on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

vibration analysis of annular like plates abstract the existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure in this paper the vibration analysis of annular like plates is presented based on numerical and experimental approaches using the finite element analysis code nastran the effects of the eccentricity hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses the results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of recessive modes of the plate with a slightly eccentric hole they will however lead to erroneous results for dominant modes in addition the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate like structures experimental modal analysis on a clamped free annular like plate is performed and the results obtained reveal good agreement with those obtained by numerical analysis this study provides guidance on modal analysis vibration measurement and damage detection of plate like structures

three dimensional vibrations of thick circular and annular plates abstract the ritz method is applied in a three dimensional 3 d analysis to obtain accurate frequencies for thick circular and annular plates the method is formulated in a manner which allows one to have any combination of free or fixed plate boundaries admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co ordinate and algebraic polynomials in the radial and axial co ordinates upper bound convergence of the non dimensional frequencies to at least four significant figures is demonstrated comparisons of results are made with ones obtained by others using 2 d mindlin thick plate theory and with other 3 d solutions extensive and accurate four significant figure frequencies are presented for completely free circular plates having thickness to diameter ratios of 0 2 0 3 0 4 and 0 5 for poisson s ratios 0 0 3 and 0 499 frequencies are also given for thick annular plates having a thickness to outer diameter of 0 2 inside to outside diameter ratios of 0 1 0 5 and 0 9 and 0 3 all 3 d modes are included in the analyses e g flexural thickness shear in plane stretching and torsional the circular and annular plate frequency data given is exact to at least four digits thus being benchmark data against which results from 2 d thick plate theories or other approximate methods e g finite elements may be compared

decay estimates for the wave equation in two dimensions abstract we establish strichartz estimates both reversed and some direct ones pointwise decay estimates and weighted decay estimates for the linear wave equation in dimension two with an almost scaling critical potential in the case when there is no resonance or eigenvalue at the edge of the spectrum we also prove some simple applications

carleman estimates and absence of embedded eigenvalues let l w be a schrodinger operator with a potential w in l frac n 1 2 mathbb r n n geq 2 we prove that there is no positive eigenvalue the main tool is an l p l p prime carleman type estimate which implies that eigenfunctions to positive eigenvalues must be compactly supported the carleman estimate builds on delicate dispersive estimates established in 7 we also consider extensions of the result to variable coefficient operators with long range and short range potentials and gradient potentials

on the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half plane we consider the navier stokes equations for viscous incompressible flows in the half plane under the no slip boundary condition by using the vorticity formulation we prove the local in time convergence of the navier stokes flows to the euler flows outside a boundary layer and to the prandtl flows in the boundary layer in the inviscid limit when the initial vorticity is located away from the boundary 2014 wiley periodicals inc

natural frequencies and mode shapes of deterministic and stochastic non homogeneous rods and beams abstract natural frequencies and mode shapes of non homogeneous deterministic and stochastic rods and beams are studied the solution is based on the functional perturbation method fpm the frequencies and mode shapes are considered as functionals of the non homogeneous properties the natural frequency and mode shape of the k th order is obtained analytically to any desired degree of accuracy once the functional derivatives with respect to the non uniform property have been found the solution for any morphology is obtained by direct integration without resolving the differential equation several examples with different non homogeneous properties are solved and compared with exact solutions as an accuracy check the fpm accuracy range for the frequency and the mode shape is less than 1 even for high heterogeneities in the stochastic case the accuracy of the natural frequencies depends on the stochastic information used given on the correlation distance roughly the grain size on the function around which the perturbation is executed and on whether we are interested in the properties of or of 2 moreover all frequency modes have the same response to heterogeneity as long as their wave length is of the order of the heterogeneity s characteristic distance in addition the heterogeneity effect on the average natural frequencies is minimal for the fundamental mode and may serve as a design tool

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

dispersive estimates for schrodinger operators in dimension two we prove l1 2 l 2 for the two dimensional schrodinger operator v with the decay rate t 1 we assume that zero energy is neither an eigenvalue nor a resonance this condition is formulated as in the recent paper by jensen and nenciu on threshold expansions for the two dimensional resolvent

a weighted dispersive estimate for schrodinger operators in dimension two let h v where v is a real valued potential on mathbb r 2 satisfying v x lesssim langle x rangle 3 we prove that if zero is a regular point of the spectrum of h v then w 1 e ith p ac f l infty mathbb r 2 lesssim frac 1 t log 2 t w f l 1 mathbb r 2 t geq 2 with w x log 2 x 2 this decay rate was obtained by murata in the setting of weighted l 2 spaces with polynomially growing weights

vibrations of non homogeneous rectangular membranes abstract an exact solution for the title problem is obtained for the case where the two subdomains of the non homogeneous membrane are of rectangular shape it is shown that the fundamental frequency coefficient obtained by means a of the classical kantorovish method and b the optimized kantorovich method are in very good agreement with the result predicted by the exact method

acoustic characteristics of annular cavities with locally non uniform media a theoretical approach is developed to obtain the natural frequencies and the mode shapes of annular cavities that have locally non uniform media the equation of motion is derived based on a special form of the wave equation that is capable of representing the variation of material properties with position and the unit step function is used in the equation to express the local non uniformity of the media the laplace transform is adopted in eigenvalue analysis to calculate the natural frequencies and the normal mode shapes of the annular cavities the validity of the presented method is verified through finite element analysis and experiments parametric studies are performed to find out the relation between the acoustic characteristics of the cavity and the local deviation of the media and the acoustic characteristics are explained in terms of the mass and stiffness effect of the local deviation in an annular cavity upon the natural vibration characteristics

vibration analysis of simply supported rectangular plates with unidirectionally arbitrarily varying thickness in this paper a practical analytical method for the free vibration analysis of a simply supported rectangular plate with unidirectional arbitrary thickness variation is proposed first the plate is divided into a number of regions of which the values of thickness are assumed to be constant and are given by the known thickness function of the plate the close form frequency function that yields the eigenvalues of the plate is extracted by considering the condition of continuity in displacement and slope between the regions and by considering the simply supported boundary condition of the plate it is shown by several case studies that the proposed method has good convergence characteristics and yields accurate eigenvalues and mode shapes compared with other analytical methods including fem ansys

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

new types of vibration modes for stepped membranes frequency spectra for vibrations of rectangular membranes with a step discontinuity in density along a line parallel to an edge are investigated particularly with a view to finding explicit analytical solutions cases of exact harmonic sub spectra with explicit trigonometrical mode functions are found it is stressed that the complete set of modes also includes hyperbolic functions in the description of the amplitude functions for one section of the membrane furthermore modes with a straight line segment in cross section are exposed at the transition between trigonometric and hyperbolic amplitude functions for certain critical density ratio values tables of spectra which incorporate numerically determined frequencies are presented for several configurational examples features such as mode crossing are revealed

vibration analysis of circular mindlin plates using the differential quadrature method abstract axisymmetric free vibrations of moderately thick circular plates described by the linear shear deformation mindlin theory are analyzed by the differential quadrature dq method the first fifteen natural frequencies of vibration are calculated for uniform circular plates with free simply supported and clamped edges through these computations the capability and simplicity of the differential quadrature method for moderately thick plate eigenvalue analysis is demonstrated and convergence and accuracy are thoughtfully examined the case of rigid point support at the plate centre is also considered in the present paper for which special attention is paid to the capability and convergence of the current method

axisymmetric vibrations of solid circular and annular membranes with continuously varying density abstract the present paper reports the results from a series of numerical experiments dealing with the determination of the lower natural frequencies for the transverse vibration of annular membranes including the special case of a solid circular membrane when the mass per unit area varies linearly quadratically and cubically with the radial co ordinate the frequency coefficients have been determined using 1 the differential quadrature method 2 the finite element technique 3 an optimized and or improved rayleigh quotient method and 4 a lower bound based on the stodola vianello method excellent agreement is achieved among the different methodologies

regularity of the velocity field for euler vortex patch evolution author s coutand daniel shkoller steve abstract we consider the vortex patch problem for both the 2 d and 3 d incompressible euler equations in 2 d we prove that for vortex patches with h k 0 5 sobolev class contour regularity k ge 4 the velocity field on both sides of the vortex patch boundary has h k regularity for all time in 3 d we establish existence of solutions to the vortex patch problem on a finite time interval 0 t and we simultaneously establish the h k 0 5 regularity of the two dimensional vortex patch boundary as well as the h k regularity of the velocity fields on both sides of vortex patch boundary for k ge 3

on the wave equation with a large rough potential we prove an optimal dispersive l decay estimate for a three dimensional wave equation perturbed with a large nonsmooth potential belonging to a particular kato class the proof is based on a spectral representation of the solution and suitable resolvent estimates for the perturbed operator

time decay estimates for the wave equation with potential in dimension two abstract we study the wave equation with potential u t t u v u 0 in two spatial dimensions with v a real valued decaying potential with h v we study a variety of mapping estimates of the solution operators cos t h and sin t h h under the assumption that zero is a regular point of the spectrum of h we prove a dispersive estimate with a time decay rate of t 1 2 a polynomially weighted dispersive estimate which attains a faster decay rate of t 1 log t 2 for t 2 finally we prove dispersive estimates if zero is not a regular point of the spectrum of h

some remarks on strichartz estimates for homogeneous wave equation abstract we give several remarks on strichartz estimates for homogeneous wave equation with special attention to the cases of l x estimates radial solutions and initial data from the inhomogeneous sobolev spaces in particular we give the failure of the endpoint estimate l t 4 l x for n 2

the natural vibration of a conical shell with an annular end plate in this paper natural frequencies and mode shapes for a conical shell with an annular end plate or a round end plate are investigated in detail by combining the vibration theory with the transfer matrix method the governing equations of vibration for this structure are expressed in terms of a matrix differential equation and a novel recurrence formula method that can close in on analytical solution of transfer matrix is presented once the transfer matrix of single component has been determined and the product of each component matrix and the joining matrix can obtain entire structure matrix the frequency equations and mode shape functions are represented in terms of the elements of the structural transfer matrices the 3d finite element numerical simulations have verified the present formulas of natural frequencies and mode shapes the conclusions show that the transfer matrix method can accurately obtain natural vibration characteristics of the conical shell with an annular end plate

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

finite element analysis of three dimensional vibrations of thick circular and annular plates abstract three dimensional vibrations of thick circular and annular plates are analyzed by a finite element method which with a properly assumed set of displacement field is different from the traditional 3 d finite element analysis and is reduced to a sequence of 2 d analyses one for each circumferential wave number the present approach has several unique features 1 it can obtain vibration frequencies which are comparable to or as accurate as those by other three dimensional approaches whenever comparisons between them are possible and yet the formulation of the present method is simpler and its application is straightforward 2 different simply supported boundary conditions can be exactly imposed with the present approach the latter feature may be quite difficult if not impossible for other methods in the present analysis vibration frequencies of a circular and an annular plate under different combinations of boundary conditions wave numbers and finite element meshes are calculated vibration characteristics are examined and some typical mode shapes are shown graphically then the results of some example problems by the present method are compared to those available in the literature to show its validity and accuracy

initial boundary layer associated with the nonlinear darcy brinkman system abstract we study the interaction of initial layer and boundary layer in the nonlinear darcy brinkman system in the vanishing darcy number limit in particular we show the existence of a function of corner layer type so called initial boundary layer in the solution of the nonlinear darcy brinkman system an approximate solution is constructed by the method of multiple scale expansion in space and in time we establish the optimal convergence rates in various sobolev norms via energy method

numerical determination of the density profile of an inhomogeneous membrane solution of the inverse vibration problem given one or more vibrational modes of a membrane the free vibration equation can be applied to infer the mass surface density this paper considers determining the surface density of an inhomogeneous membrane from digitized holographic projections interferograms of the modeshapes spatially discrete numerical models of the membrane surface are presented which can be used to solve both forward and inverse vibration problems the accuracy of the discrete models is examined for exactly solvable free vibration problems involving inhomogeneous membranes for the solution of the inverse problem error estimates are given for the mass surface density deduced from modeshape interferograms the practicability of the method is investigated using simulated experimental data for membranes with composite and continuously inhomogeneous density profiles strategies are discussed for reducing errors in the reconstructed densities

vibration analysis of membranes and plates by a discrete least squares technique abstract a discrete least squares technique for computing the free transverse vibrations of membranes and plates is presented the proposed technique consists of two steps in the first step a quadratic matrix eigenvalue problem resulting from the minimization of a discrete residual error function is solved if the accuracy of the eigenvalue approximations is not sufficient these initial approximations can be improved by using the gauss newton method numerical results concerning the vibration of the fixed circular membrane fixed circular membrane with circular ridges and clamped circular plate are reported as shown the trial functions need not satisfy any of the prescribed boundary conditions which makes possible the vibration analysis of membranes and plates with complicated shape at the end of the paper a short discussion is given on how to use the proposed technique in solving problems of higher complexity and some possible directions in the development of this technique are outlined

free vibrations of non homogeneous circular and annular membranes a non homogeneous membrane is a membrane that has variable thickness or material density several recent publications deal with the axisymmetric and antisymmetric modes of transverse vibration for a composite doubly connected and solid membrane with constant or variable density in this paper exact solutions for both the axisymmetric and antisymmetric modes of circular and annular membranes with any piecewise polynomial variation of the density are given using a power series solution the dynamic problem is solved exactly using a recurrence relationship up to any accuracy desired by deriving the dynamic stiffness matrix for circular and annular membrane elements many results for linear parabolic and cubic variation of complete and annular membranes are solved using the dynamic stiffness method and presented in the tables

transverse vibrations of composite membranes of arbitrary boundary shape this paper deals with an approximate method based on the technique of conformal mapping and a variational formulation which allows for a straightforward solution of the title problem for a certain type of composite membranes numerical results are presented for membranes of regular polygonal shape whose inner circular core possesses a density 1 while the remaining is characterized by 2 the fundamental eigenvalues are also verified by the fourier expansion collocation method and by a finite element algorithm

viscous boundary layers for the navier stokes equations with the navier slip conditions we tackle the issue of the inviscid limit of the incompressible navier stokes equations when the navier slip with friction conditions are prescribed on impermeable boundaries we justify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in prandtl s theory and a linear behavior this analysis holds for general regular domains in both dimensions two and three

note on loss of regularity for solutions of the 3 d incompressible euler and related equations one of the central problems in the mathematical theory of turbulence is that of breakdown of smooth indefinitely differentiable solutions to the equations of motion in 1934 j leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3 d incompressible navier stokes equations the problem is still open we show in this report that breakdown of smooth solutions to the 3 d incompressible slightly viscous i e corresponding to high reynolds numbers or highly turbulent navier stokes equations cannot occur without breakdown in the corresponding solution of the incompressible euler ideal fluid equation we prove then that solutions of distorted euler equations which are equations closely related to the euler equations for short term intervals do breakdown

a new boundary condition for the three dimensional navier stokes equation and the vanishing viscosity limit in this paper we propose a new vorticity boundary condition for the three dimensional incompressible navier stokes equation for a general smooth domain in r3 this boundary condition is motivated by the generalized navier slip boundary condition involving the vorticity it is shown first that such an initial boundary value problem is well posed at least local in time furthermore more importantly we obtain some estimates on rate of convergence in c 0 t h1 and c 0 t h2 of the solutions to the corresponding solutions of the ideal euler equations with the standard slip boundary condition

the euler limit of the navier stokes equations and rotating fluids with boundary in this paper we study the convergence of weak solutions of the navier stokes equations in some particular domains with different horizontal and vertical viscosities when they go to zero with different speeds the difficulty here comes from the dirichlet boundary conditions precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero then the solutions converge to the solution of the euler system we study the same limit for rotating fluids with rossby number also going to zero

regular articlegeneralized strichartz inequalities for the wave equation we make a synthetic exposition of the generalized strichartz inequalities for the wave equation obtained in 6 together with the limiting cases recently obtained in 13 with as simple proofs as possible the proofs combine stationary phase estimates dyadic decompositions the hardy littlewood inequality or the holder inequality in time and abstract duality and interpolation arguments

free vibration analysis of an eccentric hollow cylinder using exact 3d elasticity theory abstract the translational addition theorem for cylindrical wave functions in conjunction with the appropriate orthogonal series expansions and the pertinent boundary conditions are employed to develop an exact 3d elasticity solution for free vibrations of a simply shear diaphragm supported elastic circular cylinder of finite length with an eccentrically located inner circular cavity the frequency spectrum plots of the first several eigenfrequencies are presented in a wide range of dimensionless eccentricities for selected length to radius and inner outer radius ratios also a detailed study on the 2d free vibration characteristics of an infinite eccentric cylinder is included the numerical results describe the imperative influence of cavity eccentricity mode type and radii and length ratios on the vibrational characteristics of the hollow cylinder it is observed that the introduction of bore eccentricity causes not only an increase in the number of resonant frequencies through the splitting of degenerate modes of the unperturbed problem but also changes the appearance order of natural vibration modes the accuracy of solutions is checked through appropriate convergence studies and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature

on the vanishing viscosity limit of 3d navier stokes equations under slip boundary conditions in general domains we consider the vanishing viscosity limit for the navier stokes equations with certain slip without friction boundary conditions in a bounded domain with non flat boundary in particular we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary the proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity

uniform regularity for the navier stokes equation with navier boundary condition we prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the navier stokes equation with the navier boundary condition has a strong solution this solution is uniformly bounded in a conormal sobolev space and has only one normal derivative bounded in l this allows us to obtain the vanishing viscosity limit to the incompressible euler system from a strong compactness argument

the fundamental frequency of non homogeneous rectangular membranes the present study deals with the case in which the density of the membrane is a linear function of the x variable two independent solutions are obtained using the optimized galerkin kantorovich approach and the differential quadrature method

global regularity for vortex patches we present a proof of chemin s 4 result which states that the boundary of a vortex patch remains smooth for all time if it is initially smooth

axisymmetric vibrations of non homogeneous polar orthotropic annular plates of variable thickness in this study of the free axisymmetric vibrations of non homogeneous polar orthotropic annular plates of exponentially varying thickness on the basis of the classical theory of plates the chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates the non homogeneity of the plate material is assumed to arise due to the variation of young s moduli and density which are assumed to vary exponentially with the radius vector the effect of various plate parameters such as radii ratio rigidity ratio non homogeneity and thickness variation on the vibrational characteristics of the plate have been studied for three different boundary conditions normalized displacements are presented for a specified plate for the first three modes of vibration a comparison of results with those available in the literature has been presented

closed form solutions for the free longitudinal vibration of inhomogeneous rods this paper aims at presenting a family of exact solutions for the longitudinal vibration of variable area rods area variations that give solutions in terms of the confluent hypergeometric function are being sought for and the governing differential equation is appropriately reduced to the confluent hypergeometric differential equation using a generic transformation the eigenfrequencies of rods with certain area variations subjected to classical boundary conditions are obtained and the parametric space of the solutions obtained is studied these solutions are also highly useful in other topics of study such as torsional vibration of rods and wave propagation in ducts with variable cross sectional areas since the governing differential equations are very similar

transverse vibration and stability of an eccentric rotating circular plate a thin circular plate rotating at constant angular speed around the axis perpendicular to the plane of the plate is investigated in this paper the axis of rotation is parallel to the plate s axis of symmetry and the distance between them is the plate s eccentricity the outer edge of the plate is attached to a rigid body rotating together with the plate the stresses and displacements in the plate s middle plane are determined in the paper the natural frequencies of the transverse vibration with respect to angular speed and eccentricity are determined using galerkin s method the mode shapes for the certain frequencies are shown due to the plate s eccentricity and rotation the mode shapes are deformed in comparison with the plate without eccentricity it is shown that frequencies split for the asymmetric mode shapes so that there are two different frequencies in those cases the critical angular speed which results in stability loss in the first mode is determined

vibration analysis of a nearly axisymmetric shell structure using a new finite ring element abstract a new conical ring element to be used in connection with the finite element method fem is developed which considers the effects of slight local deviations from an axisymmetric ring to develop the proposed finite element the displacements of a point in the ring element are assumed by a pair of the natural modes of a ring with local deviation symmetric and asymmetric modes by using the presented finite elements a fem program is also developed to analyze free vibrations of a nearly axisymmetric shell structure the developed program is applied to a vibration analysis of a korean bell as an example which shows that the program is very efficient and saves much computation time for shell structures slightly deviating from axisymmetry compared to commercial fem codes

zero viscosity limit of the incompressible navier stokes equations with sharp vorticity gradient abstract it is well known that the 3d incompressible euler equations admit some local in time solutions for which the vorticity is piecewise smooth and discontinuous across a smooth time dependent hypersurface which evolves with the flow in this paper we prove that such a solution can be obtained as zero viscosity limit of strong solutions to the navier stokes equations whose vorticity has sharp variations near the hypersurface associated with the inviscid limit indeed we exhibit some sequences of exact solutions to the navier stokes equations with vanishing viscosity which are given by multi scale asymptotic expansions involving some characteristic boundary layers given by some linear pdes the convergence and the validity of the expansion are guaranteed on the time interval associated with the solution to the euler equations

strichartz estimates and maximal operators for the wave equation in r3 abstract we prove sharp strichartz type estimates in three dimensions including some which hold in reverse space time norms for the wave equation with potential these results are also tied to maximal operator estimates studied by rogers villarroya of which we prove a sharper version as a sample application we use these results to prove the local well posedness and the global well posedness for small initial data of semilinear wave equations in r 3 with quintic or higher monomial nonlinearities

attractors of the velocity vorticity voigt model of the 3d navier stokes equations with damping abstract in this paper we prove the existence of global and exponential attractors of optimal regularity of a regularization for the three dimensional navier stokes equations with damping which is called the three dimensional velocity vorticity voigt vvv system proposed by larios pei and rebholz larios et al 2019 differently there is no voigt term 2 a w t in the second equation of system 1 1 below the proof is based on some energy estimates in sobolev spaces and the semigroup decomposition

free vibration analysis of circular plates with multiple circular holes using indirect biems in this paper a semi analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and fourier series all the kernels in the indirect formulation are expanded into degenerate form by uniformly collocating points on the boundary a linear algebraic system can be constructed the direct searching approach is adopted to determine the natural frequency through singular value decomposition svd after determining the unknown fourier coefficients the corresponding mode shape is obtained by using the indirect boundary integral formulations the results of the annular plate as a special case are compared with the analytical solution to verify the validity of the present method for the cases of circular plates with multiple circular holes the results are also compared with those of finite element method fem using abaqus besides the effect of eccentricity of the hole on the natural frequencies is also considered good accuracy high rate of convergence and computational efficiency are the main features of the present method due to the semianalytical procedure r 2007 elsevier ltd all rights reserved

remarks about the inviscid limit of the navier stokes system in this paper we prove two results about the inviscid limit of the navier stokes system the first one concerns the convergence in hs of a sequence of solutions to the navier stokes system when the viscosity goes to zero and the initial data is in hs the second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions we present here a simple proof which also works in the 3d case the 3d case is new

strichartz estimates for dirichlet wave equations in two dimensions with applications we establish the strauss conjecture for nontrapping obstacles when the spatial dimension n is two as pointed out in 7 this case is more subtle than n 3 or 4 due to the fact that the arguments of the first two authors 11 burq 1 and metcalfe 9 showing that local strichartz estimates for obstactles imply global ones require that the sobolev index equal 1 2 when n 2 we overcome this difficulty by interpolating between energy estimates 0 and ones for 1 2 that are generalizations of minkowski space estimates of fang and the third author 4 5 the second author 12 and sterbenz 14

uniform regularity and relaxation limit for the outer pressure problem of gas dynamics with several thermal nonequilibrium modes abstract we study in this paper the uniform regularity and relaxation limit for the outer pressure problem of one dimensional gas dynamics with several thermal nonequilibrium modes the uniform regularity is established for the initial data satisfying the compatible conditions on the boundary the relaxation limit to equilibrium flow or frozen flow is also investigated by a compactness argument

on the convergence rate of the euler α an inviscid second grade complex fluid model to the euler equations we study the convergence rate of the solutions of the incompressible euler an inviscid second grade complex fluid equations to the corresponding solutions of the euler equations as the regularization parameter approaches zero first we show the convergence in hs s n 2 1 in the whole space and that the smooth euler solutions exist at least as long as the corresponding solution of the euler equations next we estimate the convergence rate for two dimensional vortex patch with smooth boundaries

free axisymmetric vibration of laminated transversely isotropic annular plates based on the basic equations of three dimensional theory of elasticity this paper establishes the state space equation of the axisymmetric vibration of laminated annular plates composed of transversely isotropic layers taking advantage of the finite hankel transform four exact solutions are obtained for four different types of boundary conditions the calculating methods of frequencies and mode shapes are presented lastly numerical results are given to validate the present method

a remark on lp boundedness of wave operators for two dimensional schrodinger operators let h v be a two dimensional schrodinger operator with a real potential v x satisfying the decay condition 6 let h0 we show that the wave operators are bounded in lp r2 under the condition that h has no zero resonances or bound states in this paper the condition imposed in a previous paper k yajima commun math phys 208 125 152 1999 is removed

the sound power of an individual mode of a clamped free annular plate abstract the main aim of this study is an analysis of sound radiation of some clamped free and free clamped annular plates the plates are embedded in some infinite perfectly rigid baffles and vibrate with the free field condition satisfied the kirchhoff love linear theory of a perfectly elastic plate is used to solve the plates equations of motion the sound pressure at the plates surfaces is expressed by its hankel transform the closed path integral technique known from the literature and the stationary phase method are used to find the standardized active and reactive sound power of an individual mode in the form of some high frequency asymptotic formulae useful for some highly efficient engineering computations their non oscillating and oscillating parts have been separated it is assumed that the vibration and sound radiation are axisymmetric and time harmonic low fluid loading is also assumed the complex sound power of an individual mode forms the basis for computing the total sound power of some excited and damped vibrations in the fluid the total sound power is not discussed in this study

bounds on natural frequencies of composite circular membranes integral equation methods this paper is concerned with finding upper and lower bounds for the natural frequencies of vibration of a circular membrane with stepped radial density such problems involving discontinuous coefficients in the differential equation may be treated by using classical variational methods however it is shown here that eigenvalue estimation techniques based on an integral equation formulation are more effective integral equation methods provide more accurate upper bounds for a comparable amount of effort and supply improvable lower bounds as well

natural frequencies of transverse vibrations of non uniform circular and annular plates abstract this paper presents a method for the free transverse vibration analysis of thin elastic isotropic uniform and non uniform circular and annular plates the circumferential mode numbers n 0 and n 1 are dealt with in this paper the method is a hybrid of plate theory and finite element analysis the plate is subdivided into one circular and many annular finite elements two new finite elements were developed the first type being a circular plate and the second an annular plate the displacement functions of the finite element model are the classical solution shape functions of plate theory mass and stiffness matrices are determined by precise analytical integration the free vibrations of uniform circular and annular plates are studied by this method as well as non uniform plates the results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors this method combines the advantages of the standard finite element analysis and the high accuracy formulation provided by the use of displacement functions derived from plate theory instead of the usual low order polynomials the present method is remarkable for the fact that it enables us to determine with equal precision both low and high natural frequencies

vibration of inhomogeneous strings rods and membranes this paper is concerned with the vibration of inhomogeneous strings rods and membranes with continuously varying properties the work has two main purposes first we provide specific examples for which closed form exact solutions are obtained apart from their intrinsic interest such examples serve as benchmark problems against which the accuracy of approximate analytical or numerical methods may be assessed the second objective is to demonstrate the effectiveness of an integral equation based method for obtaining lower bounds for vibration frequencies

vibroacoustic response of an eccentric hollow cylinder abstract the linear 3d elasticity theory in conjunction with the classical method of separation of variables and the translational addition theorem for cylindrical wave functions are employed to investigate the three dimensional steady state sound radiation characteristics of an arbitrarily thick eccentric hollow cylinder of infinite length submerged in an unbounded ideal acoustic medium and subjected to arbitrary time harmonic on surface mechanical drives the spatial fourier transform along the shell axis and fourier series expansion in the circumferential direction are utilized to obtain a formal integral expression for the radiated pressure field in the frequency domain the method of stationary phase is subsequently implemented to evaluate the integral for an observation point in the far field the analytical results are illustrated with numerical examples in which air filled water submerged concentric and eccentric steel cylinders are driven by harmonic concentrated radial and transverse surface loads effects of excitation and cylinder eccentricity on the far field radiated pressure amplitudes directivities are discussed and contributions from pseudo rayleigh whispering gallery and axially guided waves are examined through selected spatial dispersion patterns limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature

an approximate approach to study the free vibration of a string with an arbitrary variation in mass density and tension with attached concentrated masses and its application to hanging chain and rotating cord abstract a multi stepped approximation has been developed to study the free vibration of a string with arbitrary variation in the tension and the mass density to achieve this objective a novel exact approach is developed to study free vibration of a string with n uniform sections of different mass densities under n different tensions with n 1 attached concentrated masses and springs at the ends the two advantages of this approach are that it leads to a single frequency equation for any number of sections and the same computer program can be used to solve different problems using pertinent data this method is applied to cases where tension and or mass density changes continuously such as hanging chain rotating chain or inhomogeneous strings vibrating in either horizontal or vertical position in all cases the results obtained using this approach agreed with previous results obtained using exact and approximate methods it was found that natural frequencies of a fixed string under constant tension t with linear variation in the mass density x 0 1 x l can be approximated using a very simple equation n n l t 0 1 0 5 1 2 and results reasonably agree with previous results for a wide range of new results for many other cases are also presented in what follows

vanishing viscosity limit for homogeneous axisymmetric no swirl solutions of stationary navier stokes equations abstract 1 homogeneous axisymmetric no swirl solutions of three dimensional incompressible stationary navier stokes equations which are smooth on the unit sphere minus the north and south poles have been classified in this paper we study the vanishing viscosity limit of sequences of these solutions as the viscosity tends to zero some sequences of solutions c l o c m converge to solutions of euler equations on the sphere minus the poles while for other sequences of solutions transition layer behaviors occur for every latitude circle there are sequences which c l o c m converge respectively to different solutions of the euler equations on the spherical caps above and below the latitude circle we give detailed analysis of these convergence and transition layer behaviors

some exact solutions of the vibration of non homogeneous membranes the purpose of this note is to show that the linear density variation case studied by masad has a closed form exact solution also we shall present another exact solution for the vibration of a continuously non homogeneous annular membrane

an efficient approach for the assembly of mass and stiffness matrices of structures with modifications the finite element method is one of the most common tools for the comprehensive analysis of structures with applications reaching from static often nonlinear stress strain to transient dynamic analyses for single calculations the expense to generate an appropriate mesh is often insignificant compared to the analysis time even for complex geometries and therefore negligible however this is not the case for certain other applications most notably structural optimization procedures where the re meshing effort is very important with respect to the total runtime of the procedure thus it is desirable to find methods to efficiently generate mass and stiffness matrices allowing to reduce this effort especially for structures with modifications of minor complexity e g panels with cutouts therefore a modeling approach referred to as energy modification method is proposed in this paper the underlying idea is to model and discretize the basis structure e g a plate and the modifications e g holes separately the discretized energy expressions of the modifications are then subtracted from or added to the energy expressions of the basis structure and the coordinates are related to each other by kinematical constraints leading to the mass and stiffness matrices of the complete structure this approach will be demonstrated by two simple examples a rod with varying material properties and a rectangular plate with a rectangular or circular hole using a finite element discretization as basis convergence studies of the method based on the latter example follow demonstrating the rapid convergence and efficiency of the method finally the energy modification method is successfully used in the structural optimization of a circular plate with holes with the objective to split all its double eigenfrequencies