stochastic dynamics of a nonlinear aeroelastic system we investigate the asymptotic behaviors of a thin panel in high supersonic flow with a turbulent boundary layer the objective of this investigation is achieved by formulating methods to analyze complex interactions among aerodynamic structural dynamic nonlinearities turbulence and stability we reduce an infinite dimensional model to a finite dimensional system in the galerkin s sense the normal form technique is employed not only to capture the essential dynamics of the system in which significant nonlinearities are considered but also to reduce the dimensionality of the dynamical system because of the random nature of forcing characteristics associated with the turbulence the theory of stochastic processes is used to explore panel responses in the presence of turbulent boundary layer after adequate scaling of parameters a nonstandard reduction through stochastic averaging is achieved it turns out that the solution of the reduced model is approximated by a markov process that takes its value on a graph with gluing conditions that furnish the complete specification of the dynamics of the reduced model with the aid of the infinitesimal generator of the reduced markov process on the graph we examine stochastic analyses such as mean exit time probability density and stochastic bifurcation in the phenomenological sense

simple discontinuities in acoustic waveguides at low frequencies critical analysis and formulae the variational method of schwinger is applied to reach qualitative conclusions regarding the effects of symmetrical discontinuities change in cross section diaphragm of zero thickness in acoustic waveguides for bidimensional geometry the exact results from an analytical solution are used to discuss the convergence of the solutions of the modal theory when the number of modes taken into account increases the variation of the discontinuity inductances with frequency and the difference between radiation into infinite space and into a large waveguide are discussed finally by a fitting procedure a set of formulae is provided for the engineer for both the case of the radiation of a plane piston into an infinite waveguide and the case of a change in cross section in a circular guide

nonlocal theory solution of two collinear cracks in the functionally graded materials in this paper the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti plane shear loading is investigated by means of nonlocal theory the traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials to make the analysis tractable it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack by use of the fourier transform the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the displacement on the crack surfaces to solve the triple integral equations the displacement on the crack surfaces is expanded in a series of jacobi polynomials unlike the classical elasticity solutions it is found that no stress singularity is present near the crack tips the nonlocal elastic solutions yield a finite hoop stress at the crack tip thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials the magnitude of the finite stress field depends on the crack length the distance between two cracks the parameter describing the functionally graded materials and the lattice parameter of the materials

discrete singular convolution and its application to the analysis of plates with internal supports part 2 applications part 2 of this series of two papers presents the applications of the discrete singular convolution dsc algorithm the main purpose of this paper is to explore the utility test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions the effects of different size shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated the partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports several closed loop supports such as ring square and rhombus and their combinations are studied for complex internal supports convergence and comparison studies are carried out to establish the correctness and accuracy of the dsc algorithm the dsc results are compared with those in the available literature obtained by using other methods numerical results indicate that the dsc algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries boundary conditions and support conditions copyright 2002 john wiley sons ltd

a strip element method for the transient analysis of symmetric laminated plates in this article an extension of the strip element method has been developed to investigate the transient response of symmetric laminated plates in this method the two dimensional governing equations based on the classical laminated plate theory is reduced to a set of ordinary differential equations using the principle of minimum potential energy the resulting set of ordinary differential equations are then solved analytically to obtain the dynamic responses in the frequency domain the fourier transform technique is then used to obtain the time domain response an exponential window method is employed to avoid singularities associated with fourier integration transient responses of a rectangular symmetric laminated plate are presented for various loading and boundary conditions the results obtained using the strip element method were found to compare favorably with exact or analytical solutions available in the literature

periodic homogenization for hypoelliptic diffusions we study the long time behavior of an ornstein uhlenbeck process under the influence of a periodic drift we prove that under the standard diffusive rescaling the law of the particle position converges weakly to the law of a brownian motion whose covariance can be expressed in terms of the solution of a poisson equation we also derive upper bounds on the convergence rate in several metrics

isotropic hypoellipticity and trend to equilibrium for the fokker planck equation with a high degree potential we consider the fokker planck equation with a confining or anti confining potential which behaves at infinity like a possibly high degree homogeneous function hypoellipticity techniques provide the well posedness of the weak cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding witten laplacian with detailed applications

front speed enhancement by incompressible flows in three or higher dimensions we study in dimensions n 3 the family of first integrals of an incompressible flow these are h 1 rm loc functions whose level surfaces are tangential to the streamlines of the advective incompressible field one main motivation for this study comes from earlier results proving that the existence of nontrivial first integrals of an incompressible flow q is the main key that leads to a linear speed up by a large advection of pulsating traveling fronts solving a reaction advection diffusion equation in a periodic heterogeneous framework the family of first integrals is not well understood in dimensions n 3 due to the randomness of the trajectories of q and this is in contrast with the case n 2 by looking at the domain of propagation as a union of different components produced by the advective field we provide more information about first integrals and we give a class of incompressible flows which exhibit ergodic components of positive lebesgue measure and hence are not shear flows and which under certain sharp geometric conditions speed up the kpp fronts linearly with respect to the large amplitude in the proofs we establish a link between incompressibility ergodicity first integrals and the dimension to give a sharp condition about the asymptotic behavior of the minimal kpp speed in terms of the configuration of ergodic components

time scales in homogenization of periodic flows with vanishing molecular diffusion abstract we study the long time transport property of conservative systems perturbed by a small white noise we introduce the dissipation and martingale times and show how they are related to the diffusion time on which a limit theorem is valid the limit theorem is a probabilistic version of homogenization with vanishing molecular diffusion examples of nontrivial time scales are given

reflection of sound at area expansions in a flow duct an analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented the application we have in mind is large industrial duct systems where sound attenuation by reactive and absorptive baffle silencers is of great importance such devices commonly have a rectangular cross section so the model is chosen as two dimensional earlier solutions to this problem are reviewed in the paper the modelling of the flow conditions downstream of the area expansion with and without extended edges and its implications for the resulting acoustic modes are discussed here the scattering problem is solved with the wiener hopf technique and a kutta condition is applied at the edge the solution of the wave equation downstream of the expansion includes hydrodynamic waves of which one is a growing wave theoretical results are compared with experimental data for the reflection coefficient for the plane wave at frequencies below the cut on for higher order modes influence of the interaction between the sound field and the flow field is discussed a region where the reflection coefficient is strongly strouhal number dependent is found

vibration of thick skew plates based on mindlin shear deformation plate theory the free flexural vibration of thick skew plates is considered the total energy functional is derived based on the first order shear deformation plate theory by mindlin the newly developed pb 2 rayleigh ritz method is applied to obtain the solution the method features the versatile pb 2 ritz functions for approximating the deflection and rotation functions which comprise the product of 1 a two dimensional polynomial function p 2 and 2 a basic function b the basic function is the key to ensure the automatic satisfaction of the geometric boundary conditions at the outset since it is formed from the product of the boundary equations raised to appropriate powers natural frequency parameters for skew mindlin plates with different combinations of boundary conditions are presented the solutions where possible are verified by comparisons with those available in the open literature the effect of the poisson ratio on vibration frequencies of plates with free edges is also investigated

wavelets generated by using discrete singular convolution kernels this paper explores the connection between wavelet methods and an efficient computational algorithm the discrete singular convolution dsc many new dsc kernels are constructed and they are identified as wavelet scaling functions two approaches are proposed to generate wavelets from dsc kernels two well known examples the canny filter and the mexican hat wavelet are found to be special cases of the present dsc kernel generated wavelets a family of wavelet generators proposed in this paper are found to form an infinite dimensional lie group which has an invariant subgroup of translation and dilation if dsc kernels form an orthogonal system they are found to span a wavelet subspace in a multiresolution analysis

short and long time behavior of the fokker planck equation in a confining potential and applications we consider the linear fokker planck equation in a confining po tential in space dimension d 3 using spectral methods we prove bounds on the derivatives of the solution for short and long time and give some applica tions

a computational study of residual kpp front speeds in time periodic cellular flows in the small diffusion limit abstract the minimal speeds c of the kolmogorov petrovsky piskunov kpp fronts at small diffusion 1 in a class of time periodic cellular flows with chaotic streamlines is investigated in this paper the variational principle of c reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advection diffusion operator with space time periodic coefficients and small diffusion to solve the advection dominated time dependent eigenvalue problem efficiently over large time a combination of spectral methods and finite element as well as the associated fast solvers are utilized to accelerate computation in contrast to the scaling c o 1 4 in steady cellular flows a new relation c o 1 as 1 is revealed in the time periodic cellular flows due to the presence of chaotic streamlines residual propagation speed emerges from the lagrangian chaos which is quantified as a sub diffusion process

speed up of combustion fronts in shear flows this paper is concerned with the analysis of speed up of reaction diffusion advection traveling fronts in infinite cylinders with periodic boundary conditions the advection is a shear flow with a large amplitude and the reaction is nonnegative with either positive or zero ignition temperature the unique or minimal speeds of the traveling fronts are proved to be asymptotically linear in the flow amplitude as the latter goes to infinity solving an open problem from berestycki nonlinear pdes in condensed matter and reactive flows kluwer doordrecht 2003 the asymptotic growth rate is characterized explicitly as the unique or minimal speed of traveling fronts for a limiting degenerate problem and the convergence of the regular traveling fronts to the degenerate ones is proved for positive ignition temperatures under an additional hormander type condition on the flow

pulsating type entire solutions of monostable reaction advection diffusion equations in periodic excitable media abstract we establish the existence of pulsating type entire solutions of reaction advection diffusion equations with monostable nonlinearities in a periodic framework here the nonlinearities include the classic kpp case the pulsating type entire solutions are defined in the whole space and for all time t r by studying a pulsating traveling front connecting a constant unstable stationary state to a stable stationary state which is allowed to be a positive function we proved that there exist pulsating type entire solutions behaving as two pulsating traveling fronts coming from both directions and approaching each other the key techniques are to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions

dsc analysis of free edged beams by an iteratively matched boundary method this communication introduces a novel scheme for the treatment of free edge supports in the analysis of beams by using the discrete singular convolution dsc algorithm accommodating free edges has been a challenging issue in the dsc analysis of beams plates and shells an iteratively matched boundary imb method is proposed to overcome the difficulty numerical experiments are carried out to demonstrate that the proposed imb method works very well in dealing with arbitrary combinations of beam edge supports

a boundary layer theory for diffusively perturbed transport around a heteroclinic cycle we consider a two dimensional transport equation subject to small diffusive perturbations the transport equation is given by a hamiltonian flow near a compact and connected heteroclinic cycle we investigate approximately harmonic functions corresponding to the generator of the perturbed transport equation in particular we investigate such functions in the boundary layer near the heteroclinic cycle the space of these functions gives information about the likelihood of a particle moving a mesoscopic distance into one of the regions where the transport equation corresponds to periodic oscillations i e a well of the hamiltonian we find that we can construct such approximately harmonic functions which can be used as corrector functions in certain averaging questions when certain macroscopic gluing conditions are satisfied this provides a different perspective on some previous work of freidlin and wentzell on stochastic averaging of hamiltonian systems 2004 wiley periodicals inc

vibratory characteristics of general laminates i symmetric trapezoids abstract this paper presents part i of investigations of free flexural vibration of multi layered symmetric and unsymmetric composite laminates with symmetric trapezoidal planform of arbitrary combinations of edge conditions the ritz procedure withpb 2shape functions as the admissible functions is used to arrive at the governing eivenvalue equation the set ofpb 2shape functions is intrinsically a product of a class of orthogonally generated two dimensional polynomial functions and a basic function which ensures the satisfaction of geometric boundary conditions at the outset different boundary conditions with various combinations of in plane constraints are considered the effects of wide ranges of chord ratios angles of fibre orientation and stacking sequences on the vibration response are investigated with the aim of increasing the existing database sets of previously unavailable vibration frequencies and mode shapes are presented as benchmarks for future reference

free vibration analysis of embedded single layered nanoplates and graphene sheets by using the multiple time scale method an asymptotic approach using the eringen nonlocal elasticity theory and multiple time scale method is developed for the three dimensional 3d free vibration analysis of simply supported single layered nanoplates and graphene sheets gss embedded in an elastic medium in the formulation the small length scale effect is first introduced to the nonlocal constitutive equations by using a nonlocal parameter then the mathematical processes of nondimensionalization asymptotic expansion and successive integration are performed and finally recurrent sets of motion equations for various order problems are obtained the interactions between the nanoplates or gss and their surrounding medium are modeled as a two parameter pasternak foundation nonlocal classical plate theory cpt is derived as a first order approximation of the 3d nonlocal elasticity theory and the motion equations for higher order problems retain the same differential operators as those of nonlocal cpt although with different nonhomogeneous terms some 3d nonlocal elasticity solutions of the natural frequency parameters of nanoplates or gss with and without being embedded in the elastic medium and their corresponding through thickness distributions of modal field variables are given to demonstrate the performance of the 3d asymptotic nonlocal elasticity theory

einstein s relation between diffusion constant and mobility for a diffusion model an ornstein uhlenbeck process in a periodic potential inr d is considered it has been shown previously that this process satisfies a central limit theorem in the sense that by rescaling space and time in a suitable way the distribution of the process converges to that of a wiener process with nonsingular diffusion matrix here a rigorous proof is given of a version of einstein s formula for this model relating the diffusion constant to the mobility of the system

three dimensional vibration analysis of a cantilevered parallelepiped exact and approximate solutions the paper investigates the hypothetical assumption of neglecting transverse normal stress in vibration analysis for cantilevered thick plates and rectangular parallelepiped the analysis solves the three dimensional elasticity energy functional including as well as excluding transverse normal stress and obtains free vibration solutions for a cantilevered parallelepiped although it is widely accepted the omission of transverse normal stress is well justified in kirchhoff love thin plate theory and higher order thick plate models the transverse normal stress effects and thickness extent to which the thick plate models apply as the thickness increases are practically unknown the inconsistency of assuming constant transverse normal displacement through thickness for thick plate models is also addressed the paper concludes that for a rectangular parallelepiped with thickness exceeding a certain limit there is considerable discrepancy if transverse normal stress is neglected

random perturbations of dynamical systems and diffusion processes with conservation laws in this paper we consider random perturbations of dynamical systems and diffusion processes with a first integral we calculate under some assumptions the limiting behavior of the slow component of the perturbed system in an appropriate time scale for a general class of perturbations the phase space of the slow motion is a graph defined by the first integral this is a natural generalization of the results concerning random perturbations of hamiltonian systems considering diffusion processes as the unperturbed system allows to study the multidimensional case and leads to a new effect the limiting slow motion can spend non zero time at some points of the graph in particular such delay at the vertices leads to more general gluing conditions our approach allows one to obtain new results on singular perturbations of pde s

discrete singular convolution and its application to the analysis of plates with internal supports part 1 theory and algorithm this paper presents a novel computational approach the discrete singular convolution dsc algorithm for analysing plate structures the basic philosophy behind the dsc algorithm for the approximation of functions and their derivatives is studied approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels unified features of the dsc algorithm for solving differential equations are explored it is demonstrated that different methods of implementation for the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point the use of the algorithm for the vibration analysis of plates with internal supports is discussed detailed formulation is given to the treatment of different plate boundary conditions including simply supported elastically supported and clamped edges this work paves the way for applying the dsc approach in the following paper to plates with complex support conditions which have not been fully addressed in the literature yet

mathematical modeling of vibration problem of nano sized annular sector plates using the nonlocal continuum theory via eight node discrete singular convolution transformation abstract in the present study free vibration analysis of nano sized annular sector plate is analyzed using the nonlocal continuum theory the method of discrete singular convolution dsc is used for numerical computations firstly equation of motion of thin plates is formulated via nonlocal elasticity then irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation the dsc procedures are then applied to discretization of the transformed set of governing equations and related boundary conditions the effects of nonlocal parameter mode numbers sector angle and radius ratio on the vibration frequencies are investigated in detail it is seen that the size effects are significant in vibration analysis of nano scaled annular sector plates and need to be included in the mechanical model

thermostat like perturbations of an oscillator we consider an oscillator with one degree of freedom perturbed by a deterministic thermostat like perturbation and another system in particular another oscillator coupled with the first one if the hamiltonian of the first system has saddle points the whole system has in a sense a stochastic behavior on long time intervals under certain conditions one can introduce the relative entropy and describe metastability and other large deviation effects in this deterministic system if the coupled system is also an oscillator the long time evolution of the energy of this oscillator has a diffusion approximation to get these results one has to regularize the system but the results are to some extent independent of the regularization the stochasticity is due to instabilities at saddle points of the original system

homogenization of ornstein uhlenbeck process in random environment we consider a tracer particle moving in a random environment the velocity of the tracer is modelled by an ornstein uhlenbeck process which takes into account inertia and friction the medium results in a possibly unbounded random potential we prove an invariance principle for this kind of motion the method used is generalized in order to obtain a central limit theorem for a large class of process the most interesting application being a tagged particle in a medium of infinitely many ornstein uhlenbeck particles

random perturbations of 2 dimensional hamiltonian flows we consider the motion of a particle in a periodic two dimensional flow perturbed by small molecular diffusion the flow is generated by a divergence free zero mean vector field the long time behavior corresponds to the behavior of the homogenized process that is diffusion process with the constant diffusion matrix effective diffusivity we obtain the asymptotics of the effective diffusivity when the molecular diffusion tends to zero

computing reactive front speeds in random flows by variational principle we study reactive front speeds in randomly perturbed cellular flows using a variational representation for the front speed we develop this representation into a computational tool for computing the front speeds without resorting to closure approximations we demonstrate that the front speeds depend on flow statistics and topologies in a complex and dramatic manner

numerical aspects for free vibration of thick plates part i formulation and verification abstract this paper investigates the numerical aspects for free vibration analysis of a class of thick relative thickness ratio t b 0 2 shear deformable rectangular plates with all possible combinations of edge conditions these thick plate vibration frequencies most probably cannot be accurately determined using the classical thin plate theory or the mindlin plate theory the effect of transverse shear strain has been considered by using a higher order plate theory without the need for a shear correction factor unlike some domain discretization methods this analysis assumes a single global element for the entire plate the strain and kinetic energy integrals of the global plate element are formulated and the energy functional is minimized to yield the natural frequencies a set of boundary compliant admissible shape functions is developed to obtain solutions which are unattainable using the classical trigonometric admissible functions the numerical efficiency of symmetry classification is investigated and on certain computational platforms more than 80 of the execution time can be saved while maintaining the same level of accuracy

a numerical method for magneto hygro thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions abstract many researchers work on the mechanical analysis of perfect graphene sheets while these structures have some defects actually in this paper postbuckling of the defective quadrilateral single layered graphene sheets slgs is presented for the first time three types of defects including single vacancy sv double vacancy dv and stone wales sw in conjunction with the influence of vacancy defect reconstruction are considered nonlocal higher order strain gradient theory with three parameters for size effects is used the quadrilateral graphene sheet is subjected to temperature moisture and in plane magnetic loads the elastic foundation is modelled by pasternak medium the equations of motion are obtained imposing higher order shear deformation theory and hamilton s principle the transformed weighing tw and differential quadrature dq method are applied for postbuckling load deflection relation of the structure due to the hygrothermal load different movable boundary conditions are used the influences of various parameters such as defect types defect degree defect reconstruction hygrothermal load magnetic field nonlocal parameters 7 different quadrilateral slgs boundary conditions and elastic medium on the postbuckling behaviour of the quadrilateral graphene sheet are shown the numerical results are validated with other published works in the literature results show that with increasing the defect degree the buckling load decreases

the long time behavior of brownian motion in tilted periodic potentials a b s t r a c t a variety of phenomena in physics and other fields can be modeled as brownian motion in a heat bath under tilted periodic potentials we are interested in the long time average velocity considered as a function of the external force that is the tilt of the potential in many cases the long time behavior pinning and de pinning phenomenon has been observed we use the method of stochastic differential equation to study the langevin equation describing such diffusion in the over damped limit we show the convergence of the long time average velocity to that of the smoluchowski kramers approximation and carry out asymptotic analysis based on risken s and reimann et al s formula in the under damped limit applying freidlin et al s theory we first show the existence of three pinning and de pinning thresholds of the normalized tilt corresponding to the bi stability phenomenon and second as noise approaches zero derive formulas of the mean transition times between the pinning and running states

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

averaging of hamiltonian flows with an ergodic component we consider a process on t2 which consists of fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise it gives rise to a process on the graph naturally associated to the structure of the stream lines of the unperturbed flow it has been shown by freidlin and wentzell random perturbations of dynamical systems 2nd ed springer new york 1998 and mem amer math soc 109 1994 that if the stream function of the flow is periodic then the corresponding process on the graph weakly converges to a markov process we consider the situation where the stream function is not periodic and the flow when considered on the torus has an ergodic component of positive measure we show that if the rotation number is diophantine then the process on the graph still converges to a markov process which spends a positive proportion of time in the vertex corresponding to the ergodic component of the flow

a frequency domain linearized navier stokes equations approach to acoustic propagation in flow ducts with sharp edges acoustic wave propagation in flow ducts is commonly modeled with time domain non linear navier stokes equation methodologies to reduce computational effort investigations of a linearized approach in frequency domain are carried out calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present results of transmission and reflections at the orifice are presented on a two port scattering matrix form and are compared to measurements with good agreement the wave propagation is modeled with a frequency domain linearized navier stokes equation methodology this methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field i e when whistling does not occur

an efficient computational approach for size dependent analysis of functionally graded nanoplates abstract in this paper an efficient computational approach based on refined plate theory rpt including the thickness stretching effect namely quasi 3d theory in conjunction with isogeometric formulation iga is proposed for the size dependent bending free vibration and buckling analysis of functionally graded nanoplate structures the present novel quasi 3d theory not only possesses 4 variables as refined plate theory but also accounts for both shear deformation and stretching effect without any requirement of shear correction factors scfs the size dependent effect is taken into account by nonlocal elasticity theory isogeometric analysis shows a great advantage in dealing with the high continuity and high order derivative requirements of the displacement fields used in quasi 3d and nonlocal theory the reliability and accuracy of the present method are ascertained by comparing the obtained results with other published ones numerical examples are also performed to show the significance of nonlocal effect material distribution profile aspect ratios and boundary conditions on the behaviour of fgm nanoplates

vibrations of skewed cantilevered triangular trapezoidal and parallelogram mindlin plates with considering corner stress singularities based on the mindlin shear deformation plate theory a method is presented for determining natural frequencies of skewed cantilevered triangular trapezoidal and parallelogram plates using the ritz method considering the effects of stress singularities at the clamped re entrant corner the admissible displacement functions include polynomials and corner functions the admissible polynomials form a mathematically complete set and guarantee the solution convergent to the exact frequencies when sufficient terms are used the corner functions properly account for the singularities of moments and shear forces at the re entrant corner and accelerate the convergence of the solution detailed convergence studies are carried out for plates of various shapes to elucidate the positive effects of corner functions on the accuracy of the solution the results obtained herein are compared with those obtained by other investigators to demonstrate the validity and accuracy of the solution copyright 2005 john wiley sons ltd

on the smoluchowski kramers approximation for a system with an infinite number of degrees of freedom according to the smolukowski kramers approximation we show that the solution of the semi linear stochastic damped wave equations utt t x u t x ut t x b x u t x qopen image in new window t u 0 u0 ut 0 v0 endowed with dirichlet boundary conditions converges as goes to zero to the solution of the semi linear stochastic heat equation ut t x u t x b x u t x qopen image in new window t u 0 u0 endowed with dirichlet boundary conditions moreover we consider relations between asymptotics for the heat and for the wave equation more precisely we show that in the gradient case the invariant measure of the heat equation coincides with the stationary distributions of the wave equation for any 0

vibration of arbitrarily laminated plates of general trapezoidal planform this study forms a generalization of the free vibration analysis of thin composite plates it extends previous analyses and presents benchmark results for the effects of general lamination and geometric unsymmetry parameters on the natural frequencies of general trapezoidal plates the ritz extremum energy principle with kinematically oriented pb 2 shape functions transformed into efficient numerical procedures have been further exploited to obtained fast converging and accurate results selected new transverse vibration mode shapes are presented to illustrate the effects of boundary constraints aspect ratio and fiber orientation

boundary layers for cellular flows at high peclet numbers we analyze the behavior of solutions of steady advection diffusion problems in bounded domains with prescribed dirichlet data when the peclet number pe 1 is large we show that the solution converges to a constant in each flow cell outside a boundary layer of width o 1 2 pe 1 around the flow separatrices we construct an dependent approximate water pipe problem purely inside the boundary layer that provides a good approximation of the solution of the full problem but has independent computational cost we also define an asymptotic problem on the graph of streamline separatrices and show that solution of the water pipe problem itself may be approximated by an asymptotic independent problem on this graph finally we show that the dirichlet to neumann map of the water pipe problem approximates the dirichlet to neumann map of the separatrix problem with an error independent of the flow outside the boundary layers 2004 wiley periodicals inc

nonlinear thermo elastic bending behavior of graphene sheets embedded in an elastic medium based on nonlocal elasticity theory this paper investigates the large deflection behavior of orthotropic single layered graphene sheet slgs embedded in a winkler pasternak elastic medium under a uniform transverse load in thermal environments using the nonlocal differential constitutive relations of eringen the slgs is modeled as a nonlocal orthotropic plate using the principle of virtual work the coupled nonlinear equilibrium equations are obtained based on first order shear deformation theory fsdt and the von karman geometrical model the differential quadrature dq discretized form of the governing equations with clamped and simply supported boundary conditions is derived the newton raphson iterative scheme is used to solve the resulting system of nonlinear algebraic equations effects of small scale parameter thermal environment width to length elasticity ratio aspect ratio thickness elastic foundation load value and boundary conditions are considered in detail the results show that unlike the simply supported boundary conditions increase of small scale parameter plays a decreasing role in effect of thermal environment on the deflections of nanoplates with clamped edges it is also observed that increasing the plate thickness thermal load effects decline noticeably and depending on the small scale value the thermal loads do not have any significant effect on the results beyond a specified thickness

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

diffusion advection in cellular flows with large peclet numbers for periodic two dimensional cellular flows in incompressible fluids we provide explicit upper and lower estimates of the effective diffusivity which have the correct scaling behavior for large peclet numbers we demonstrate that all allowed scaling laws can occur the bounds prove that there is no residual diffusion in the infinite peclet number limit for holder continuous flows answering a problem posed by kozlov

assessment and applications of point interpolation methods for computational mechanics two meshfree point interpolation methods pims which are based on the polynomial and the radial basis functions have been proposed recently in addition to the earlier work with the moving least squares mls approximation for the field function approximation however it is found that pims cannot automatically ensure the compatibility of the solution when they are used together with the energy principles in this paper issues related to the compatibility of pims are studied a technique of background cell based nodal selections and a penalty method are proposed to enforce the compatibility of the solution of pims the patch test is studied in great detail the convergences and performances are investigated for both conforming and non conforming pims it is found that those methods of the pim family are very easy to implement and are very efficient in obtaining numerical solutions for problems of computational mechanics copyright 2004 john wiley sons ltd

random perturbations of nonlinear oscillators degenerate white noise perturbations of hamiltonian systems in r 2 are studied in particular perturbations of a nonlinear oscillator with 1 degree of freedom are considered if the oscillator has more than one stable equilibrium the long time behavior of the system is defined by a diffusion process on a graph inside the edges the process is defined by a standard averaging procedure but to define the process for all t 0 one should add gluing conditions at the vertices calculation of the gluing conditions is based on delicate hormander type estimates

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

boundary layers and kpp fronts in a cellular flow we study an eigenvalue problem associated with a reaction diffusion advection equation of the kpp type in a cellular flow we obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude a 1 it follows that the minimal pulsating traveling front speed c a satisfies the upper and lower bounds c1a1 4 c a c2a1 4 physically the speed enhancement is related to the boundary layer structure of the associated eigenfunction accordingly we establish an averaging along the streamlines principle for the unique positive eigenfunction

comment on nonlocal third order shear deformation plate theory with application to bending and vibration of plates by r aghababaei and j n reddy journal of sound and vibration 326 2009 277 289 abstract this paper aims to prove the inaccuracy of the navier solution presented by aghababaei and reddy 1 for the bending analysis of nanoplates based on the nonlocal theory of eringen according to the derived relations for bending of the nonlocal plate model the main cause of this inaccuracy is attributed to an incorrect approximation of the navier solution for a uniform transverse load of course this problem does not inherently occur for the navier solution in cases such as free vibration or the buckling of a nonlocal plate model in which the amount of transverse load is zero in order to obtain further verification the results reported based on the navier solution by aghababaei and reddy 2009 1 for the bending analysis of a nanoplate are compared with those computed by the differential quadrature dq and finite difference fd methods as shown the results obtained by both the fd and dq methods are consistently alike and unlike the solutions reported by aghababaei and reddy 2009 1 they are independent from small scale effect

large deflection of thermo mechanical loaded bilayer orthotropic graphene sheet in on polymer matrix based on nonlocal elasticity theory abstract in this paper large deflection behavior of a bilayer graphene sheet blgs is investigated under uniformly transverse load in thermal environment with various boundary conditions using the principle of virtual work the non linear formulations are derived based on first order shear deformation plate theory fsdt and large deflection von karman equations that includes the thermal effects differential quadrature dq method and the newton raphson iterative technique is employed to solve the system of nonlinear algebraic equations to study the effect of elastic foundation on the results two types of embedded in polymer matrix eipm and resting on polymer matrix ropm are considered besides the influences of temperature rise material properties boundary conditions small scale effect thickness to length ratio aspect ratio and polymer matrix properties are studied in detail

from ballistic to diffusive behavior in periodic potentials the long time large scale small friction asymptotic for the one dimensional langevin equation with a periodic potential is studied in this paper it is shown that the freidlin wentzell and central limit theorem homogenization limits commute we prove that in the combined small friction long time large scale limit the particle position converges weakly to a brownian motion with a singular diffusion coefficient which we compute explicitly we show that the same result is valid for a whole one parameter family of space time rescalings the proofs of our main results are based on some novel estimates on the resolvent of a hypoelliptic operator

anomalous diffusion in fast cellular flows at intermediate time scales it is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a brownian motion this paper studies the behaviour on intermediate time scales before diffusion sets in various heuristics suggest that an anomalous diffusive behaviour should be observed we prove that the variance on intermediate time scales grows like o sqrt t hence on these time scales the effective behaviour can not be purely diffusive and is consistent with an anomalous diffusive behaviour

some remarks on the smoluchowski kramers approximation according to the smoluchowski kramers approximation solution qt of the equation mu ddot q t mu b q t mu dot q t mu sigma q t mu dot w t q 0 q dot q p where dot w t is the white noise converges to the solution of equation dot q t b q t sigma q t dot w t q 0 q as 0 many asymptotic problems for the last equation were studied in recent years we consider relations between asymptotics for the first order equation and the original second order equation homogenization large deviations and stochastic resonance approximation of brownian motion wt by a smooth stochastic process stationary distributions are considered

ohrnstein uhlenbeck process in a random potential on considere le processus d ohmstein uhlenbeck sur r d r d dans le potentiel aleatoire q x on montre que le processus d echelle x e t ex t e2 obeit au theoreme de la limite centrale en probabilite par rapport a

two dimensional vocal tracts with three dimensional behavior in the numerical generation of vowels two dimensional 2d numerical simulations of vocal tract acoustics may provide a good balance between the high quality of three dimensional 3d finite element approaches and the low computational cost of one dimensional 1d techniques however 2d models are usually generated by considering the 2d vocal tract as a midsagittal cut of a 3d version i e using the same radius function wall impedance glottal flow and radiation losses as in 3d which leads to strong discrepancies in the resulting vocal tract transfer functions in this work a four step methodology is proposed to match the behavior of 2d simulations with that of 3d vocal tracts with circular cross sections first the 2d vocal tract profile becomes modified to tune the formant locations second the 2d wall impedance is adjusted to fit the formant bandwidths third the 2d glottal flow gets scaled to recover 3d pressure levels fourth and last the 2d radiation model is tuned to match the 3d model following an optimization process the procedure is tested for vowels a i and u and the obtained results are compared with those of a full 3d simulation a conventional 2d approach and a 1d chain matrix model

dsc ritz method for high mode frequency analysis of thick shallow shells this paper addresses a challenging problem in computational mechanics the analysis of thick shallow shells vibrating at high modes existing methods encounter significant difficulties for such a problem due to numerical instability a new numerical approach dsc ritz method is developed by taking the advantages of both the discrete singular convolution dsc wavelet kernels of the dirichlet type and the ritz method for the numerical solution of thick shells with all possible combinations of commonly occurred boundary conditions as wavelets are localized in both frequency and co ordinate domains they give rise to numerical schemes with optimal accurate stability and flexibility numerical examples are considered for mindlin plates and shells with various edge supports benchmark solutions are obtained and analyzed in detail experimental results validate the convergence stability accuracy and reliability of the proposed approach in particular with a reasonable number of grid points the new dsc ritz method is capable of producing highly accurate numerical results for high mode vibration frequencies which are hitherto unavailable to engineers moreover the capability of predicting high modes endows us the privilege to reveal a discrepancy between natural higher order vibration modes of a mindlin plate and those calculated via an analytical relationship linking kirchhoff and mindlin plates copyright 2004 john wiley sons ltd

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena this paper is concerned with the asymptotic behaviour of the principal eigenvalue of some linear elliptic equations in the limit of high first order coefficients roughly speaking one of the main results says that the principal eigenvalue with dirichlet boundary conditions is bounded as the amplitude of the coefficients of the first order derivatives goes to infinity if and only if the associated dynamical system has a first integral and the limiting eigenvalue is then determined through the minimization of the dirichlet functional over all first integrals a parabolic version of these results as well as other results for more general equations are given some of the main consequences concern the influence of high advection or drift on the speed of propagation of pulsating travelling fronts

vibration analysis of skew fibre reinforced composite laminated plates the vibration of skew laminated composite plates with simply supported and clamped edges is studied the skew plate is mapped into a unit square by linear transformation orthogonal polynomials are used with the ritz method to determine the natural frequencies the effects of skew angle and lamination scheme on natural frequencies are studied results are tabulated for different lamination schemes and compared to available studies in the literature

stochastic averaging with a flattened hamiltonian a markov process on a stratified space a whiskered sphere we consider a random perturbation of a 2 dimensional hamiltonian ode under an appropriate change of time we identify a reduced model which in some aspects is similar to a stochastically averaged model the novelty of our problem is that the set of critical points of the hamiltonian has an interior thus we can stochastically average outside this set of critical points but inside we can make no model reduction the result is a markov process on a stratified space which looks like a whiskered sphere i e a 2 dimensional sphere with a line attached at the junction of the sphere and the line glueing conditions identify the behavior of the markov process

exponential return to equilibrium for hypoelliptic quadratic systems we study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators quadratic operators are non selfadjoint differential operators with complex valued quadratic symbols under appropriate assumptions a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven some applications to the study of chains of oscillators and to the generalized langevin equation are given

sharp asymptotics for kpp pulsating front speed up and diffusion enhancement by flows we study kpp pulsating front speed up and effective diffusivity enhancement by general periodic incompressible flows we prove the existence of and determine the limits c e a a and de a a2 as the flow amplitude a with c e a the minimal front speed and de a the effective diffusivity in direction e

lyapunov exponents for small random perturbations of hamiltonian systems consider the stochastic nonlinear oscillator equation ddot x x x 3 varepsilon 2 beta dot x varepsilon sigma x dot w t with beta 0 and sigma neq 0 if 4 beta sigma 2 0 then for small enough varepsilon 0 the system x dot x is positive recurrent in bf r 2 setminus 0 0 now let overline lambda varepsilon denote the top lyapunov exponent for the linearization of this equation along trajectories the main result asserts that overline lambda varepsilon varepsilon 2 3 overline lambda o varepsilon 4 3 qquad mbox as varepsilon to 0 with overline lambda 0 this result depends crucially on the fact that the system above is a small perturbation of a hamiltonian system the method of proof can be applied to a more general class of small perturbations of two dimensional hamiltonian systems the techniques used include i an extension of results of pinsky and wihstutz for perturbations of nilpotent linear systems and ii a stochastic averaging argument involving

nonlocal third order shear deformation plate theory with application to bending and vibration of plates abstract the third order shear deformation plate theory of reddy a simple higher order theory for laminated composite plates j appl mech 51 1984 745 752 is reformulated using the nonlocal linear elasticity theory of eringen this theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness analytical solutions of bending and free vibration of a simply supported rectangular plate are presented using this theory to illustrate the effect of nonlocal theory on deflection and natural frequency of the plates finally the relations between nonlocal third order first order and classical theories are discussed by numerical results

non local elastic plate theories a non local plate model is proposed based on eringen s theory of non local continuum mechanics the basic equations for the non local kirchhoff and the mindlin plate theories are derived these non local plate theories allow for the small scale effect which becomes significant when dealing with micro nanoscale plate like structures as illustrative examples the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non local solutions are discussed in relation to their corresponding local solutions

a non local asymptotic theory for thin elastic plates the three dimensional dynamic non local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size the integral constitutive relations incorporating the variation of an exponential non local kernel across the thickness are adopted long wave low frequency approximations are derived for both bending and extensional motions boundary layers specific for non local behaviour are revealed near the plate faces it is established that the effect of the boundary layers leads to the first order corrections to the bending and extensional stiffness in the classical two dimensional plate equations

non equilibrium statistical mechanics of strongly anharmonic chains of oscillators we study the model of a strongly non linear chain of particles coupled to two heat baths at different temperatures our main result is the existence and uniqueness of a stationary state at all temperatures this result extends those of eckmann pillet rey bellet epr99a epr99b to potentials with essentially arbitrary growth at infinity this extension is possible by introducing a stronger version of hormander s theorem for kolmogorov equations to vector fields with polynomially bounded coefficients on unbounded domains

an explicit kernel split panel based nystrom scheme for integral equations on axially symmetric surfaces a high order accurate explicit kernel split panel based fourier nystrom dis cretization scheme is developed for integral equations associated with the helm holtz equation in axially symmetric domains extensive incorporation of ana lytic information about singular integral kernels and on the y computation of nearly singular quadrature rules allow for very high achievable accuracy also in the evaluation of elds close to the boundary of the computational domain

reply to the comments of m e golmakani and j rezatalab comment on nonlocal third order shear deformation plate theory with application to bending and vibration of plates by r aghababaei and j n reddy journal of sound and vibration 326 2009 277 289 journal of sound vibration 333 2014 3831 3835 abstract golmakani and rezatalab 1 suggested in their paper that the deflection of a simply supported nonlocal elastic plate under uniform load is not affected by the small length scale terms they based their proof on the use of navier s method using a sinusoidal based deflection solution this insensitivity of the deflection solution of a simply supported nonlocal elastic plate with respect to the small length terms of eringen s model is not correct as already detailed in the literature for example see 2 for beam problems in fact the deflection of the nonlocal plate in the eringen sense is larger than the one of the local case as shown in many papers available in the literature we prove in this reply to the authors that the navier s method has to be correctly applied for highlighting the specific sensitivity phenomenon of the deflection solution as compared to exact analytical solution the problem is exactly the same as for the bending of a beam

non equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures we study the statistical mechanics of a finite dimensional non linear hamiltonian system a chain of anharmonic oscillators coupled to two heat baths described by wave equations assuming that the initial conditions of the heat baths are distributed according to the gibbs measures at two different temperatures we study the dynamics of the oscillators under suitable assumptions on the potential and on the coupling between the chain and the heat baths we prove the existence of an invariant measure for any temperature difference i e we prove the existence of steady states furthermore if the temperature difference is sufficiently small we prove that the invariant measure is unique and mixing in particular we develop new techniques for proving the existence of invariant measures for random processes on a non compact phase space these techniques are based on an extension of the commutator method of hormander used in the study of hypoelliptic differential operators

differential quadrature method for thick symmetric cross ply laminates with first order shear flexibility a global numerical technique the differential quadrature dq method is examined here for its suitability to solve the boundary value problem of symmetric cross ply laminates using the first order shear deformation plate theory by whitney and pagano j appl mech 37 1031 1036 1970 the bending behaviours of symmetric cross ply laminates subject to different boundary constraints are investigated in this study the method is used to transform the sets of governing differential equations and boundary conditions of the laminated plates into sets of linear algebraic equations boundary conditions along the edges are implemented through the discrete grid points by constraining the displacements bending moments and rotations the theoretical formulations and solution procedures of the method are illustrated through solving several numerical examples the accuracy and validity of the present formulation if available are examined by direct comparison with the known values

a pde approach to small stochastic perturbations of hamiltonian flows abstract in this note we present a unified approach based on pde methods for the study of averaging principles for small stochastic perturbations of hamiltonian flows in two space dimensions such problems were introduced by freidlin and wentzell and have been the subject of extensive study in the last few years using probabilistic arguments when the hamiltonian flow has critical points it exhibits complicated behavior near the critical points under a small stochastic perturbation asymptotically the slow averaged motion takes place on a graph the issues are to identify both the equations on the sides and the boundary conditions at the vertices of the graph our approach is very general and applies also to degenerate anisotropic elliptic operators which could not be considered using the previous methodology

transverse vibration of trapezoidal plates of variable thickness unsymmetric trapezoids abstract a set of simple two dimensional polynomial functions is employed as the admissible displacement function in the rayleigh ritz energy approach for the free transverse vibration analysis of symmetric trapezoidal plates with linearly varying thickness the admissible function consists the product of i a two dimensional polynomial function and ii a basic function the basic function is defined by the product of the equations of the prescribed continuous piecewise boundary shape each raised to the power of 0 1 or 2 corresponding to a free simply supported or clamped edge respectively the set of functions generated ensures the satisfaction of all the kinematic boundary conditions at the outset the proposed method is applied to solve several symmetric trapezoidal plates with different combinations of boundary conditions and variable thickness the results for some cases are compared with the available published values from the open literature these new results may serve as benchmark data for the development of other numerical methods

extinction versus persistence in strong oscillating flows in this paper we give some conditions for finite time extinction or persistence of the solutions of diffusion advection equations in strong and oscillating flows under dirichlet boundary conditions the enhancement of the diffusion rate depends on the interplay between strong advection and time homogenization and in particular on the ratio between the strength of the flow and its frequency parameter quantitative estimates of this ratio which depend on the geometry of the domain are provided in the case of a uniform flow in the general time space dependent case the finite time behavior of the solutions is related to the existence of first integrals of the flow

a numerical study of turbulent flame speeds of curvature and strain g equations in cellular flows abstract we study front speeds of curvature and strain g equations arising in turbulent combustion these g equations are hamilton jacobi type level set partial differential equations pdes with non coercive hamiltonians and degenerate nonlinear second order diffusion the hamiltonian of a strain g equation is also non convex numerical computation is performed based on monotone discretization and weighted essentially nonoscillatory weno approximation of transformed g equations on a fixed periodic domain the advection field in the computation is a two dimensional hamiltonian flow consisting of a periodic array of counter rotating vortices or cellular flows depending on whether the evolution is predominantly in the hyperbolic or parabolic regimes suitable explicit and semi implicit time stepping methods are chosen the turbulent flame speeds are computed as the linear growth rates of large time solutions a new nonlinear parabolic pde is proposed for the reinitialization of level set functions to prevent piling up of multiple bundles of level sets on the periodic domain we found that the turbulent flame speed s t of the curvature g equation is enhanced as the intensity a of cellular flows increases at a rate between those of the inviscid and viscous g equations the s t of the strain g equation increases in small a decreases in larger a then drops down to zero at a large enough but finite value a the flame front ceases to propagate at this critical intensity a and is quenched by the cellular flow

averaging of incompressible flows on two dimensional surfaces we consider a process on a compact two dimensional surface which consists of the fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise it gives rise to a process on the graph naturally associated to the structure of the stream lines of the unperturbed flow it has been shown by freidlin and wentzell that if the unperturbed motion is periodic for almost all the initial points then the corresponding process on the graph weakly converges to a markov process we consider the situation when the unperturbed motion is not periodic and the flow has ergodic components of positive measure we show that the process on the graph still converges to a markov process which spends a positive proportion of time in the vertices corresponding to the ergodic components of the flow as shown in a companion paper 5 these results allow one to describe the viscosity regularization of dissipative deterministic perturbations of incompressible flows in the case of surfaces of higher genus the limiting process may exhibit intermittent behavior in the sense that the time axis can be divided into the intervals of random lengths where the particle stays inside one ergodic component separated by the intevals where the particle moves deterministically between the components