free vibrations of rectangular plates with interior point supports abstract a new approach for the representation of point supports in the vibration analysis of plates was presented in earlier work 1 3 the approach was based on simulating a point support on a free edge as a zero of a flexibility function representing a fictitious elastic restraint distribution over the free edge the application of this approach to a variety of problems concerning rectangular plates with point supports located on the free edges was demonstrated in subsequent studies 4 5 the present study provides an extension of the flexibility function approach to the problem of rectangular plates with interior point supports in the analysis a rectangular plate is considered with two opposite edges simply supported and classical boundary conditions on the other two edges with one or more interior point supports along the line perpendicular to the simply supported edges extensive numerical results for a range of problem parameters have been obtained the results show the versatility of the flexibility function approach in the vibration analysis of rectangular plates with arbitrarily located interior point supports

an analytical solution for the free vibration analysis of rectangular plates resting on symmetrically distributed point supports abstract a general analytical solution is obtained for the free vibration of rectangular plates supported on their lateral surface by symmetrically distributed point supports highly accurate eigenvalues are provided for a square plate supported at various points along the diagonal results are compared with earlier findings obtained by a finite element method it is shown that the method may be extended to solve various other problems the tabulation of eigenvalues appears to be the most comprehensive yet made for a square plate with point supports on the diagonals

a geometric approach to the linear penrose transform on montre que sous une certaine condition cohomologique le theoreme de witten iseuberg yasskin et green sur la transformee de penrose inverse d une connexion est vraie dans une situation generale

physical space time and nonrealizable text cr structures space time views leading up to einstein s general relativity are described in relation to some of poincare s early ideas on the subject the basic geometry of twistor theory is introduced as it arises both from minkowski space time and the more general curved einstein models it is shown how this provides a cr structure this being in essence another of poincare s poioneering concepts in a natural way nonrealizable cr structure can arise and an example is presented due to c d hill g a j sparling and the author of a complex manifold with boundary which cannot be extended as a complex manifold beyond its c sup infinity boundary

variational formulation of acoustic radiation from submerged spheroidal shells the surface variational principle svp governing acoustic interaction between a vibrating surface and a surrounding fluid is combined with the dynamic equations governing response of a shell of revolution subjected to axisymmetric harmonic excitation ritz series representations are used to represent the spatial dependence of the surface pressure and shell displacement components two formulations are presented with the difference being whether an intermediate computation of the in vacuo modes is performed the direct approach in which the ritz coefficients are determined directly from the coupled formulation is used to validate the svp approach for the case of a spherical shell whose response is known analytically for the case of a slender spheroidal shell the direct approach is compared to the results obtained from the modal approach in which a truncated set of in vacuo modes forms the basis functions representing displacement the aspect ratio and shell properties for this evaluation are select

radon penrose transform for d modules abstract let formula be a correspondence of complex analytic manifolds fbe a sheaf onx and m be a coherent d x module consider the associated sheaf theoretical and d module integral transforms given by sf rg f 1f d and s m g f 1 m whererg andf 1 resp g and f 1 denote the direct and inverse image functors for sheaves resp for d modules andd ds dyis the difference of dimension betweensandy in this paper assuming thatfis smooth gis proper and f g is a closed embedding we prove some general adjunction formulas for the functors sand s moreover under an additional geometrical hypothesis we show that the transformation sestablishes an equivalence of categories between coherent d x modules modulo flat connections and coherent d y modules with regular singularities along an involutive manifoldv modulo flat connections herevis determined by the geometry of the correspondence applications are given to the case of penrose s twistor correspondence

plate vibration under irregular internal supports this paper studies the problem of plate vibration under complex and irregular internal support conditions such a problem has its widely spread industrial applications and has not been addressed in the literature yet partially due to the numerical difficulties a novel computational method discrete singular convolution dsc is introduced for solving this problem the dsc algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries boundary conditions and internal support conditions convergence and comparison studies are carried out to check the validity and accuracy of the dsc method case studies are considered to the combination of a few different boundary conditions and irregular internal supports the latter are generated by using an image processing algorithm completely independent verifications are conducted by using the established pb 2 ritz method which is available for two relatively simpler support patterns the morphology of the first few eigenmodes is found to be localized to largest support free spatial regions

a unified approach for the solution of the fokker planck equation this paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the fokker planck equation the unified features of the discrete singular convolution algorithm are discussed it is demonstrated that different implementations of the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point three benchmark stochastic systems the repulsive wong process the black scholes equation and a genuine nonlinear model are employed to illustrate the robustness and to test the accuracy of the present approach for the solution of the fokker planck equation via a time dependent method an additional example the incompressible euler equation is used to further validate the present approach for more difficult problems numerical results indicate that the present unified approach is robust and accurate for solving the fokker planck equation

variational formulation of interior cavity frequencies for spheroidal bodies this paper presents interior cavity frequencies for spheroidal bodies in cases of neumann and dirichlet homogenous boundary conditions the helmholtz wave equation is expressed in terms of prolate spheroidal coordinates from which a variational formulation is derived for the determination of the interior cavity frequencies the search of stationarity is performed by means of a rayleigh ritz type expansion of trial functions the trial functions are expressed as a double summation of basis functions in radial and angular coordinates a variable transformation is applied to the variational form in order to have homogenous boundary conditions which are essential for establishing a complete function space of the associated boundary conditions the present analysis is verified by comparisons of interior frequencies of a spherical body of prolate spheroidal bodies and of the interior characteristic functions with the radial and angular functions obtained from prolate spheroidal differential equations interior frequencies are tabulated for various aspect ratios of spheroidal bodies in accordance with harmonic orders in azimuthal directions for both neumann and dirichlet conditions

on the free flexural vibration of rectangular plates with straight or curved internal line supports abstract the rayleigh ritz method is used with simple polynomials as admissible functions to obtain the eigenvalue equation for the free vibration of a rectangular plate which has an internal line support lying along a line describable in terms of a general polynomial numerical and graphical results are presented for plates with internal supports lying along straight lines for which comparison results also exist and for plates with the supports lying along different types of curves including a central circular support

complex power reciprocity and radiation modes for submerged bodies this study of the surface interaction between a submerged body and the surrounding fluid begins by developing reciprocity relations between alternative pressure and normal velocity distributions on the wetted surface a corollary of these principles is proof of the symmetry of the matrix representing the acoustic contribution to the structural impedance even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric the reciprocity properties lead to two eigenvalue problems whose solution yields velocity and pressure radiation modes each of which decouples the complex surface acoustic power the matrices required to obtain the eigensolutions are shown to arise in the ordinary course of modeling fluid structure interaction further analysis reveals that the velocity and pressure modes occur in a one to one correspondence with a relative phase angle that decreases monotonically as the radiated power increases relative to the reactive power using the radiati

derivation of a ritz series modeling technique for acoustic cavity structural systems based on a constrained hamilton s principle hamilton s principle for dynamic systems is adapted to describe the coupled response of a confined acoustic domain and an elastic structure that forms part or all of the boundary a key part of the modified principle is the treatment of the surface traction as a lagrange multiplier function that enforces continuity conditions at the fluid solid interface the structural displacement fluid velocity potential and traction are represented by ritz series where the usage of the velocity potential as the state variable for the fluid assures that the flow is irrotational designation of the coefficients of the potential function series as generalized velocities leads to corresponding series representations of the particle velocity displacement and pressure in the fluid which in turn leads to descriptions of the mechanical energies and virtual work application of the calculus of variations to hamilton s principle yields linear differential algebraic equations whose form is identical to those governing mech

on some integral inequalities similar to hardy s inequality abstract the aim of the present paper is to establish some new integral inequalities which claim their origin in the well known hardy s integral inequality the method by which we obtain our results is quite elementary and based on the idea used by levinson to obtain the generalizations of hardy s integral inequality

some hardy type inequalities in this paper some new hardy type inequalities involving many functions are obtained these on the one hand generalize and on the other hand improve some existing results by isumi and isumi levinson and pachpatte on this famous type of inequalities

vibrations of composite plates with intermediate line supports abstract free vibrations of rectangular composite plates with arbitrary support conditions along the edges and an arbitrary number of intermediate line supports are investigated using the rayleigh ritz method a procedure is presented for generating polynomial approximation functions that satisfy the essential boundary conditions and zero displacement constraints along each line support and the stiffness and mass matrix coefficients are obtained by exact integration plates that are continuous over many supports are analyzed and the effects lay up and material properties are investigated an exact solution is found for predicting some of the vibration modes of plates with simple supports along the edges and equal length spans in each direction in this case the fundamental natural frequency is always predicted exactly and simple results are obtained for finding which lay up maximizes the natural frequency of the plate

on dowell s simplification for acoustic cavity structure interaction and consistent alternatives a widely employed description of the acoustical response in a cavity whose walls are compliant which was first proposed by dowell and voss 1962 aiaa j 1 476 477 uses the modes of the corresponding cavity with rigid walls as basis functions for a series representation of the pressure it yields a velocity field that is not compatible with the movement of the boundary and the system equations do not satisfy the principle of reciprocity the simplified formulation is compared to consistent solutions of the coupled field equations in the time and frequency domains in addition this paper introduces an extension of the ritz series method to fluid structure coupled systems that satisfies all continuity conditions by imposing constraint equations to enforce any such conditions that are not identically satisfied by the series a slender waveguide terminated by an oscillator is analyzed by each method the simplified formulation is found to be very accurate for light fluid loading except for the pressure field at frequencies below the fundamental rigid cavity resonance whereas the ritz series solution is found to be extremely accurate in all cases

weak solutions of the massless field equations we consider weak solutions of the zero rest mass z r m equations described in eastwood et al 1981 the space of hyperfunctions which contains the space of distributions is defined and we consider hyper function solutions of the equations on real minkowski space m i and its conformal compactification m we define a hyperfunction z r m field to be future or past analytic if it is the boundary value of a holomorphic z r m field on the future or past tube of complex minkowski space respectively and we demonstrate that any field on m i that is the sum of future and past analytic fields extends as a hyperfunction z r m field to all of m it is shown that any distribution solution on m i splits as required and hence extends as a hyperfunction solution to m twistor methods are then used to show that the same applies in the more general case of hyperfunction solutions on m i this leads to an alternative proof of the main result of wells 1981 a hyperfunction z r m field on compactified real minkowski space is a unique sum of future and past analytic solutions

hyperfunction solutions of the zero rest mass field equations in this paper it is shown how the penrose transform maps tangential hyperfunction dolbeault groups with coefficients in a power of the hyperplane section bundle on the hyperquadric of null twistors in projective twistor space isomorphically to all hyperfunction solutions of the massless field equations of nonnegative helicity on compactified minkowski space this is an extension of the penrose transform which generated real analytic solutions of the same field equations on the same space cf eastwood m penrose r wells r o 10 in additions one obtains the result that each hyperfunction solution of the massless field equations of nonnegative helicity is the sum of massless fields of positive and negative frequency a generalization of the usual fourier decomposition for solutions with appropriate growth conditions

a conformal holomorphic field theory a formulation of a field theory on the complex minkowski space in terms of complex differential geometry is proposed it is also shown that our model of field theory differs from the standard model on the real minkowski space only in the limit of high energy

on a new class of hardy type inequalities in this paper we establish a new class of integral inequalities which originate from the well known hardy s inequality the analysis used in the proofs is quite elementary and is based on the idea used by levinson to obtain generalisations of hardy s inequality

implementation of a constrained ritz series modeling technique for acoustic cavity structural systems a prior study ginsberg j h 2010b j acoust soc am 127 2749 2758 used ritz series in conjunction with hamilton s principle to derive general equations describing the time domain response of an acoustic cavity bounded by an elastic structure the equations of motion are supplemented by constraint equations that explicitly enforce velocity continuity at the cavity s surface these constraints are imposed by the surface traction which is represented by unknown coefficients of ritz type series the resulting set of equations are differential algebraic type three methods are presented to convert the governing equations to forms that are familiar to structural acoustics including one that transforms them from differential algebraic type to the standard ordinary differential equations associated with linear multi degree of freedom vibratory systems in cases where only the structure is excited the formulation offers options as to how displacement velocity boundary conditions on the nonstructural b

eigenfrequencies of line supported rectangular plates abstract a set of series consisting of a combination of free vibrating beam functions and polynomials is used as the admissible functions in the rayleigh ritz method to study the problem of the flexural vibration of thin uniform thickness orthotropic rectangular plates which may be continuous over several supports in one or two directions in practice which kind of free vibrating beam functions are used is determined by the boundary conditions of the plate the starting order of the beam eigenfunctions and the number of terms in the polynomials in each direction depend on the number of intermediate line supports in that direction the coefficients of the polynomials are decided by the boundary conditions of the plate and the locations of the line supports some numerical results are given for the simply supported and or clamped rectangular plates with two and three spans in one and two directions it is demonstrated that the method may be used to tackle such plate problems and has considerable accuracy and fast convergence compared with the available results the difficulty of application not being greater than any other methods

vibration analysis of corner supported mindlin plates of arbitrary shape using the lagrange multiplier method abstract this paper presents the first known solutions of the problem of free flexural vibration of corner supported mindlin plates of arbitrary shape a hybrid numerical approach combining the rayleigh ritz method and the lagrange multiplier method has been developed to solve the plate vibration problem the algorithm uses the pb 2 shape functions to account for different geometries and lagrange multipliers to impose zero lateral deflection constraints at plate corners the method of solution is applicable to arbitrarily shaped plates with corner supports in this paper however only triangular skew and annular sector plates are chosen for the purpose of demonstration some comparison studies for corner supported thin square plates are made to verify the accuracy of the derived solutions

on the numerical solution of the sine gordon equation in this the first of two papers on the numerical solution of the sine gordon equation we investigate the numerical behavior of a double discrete completely integrable discretization of the sine gordon equation for certain initial values in the vicinity of homoclinic manifolds this discretization admits an instability in the form of grid scale oscillations we clarify the nature of the instability through an analytical investigation supported by numerical experiments in particular a perturbation analysis of the associated linear spectral problem shows that the initial values used for the numerical experiments lie exponentially close to a homoclinic manifold this paves the way for the second paper where we use the non linear spectrum as a basis for comparing different numerical schemes

reduced models in the medium frequency range for general external structural acoustic systems this paper presents a theoretical approach for constructing a reduced model in the medium frequency range in the area of structural acoustics for a general three dimensional dissipative structure made of an anisotropic inhomogeneous viscoelastic bounded medium coupled with an external acoustic fluid all the results presented can be used if the structure is made of beams plates and shells the boundary value problem in the frequency domain and its variational formulation are presented for a fixed medium frequency band an energy operator related to the structural acoustic system is introduced this operator is symmetric positive definite and has a countable set of positive eigenvalues its dominant eigensubspace allows a reduced model to be constructed using the ritz galerkin method a finite dimension approximation of the three dimensional continuous case is presented and an effective construction of the dominant subspace using the subspace iteration method is developed as an example the reduced model is used for constructing the time stationary random response of the structural acoustic system submitted to a random wall pressure field finally the theory is validated for a finite length circular cylindrical shell coupled with several dashpots and springs and immersed in a gas air and in a liquid water

vibration of annular sector mindlin plates with internal radial line and circumferential arc supports an energy approach is presented for the free vibration analysis of thick annular sector plates with internal line arc supports this has been a topic of practical interest but there appears to have been no previous work reported based on the stationary energy principle and the recently proposed pb 2 rayleigh ritz method the governing eigenvalue equation is derived for internally supported thick annular sector plates of different radii relative thickness ratios sector angles and with various end conditions along the radial and circumferential edges the proposed solution algorithm involves 1 sets of mathematically complete two dimensional polynomials p 2 used as the admissible displacement and rotational functions and 2 a basic function b formed from the piecewise expressions for the boundary and internal line arc supports these functions automatically satisfy all the kinematic boundary conditions of the four edges and internal supports the numerical procedure has been demonstrated by several example plate problems convergence and comparison studies for simple examples are used to verify the accuracy of the present method

on some generalizations of hardy s integral inequality in this paper we establish some new generalizations of the hardy s inequality by using a fairly elementary analysis the inequalities given here contain in the special cases some of the recent generalizations of hardy s integral inequality appearing in the literature

the surface variational principle applied to an acoustic cavity this paper presents the development and application of the surface variational principle svp for the evaluation of axisymmetric interior acoustic domains the interior form of the svp is first developed in the same manner as the existing exterior form then the surface pressure and normal velocity are represented with a ritz expansion using basis functions that span the entire wetted surface of the object of interest the resultant formulation is used to analyze the interior acoustic response of a harmonically forced right circular elastic cylinder this validation model was chosen as both the structural and acoustic responses can be solved analytically results are presented for two models one with a length to radius ratio of 2 4 and another with a ratio of 12 3 the svp is shown to well reproduce the analytical solution for this geometry and displays the asymptotic convergence expected of its variational formulation the svp formulation developed here is not restricted to right circular cylindrical geometries and may indeed be readily applied to any axisymmetric body

on some variants of hardy s inequality abstract the present paper deals with some new generalizations and extensions of a certain variant of hardy s inequality given by izumi and izumi the method employed in our analysis is quite elementary and the results established in this paper provide new estimates on this type of integral inequalities