizing effect this work also showed that the use of the finite element method and floquet theory is an effective combination to analyze stability in gyroscopic systems with stationary friction loads

self diffusion for brownian motions with local interaction we derive explicitly the asymptotic law of the tagged particle process in a system of interacting brownian motions in the presence of a diffusive scaling in nonequilibrium the interaction is local and interpolates between the totally independent case noninteracting and the totally reflecting case and can be viewed as the limiting local version of an interaction through a pair potential as its support shrinks to zero we also prove the independence of two tagged particles in the limit

large deviations for the current and tagged particle in 1d nearest neighbor symmetric simple exclusion laws of large numbers starting from certain nonequilibrium measures have been shown for the integrated current across a bond and a tagged particle in one dimensional symmetric nearest neighbor simple exclusion ann inst henri poincare probab stat 42 2006 567 577 in this article we prove corresponding large deviation principles and evaluate the rate functions showing different growth behaviors near and far from their zeroes which connect with results in j stat phys 136 2009 1 15

stability analysis for the flapwise motion of a cantilever beam with rotary oscillation abstract the flapwise motion of a cantilever beam with rotary oscillation is analyzed to investigate the dynamic stability of the beam the cantilever beam is regarded as a system subjected to parametric excitation because the angular speed of the cantilever beam varies harmonically to consider the stiffening effect due to the centrifugal force this study adopts the linear partial differential equation of flapwise motion which is derived by a modelling method using the stretch deformation instead of the conventional longitudinal deformation after the partial differential equation is discretized by the galerkin method the method of multiple scales is applied using this method the stability of the beam is analyzed for the variations of the oscillating frequency and the maximum angular speed in addition to verify the stability results the time responses of flapwise motion are computed by the generalized time integration method

dynamics of rectangular plates undergoing prescribed overall motion a set of linear equations of motion for rectangular plates undergoing prescribed overall motion is derived in this paper two in plane stretch variables with which the in plane strain energy of the plate can be expressed in an exact quadratic form are employed and approximated to derive the equations of motion the equations of motion include motion induced stiffness variation terms which are expressed as explicit functions of the prescribed overall motion the effects of the motion induced stiffness variation terms which are neglected in the conventional linear modelling method on the dynamic response of the plate are investigated the reliability and the accuracy of the equations of motion which are derived in the present work are examined through the numerical study

dynamics of flexible beams undergoing overall motions abstract a modelling method for straight beams undergoing large overall motions as well as small elastic deformations is presented in this paper different from the classical linear cartesian modelling method which employs three cartesian deformation variables the present modelling method uses a non cartesian variable along with two cartesian variables to describe the elastic deformation a quadratic form of the strain energy expressed with the hybrid set of deformation variables is used to obtain the generalized active forces and a geometric constraint equation relating the non cartesian variable and cartesian variables is used to obtain the generalized inertia forces in the equations of motion the present modelling method not only provides accurate simulation results but also clarifies the limit of validity of the classical linear cartesian modelling method

stochastic homogenization of hamilton jacobi bellman equations we study the homogenization of some hamilton jacobi bellman equations with a vanishing second order term in a stationary ergodic random medium under the hyperbolic scaling of time and space imposing certain convexity growth and regularity assumptions on the hamiltonian we show the locally uniform convergence of solutions of such equations to the solution of a deterministic effective first order hamilton jacobi equation the effective hamiltonian is obtained from the original stochastic hamiltonian by a minimax formula our homogenization results have a large deviations interpretation for a diffusion in a random environment c 2006 wiley periodicals inc

characteristics of steady vibration in a rotating hub beam system abstract a rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub s inertia and its rotating speed to highlight the essential nature behind the vibration phenomena we analyze the steady vibration of a rotating euler bernoulli beam with a quasi steady state stretch newton s law is used to derive the equations governing the beam s elastic motion and the hub s rotation a combination of these equations results in a nonlinear partial differential equation pde that fully reflects the mutual interaction between the two kinds of motion via the fourier series expansion within a finite interval of time we reduce the pde into an infinite system of a nonlinear ordinary differential equation ode in spatial domain we further nondimensionalize the ode and discretize it via a difference method the frequencies and modal shapes of a general rotating beam are then determined numerically for a low speed beam where the ignorance of geometric stiffening is feasible the beam s vibration characteristics are solved analytically we validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature finally systematic simulations are performed to demonstrate how the beam s eigenfrequencies vary with the hub s inertia and rotating speed

infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations abstract the transverse vibrations of simply supported axially moving euler bernoulli beams are investigated the beam has a time varying axial velocity with viscous damping traveling beam eigenfunctions with infinite number of modes are considered approximate analytical solutions are sought using the method of multiple scales a perturbation technique a detailed analysis of the resonances in which upto four modes of vibration involved are performed stability analysis is treated for each type of resonance approximate stability borders are given for the resonances involving only two modes for higher number of modes involved in a resonance sample numerical examples are presented for stabilities

free vibration of rotating tapered beams using the dynamic stiffness method abstract the free bending vibration of rotating tapered beams is investigated by using the dynamic stiffness method the range of problems considered includes beams for which the depth and or width of the cross section vary linearly along the length first the governing differential equation of motion of the rotating tapered beam in free flap bending vibration is derived for the most general case using hamilton s principle allowing for the effects of centrifugal stiffening an arbitrary outboard force and the hub radius term for harmonic oscillation the differential equation is solved for bending displacement by applying the frobenius method of series solution the expressions for bending rotation shear force and bending moment at any cross section of the beam are also obtained in explicit analytical form then the dynamic stiffness matrix is developed by relating the amplitudes of forces and moments to those of the displacements and rotations at the ends of the harmonically vibrating tapered beam next the wittrick williams algorithm is used as a solution technique to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of some illustrative examples a parametric study is carried out to demonstrate the effects of rotational speed taper ratio and hub radius on the results which are discussed and compared with the published ones finally some conclusions are drawn

on weakly locally uniformly rotund banach spaces abstract we show that every normed space e with a weakly locally uniformly rotund norm has an equivalent locally uniformly rotund norm after obtaining a discrete network of the unit sphere s e for the weak topology we deduce that the space e must have a countable cover by sets of small local diameter which in turn implies the renorming conclusion this solves a question posed by deville godefroy haydon and zizler for a weakly uniformly rotund norm we prove that the unit sphere is always metrizable for the weak topology despite the fact that it may not have the kadec property moreover banach spaces having a countable cover by sets of small local diameter coincide with the descriptive banach spaces studied by hansell so we present here some new characterizations of them

nonlinear diffusion limit for a system with nearest neighbor interactions we consider a system of interacting diffusions the variables are to be thought of as charges at sites indexed by a periodic one dimensional lattice the diffusion preserves the total charge and the interaction is of nearest neighbor type with the appropriate scaling of lattice spacing and time a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density

large deviation principle for interacting brownian motions we prove the large deviation principle for the empirical process in a system of locally interacting brownian motions in the nonequilibrium such a phenomenon has been proven only for two lattice systems the symmetric simple exclusion process and the zero range process therefore we have achieved the third result in this context and moreover the first result for the diffusion type interacting particle system 2016 wiley periodicals inc

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

lie group theory and analytical solutions for the axially accelerating string problem abstract transverse vibrations of a string moving with time dependent velocity v t have been investigated analytical solutions of the problem are found using the systematic approach of lie group theory group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations from the symmetries of the partial differential equation the method for deriving exact solutions for the arbitrary velocity case is shown special cases of interest such as constant velocity constant acceleration harmonically varying velocity and exponentially decaying velocity are investigated in detail finally for a simply supported strip approximate solutions are presented for the exponentially decaying and harmonically varying cases

on weakly countably determined banach spaces for a topological space x let ci x denote the banach space of all bounded functions x r such that for every e 0 the set x x f x e is closed and discrete in x endowed with the supremum norm the main theorem is the following let l be a weakly countably determined subset of a banach space then there exist a subset e of the baire space e a compact space k and a bounded linear one to one operator t c l ci e x k that is pointwise to pointwise continuous in the case where l is weakly analytic e can be replaced by e this theorem is connected with the basic result of amir lindenstrauss on wcg banach spaces and has corresponding consequences such as the representation of gulko resp ta lagrand compact spaces as pointwise compact subsets of ci e x k resp ci e x k a compact space f is called gulko or talagrand compact if c o is wcd or a weakly k analytic banach space the characterization of wcd resp weakly k analytic banach spaces e using one to one operators from e into ci e x k resp ci e x k and the existence of equivalent good norms on e and e simultaneously

dynamic analysis of a rotating cantilever beam by using the finite element method a finite element analysis for a rotating cantilever beam is presented in this study based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation three linear partial differential equations are derived from hamilton s principle two of the linear differential equations are coupled through the stretch and chordwise deformations the other equation is an uncoupled one for the flapwise deformation from these partial differential equations and the associated boundary conditions are derived two weak forms one is for the chordwise motion and the other is for the flapwise motion the weak forms are spatially discretized with newly defined two node beam elements with the discretized equations the behaviours of the natural frequencies are investigated for the variation of the rotating speed in addition the time responses and distributions of the deformations and stresses are computed when the rotating speed is prescribed the effects of the rotating speed profile on the vibrations of the beam are also investigated

large deviations for the symmetric simple exclusion process in dimensions d 3 we consider symmetric simple exclusion processes with l macr nd particles in a periodic d dimensional lattice of width n we perform the diffusive hydrodynamic scaling of space and time the initial condition is arbitrary and is typically far away form equilibrium it specifies in the scaling limit a density profile on the d dimensional torus we are interested in the large deviations of the empirical process n d l1 xi as random variables taking values in the space of measures on d 0 1 we prove a large deviation principle with a rate function that is more or less universal involving explicity besides the initial profile only such canonical objects as bulk and self diffusion coefficients

free vibration analysis of rotating thick plates abstract a finite element formulation for vibration analysis of rotating thick plates is developed mindlin plate theory combined with second order strain displacement assumptions are applied for plate modeling kane dynamic method is employed for the derivation of nonlinear governing equations of motion which include coriolis effects and the couplings between in plane and out of plane deformations the nonlinear equations of motion are linearized using the conventional quasi static method and frequency results are obtained the effects of different parameters including aspect ratio thickness ratio hub radius ratio and rotation speed on dimensionless natural frequencies are investigated and discussed in addition the differences between linear and nonlinear approaches toward in plane vibration analysis of rotating plates are studied tune speeds are observed for the in plane vibration frequencies the results are in good agreement with those of other theories and experiments

scaling limits for interacting diffusions we consider a large number of particles diffusing on a circle interacting through a drift resulting from the gradient of a pair potential whose support is of the order of the interparticle distance we derive a nonlinear bulk diffusion equation for the density of the particle distribution on the circle the diffusion coefficient is determined as a function of density in terms of standard thermodynamical objects

eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method abstract in this paper free vibrations of a rotating clamped euler bernoulli beams with uniform cross section are studied using continuation method namely asymptotic numerical method the governing equations of motion are derived using lagrange s method the kinetic and strain energy expression are derived from rayleigh ritz method using a set of hybrid variables and based on a linear deflection assumption the derived equations are transformed in two eigenvalue problems where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms while the second is standard eigenvalue problem and corresponds to the flapping motion those two eigenvalue problems are transformed into two functionals treated by continuation method the asymptotic numerical method new method proposed for the solution of the linear gyroscopic system based on an augmented system which transforms the original problem to a standard form with real symmetric matrices by using some techniques to resolve these singular problems by the continuation method evolution curves of the natural frequencies against dimensionless angular velocity are determined at high angular velocity some singular points due to the linear elastic assumption are computed numerical tests of convergence are conducted and the obtained results are compared to the exact values results obtained by continuation are compared to those computed with discrete eigenvalue problem

solvability condition in multi scale analysis of gyroscopic continua abstract the solvability condition is investigated for the method of multiple scales applied to gyroscopic continua the general framework of the multi scale analysis is proposed for a linear gyroscopic continuous system under small nonlinear time dependent disturbances the solvability condition is derived from the properties of the systems the condition holds only for appropriate boundary conditions the appropriateness of the boundary conditions can be examined for unperturbed linear systems an example is presented to highlight the requirements on the boundary conditions

free in plane vibration of an axially moving membrane the free in plane vibration of an axially moving membrane is studied considering the effects of both the translating speed and aspect ratio of the membrane two sets of boundary conditions which are free and fixed constraints in the lateral direction at boundaries with mass transport are discussed in this study from the extended hamilton principle the coupled equations of the longitudinal and lateral motions are derived these equations are then discretized by using the galerkin method from the discretized equations the natural frequencies and mode shapes are obtained for the variations of the translating speed and aspect ratio the results show that the translating speed aspect ratio and boundary conditions have significant effects on the in plane vibrations of the moving membrane

dynamic modelling and stability analysis of axially oscillating cantilever beams dynamic stability of an axially oscillating cantilever beam is investigated in this paper equations of motion for the axially oscillating beam are derived and transformed into dimensionless forms the equations include harmonically oscillating parameters which are related to the motion induced stiffness variation stability diagrams of the first and the second order approximate solutions are obtained by using the multiple scale perturbation method the stability diagrams show that there exist significant difference between the first and the second order approximate solutions it is also found that relatively large unstable regions exist around the first bending natural frequency twice the first bending natural frequency and twice the second being natural frequency the validity of the stability diagram is verified by direct numerical integrations of the equations of motion of the system

inner characterizations of weakly compactly generated banach spaces and their relatives we give characterizations of weakly compactly generated spaces their subspaces vasak spaces weakly lindelof determined spaces as well as several other classes of banach spaces related to uniform g teaux smoothness in terms of the presence of a total subset of the space with some additional properties in addition we describe geometrically when possible these classes by means of suitable smoothness or rotundity of the norm as a consequence we get new functional analytic proofs of several theorems on uniform eberlein gul ko and talagrand compacta

entropy large deviations and scaling limits we often model the evolution of a complex system at the lowest or micro level because that is what makes the most physical sense but if the system is large we invariably want answers to questions posed on the larger macro or global scale this then involves the study of equations with a large number of variables and extracting useful information from their solutions the macroscopic quantities of interest may not contain complete information about the microscopic variables that drive their evolution something has to be done to obtain a closed system of equations for quantities of interest different contexts require different approaches we are concerned here with the evolution of large systems of interacting particles or field variables that have some built in noise and outline some of the work done at the institute during the last 25 years 2013 wiley periodicals inc

diffusion of color in the simple exclusion process we prove a diffusion scaling limit for the macroscopic densities of colored particles performing the simply excluded random walk and relate this to the limiting behavior of a test particle in equilibrium

dynamic modeling and stability analysis of an axially oscillating beam undergoing periodic impulsive force a dynamic modeling method of an axially oscillating beam undergoing periodic impulsive force is proposed in the present work an element specific modeling method using a stretch deformation variable is employed to derive the linear equations of motion the stiffness variation effect induced by the periodic impulsive force as well as the axially oscillating motion is included in the linear equations of motion the accuracy of the proposed modeling method is verified by comparing its numerical solutions to those of a nonlinear finite element code the effects of the impulse magnitude the oscillating frequency the oscillating speed amplitude and the modal damping ratio on the dynamic stability of the beam are investigated with the modeling method

dynamic model for free vibration and response analysis of rotating beams abstract a new modeling method for the vibration analysis of a rotating cantilever beam is proposed and compared to the other modeling methods applying the hamilton principle the equations for the axial chordwise and flapwise motions are derived during the derivation of these equations the nonlinear von karman strain and the corresponding linear stress are used to consider the stiffening effect due to rotation the derived equations of motion obtained from the proposed method are analytically and numerically compared to equations from the previous modeling methods computations of the natural frequencies and time responses show that the described equations of motion are more reliable than the equations of the other modeling methods

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

transient vibration of gyroscopic systems with unsteady superposed motion abstract the equation of motion for a gyroscopic system with unsteady superposed motion is derived for the prototypical problem in which motion of an oscillating particle is measured relative to a non inertial frame the resulting coefficient matrices are time dependent and skew symmetric acceleration terms are present both as coriolis acceleration and as a component of net stiffness such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems including flexible media that translate with time dependent speed following the asymptotic approach of krylov bogoliubov and mitropolsky a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the system s natural periods of oscillation first order approximations for the modal amplitude and phase are obtained in closed form the method is illustrated through two examples of technical interest a two degree of freedom model of a rotating shaft and a distributed parameter model of a moving tape or web