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

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

explicit recursive and adaptive filtering in reproducing kernel hilbert spaces this brief presents a methodology to develop recursive filters in reproducing kernel hilbert spaces unlike previous approaches that exploit the kernel trick on filtered and then mapped samples we explicitly define the model recursivity in the hilbert space for that we exploit some properties of functional analysis and recursive computation of dot products without the need of preimaging or a training dataset we illustrate the feasibility of the methodology in the particular case of the gamma filter which is an infinite impulse response filter with controlled stability and memory depth different algorithmic formulations emerge from the signal model experiments in chaotic and electroencephalographic time series prediction complex nonlinear system identification and adaptive antenna array processing demonstrate the potential of the approach for scenarios where recursivity and nonlinearity have to be readily combined

vibration of a solid rectangular plate on an eccentric annular elastic support abstract the free transverse vibrations of a solid rectangular plate on an eccentric annular elastic support are discussed in the analysis the reaction force of the inner annular support is assumed to be an unknown external force the exact solution of the equation of motion which includes terms representing the reaction force of the support is applied the condition of continuity between the inner annular support and the plate is satisfied exactly the boundary conditions of the outer edge of the plate are satisfied directly by making use of the fourier expansion collocation method which has been developed in the author s previous reports concerning vibration dynamic response and wave propagation problems of membranes plates and rods with arbitrary shape numerical calculations have been carried out for plates with clamped and simply supported edges

three dimensional vibration analysis of cantilevered and completely free isosceles triangular plates the free vibration of cantilevered and completely free isosceles triangular plates based on exact three dimensional elasticity theory is investigated the actual plate domain is first mapped onto a basic cubic domain then the ritz method is applied to derive the eigenfrequency equation from the strain energy and the kinetic energy of the plate a set of chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component the convergence and comparison studies show that rather accurate results can be obtained by using this approach the effects of thickness to width ratio and apex angle on eigenfrequencies of the plates are studied in detail sets of valuable results are presented which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis data for the completely free isosceles triangular plates are presented for the first time

a hybrid energy approach for vibrational modelling of laminated trapezoidal plates with point supports abstract an investigation on the free flexural vibration of symmetric angle ply thin trapezoidal plates continuous over arbitrarily distributed point supports is reported a hybrid energy approach which combines the pb 2 rayleigh ritz method with the lagrangian multiplier method is proposed for the modelling of the aforementioned plate problem the pb 2 rayleigh ritz method uses a set of ritz functions generated from the product of a two dimensional polynomial and the equations of boundaries each raised to the power of 0 1 or 2 corresponding to a free simply supported or clamped edge respectively the geometric boundary conditions associated with the point supports are satisfied through the use of lagrangian multipliers in this paper some new solutions for the natural frequencies of several laminated trapezoidal plates with different stacking sequences and location of point supports are presented the first known mode shapes by means of contour plots for such laminated plates are also included

large amplitude dynamic analysis of simply supported skew plates by a variational method abstract large amplitude free vibration analysis of simply supported thin isotropic skew plates has been presented the large deformation is imparted statically by subjecting the plate under uniform transverse pressure the mathematical formulation is based on the variational principle in which the displacement fields are assumed as a combination of orthogonal polynomial or transcendental functions each satisfying the corresponding boundary conditions of the plate the large amplitude dynamic problem is addressed by solving the corresponding static problem first and subsequently with the resultant displacement field the problem is formulated the vibration frequencies are obtained from the solution of a standard eigenvalue problem entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique results of the reduced problem revealed excellent agreement with other studies and a typical comparison of the actual problem is also carried out successfully results are furnished in dimensionless amplitude frequency plane in the form of backbone curves and pictorial representations of some vibration mode shapes are made

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

optimum laguerre networks for a class of discrete time systems an analytical approach is introduced that directly yields the optimum value of the laguerre parameter b this is achieved by minimizing the mean square error between the unit sample response of the given discrete system and that of its laguerre counterpart it is shown that laguerre networks are best suited to realized systems whose exponential unit sample responses die down rapidly

buckling of arbitrary quadrilateral plates with intermediate supports using the galerkin method abstract a numerical method is developed for the stability analysis of arbitrary quadrilateral shaped elastic plates with internal supports the procedure uses the galerkin method in conjunction with the natural coordinates of the plate as a basis for the analysis of general plates the method is programmed and several numerical exaples are presented to illustrate the scope and efficacy of the procedure local plate buckling loads of skew rhombic trapezoidal and rectangular plates with intermediate line supports are obtained and where possible the results are compared with known solutions in the literature

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

blind input initial state and system identification of simo laguerre systems laguerre filters have infinite impulse responses iirs but with finite tapped delay line parameterizations this paper investigates subspace based blind identification of laguerre filter tap coefficients the internal filter state and the input given only noisy observations of the output this paper deals only with single input multiple output simo laguerre models a state space model for the simo laguerre system is derived from which blind estimation algorithms are developed as in the finite impulse response fir case the laguerre filter taps coefficients can be estimated from the column space of a certain hankel matrix constructed from noisy output observations whereas the internal state and input can be estimated from the row space by exploiting state space structure while not exactly uniquely identifiable conditions are given for which the tap coefficients the internal state and the input can be determined to within a multiplicative scalar factor

a categorification of morelli s theorem we prove a theorem relating torus equivariant coherent sheaves on toric varieties to polyhedrally constructible sheaves on a vector space at the level of k theory the theorem recovers morelli s description of the k theory of a smooth projective toric variety morelli in adv math 100 2 154 182 1993 specifically let x be a proper toric variety of dimension n and let m mathbb r mathrm lie t mathbb r vee cong mathbb r n be the lie algebra of the compact dual real torus t mathbb r vee cong u 1 n then there is a corresponding conical lagrangian t m and an equivalence of triangulated dg categories mathcal p mathrm erf t x cong mathit sh cc m mathbb r lambda where mathcal p mathrm erf t x is the triangulated dg category of perfect complexes of torus equivariant coherent sheaves on x and shcc m is the triangulated dg category of complex of sheaves on m with compactly supported constructible cohomology whose singular support lies in this equivalence is monoidal it intertwines the tensor product of coherent sheaves on x with the convolution product of constructible sheaves on m

free vibration analysis of orthotropic elliptical plates resting on arbitrarily distributed point supports the free vibration of point supported elliptical plates is studied analytically with consideration of rectangular orthotropy apparently this problem has been previously unsolved in the literature an analytical method used is an accurate variational approach the ritz lagrange multiplier method which constitutes an extension of the classical ritz method in numerical examples elliptical plates on some symmetric point supports are considered and it is shown that the method is straightforwardly applicable to determination of frequencies for elliptical plates resting on various support configurations

transverse vibrations of circular plates and membranes with intermediate supports the present paper deals with an approximate solution of the title problem in the case of a a concentric circular support and b a secant support fundamental frequency coefficients are determined by means of the rayleigh minimization procedure the modal shapes been approximated by simple polynomial co ordinate functions in the case of a circular plate with a secant support an independent solution is obtained by means of a finite element code and very good agreement is shown to exist

a ritz vibration analysis of doubly curved rectangular shallow shells using a refined first order theory integral expressions for strain and kinetic energies in vibration analysis of shear deformable doubly curved shallow shells are presented although the formulation follows the first order shear deformation theory the consideration of lame parameters for the transverse shear strain through shell thickness which have been hitherto neglected by other researchers shows linear distribution functions instead of constant values if the lame parameters were dropped finite higher order two dimensional orthogonal polynomials pb 2 functions previously used in thin shell analyses 3 6 have been generalized from three to five degrees to account for the additional rotation fields of a moderately thick shell these global shape functions satisfy the kinematic boundary conditions at the outset the excellent performance and versatility of the computational methodology of the pb 2 ritz method are illustrated in representative numerical simulations the resultant matrix size is far smaller than other discretization methods and yet accurate solutions can be obtained the validity of the results is verified through direct comparisons the discrepancy of various formulations with and without the lame parameters is presented and discussed

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

order recursive rls laguerre adaptive filtering this paper solves the problem of designing recursive least squares rls lattice or order recursive algorithms for adaptive filters that do not involve tapped delay line structures in particular an rls laguerre lattice filter is obtained

free vibration of super elliptical plates with constant and variable thickness by ritz method in this study free vibration of simply supported and clamped super elliptical plates is investigated this class of plates includes a wide range of external boundaries varying from an ellipse to a rectangle although studies on the upper and lower bounds of these plate geometries namely circle and rectangle are quite extensive contributions on the mid shapes especially for simply supported boundary edges are very limited the kirchhoff plate model with isotropic and homogeneous material is studied the super elliptical powers are chosen from 1 to 10 the ritz method is employed for the solution of the energy equations of the plates the effects of poisson s ratio which should not be neglected for simply supported plates with curved boundaries and the aspect ratio of the plate are both examined in detail the effect of thickness variation is also considered in this study in order to avoid long computational run times physically pertinent trial functions are utilized the frequency parameters obtained are presented and compared with published results for plate shapes that match the current cases

the gamma filter a new class of adaptive iir filters with restricted feedback generalized feedforward filters a class of adaptive filters that combines attractive properties of finite impulse response fir filters with some of the power of infinite impulse response iir filters are described a particular case the gamma filter generalizes widrow s adaptive transversal filter adaline to an infinite impulse response filter yet the stability condition for the gamma filter is trivial and lms adaptation is of the same computational complexity as the conventional transversal filter structure preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter the authors extend the wiener kopf equation to the gamma filter and develop some analysis tools

simplified method for solving problems of vibrating plates of doubly connected arbitrary shape part ii applications and experiments abstract the eigenfrequencies of ring shaped polygonal plates ring shaped elliptical plates rectangular plates with elliptical inner boundaries and circular plates with elliptical inner boundaries are obtained the method developed by the author in the companion paper part i is applied for finding the eigenfrequencies to verify the present results experimental tests have also been carried out for some important cases

numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the rayleigh ritz method unilateral buckling is a contact problem whereby buckling is confined to take place in only one lateral direction for plate structures this can occur when a thin steel plate is juxtaposed with a rigid concrete medium and the steel may only buckle locally away from the concrete core this paper investigates the use of simple and orthogonal polynomials in the rayleigh ritz method for unilateral plate buckling the orthogonal polynomials used are the classical chebyshev types 1 and 2 legrende hermite and laguerre the study presents a comparison between the efficiency of the polynomial based displacement functions with regard to elastic bilateral and unilateral plate buckling where efficiency is measured as a function of their convergence characteristics some buckling solutions for plates with varying boundary conditions and in plane shear loads are also provided as an illustration copyright 1999 john wiley sons ltd

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

effects of initial twist and thickness variation on the vibration behaviour of shallow conical shells abstract a thorough computational investigation is presented into the effects of initial twist and thickness variation on the vibratory characteristics of cantilevered pretwisted thin shallow conical shells with generally varying thickness an energy approach with the ritz minimization procedure is employed to arrive at a governing eigenvalue equation the admissiblepb 2shape functions which comprise sets of mathematically complete two dimensional orthogonal polynomials and a basic function are introduced to account for the boundary constraints and to approximate the three dimensional displacements of the conical shell the effects of angle of twist thickness variation and geometric parameters on the vibration response are presented in a comprehensive parametric study which provides useful new design data selected vibration mode shapes are also included to enhance the existing literature it is found that an increase in the angle of twist does not necessarily increase the torsional stiffness on the contrary the fundamental frequencies is reduced in the present analysis it is also observed that non zero angle of twist and non uniform chordwise thickness variation cause the absent of vibration mode symmetry

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

analysis and design of echo state networks the design of echo state network esn parameters relies on the selection of the maximum eigenvalue of the linearized system around zero spectral radius however this procedure does not quantify in a systematic manner the performance of the esn in terms of approximation error this article presents a functional space approximation framework to better understand the operation of esns and proposes an information theoretic metric the average entropy of echo states to assess the richness of the esn dynamics furthermore it provides an interpretation of the esn dynamics rooted in system theory as families of coupled linearized systems whose poles move according to the input signal dynamics with this interpretation a design methodology for functional approximation is put forward where esns are designed with uniform pole distributions covering the frequency spectrum to abide by the richness metric irrespective of the spectral radius a single bias parameter at the esn input adapted with the modeling error configures the esn spectral radius to the input output joint space function approximation examples compare the proposed design methodology versus the conventional design

analysis of dynamic instability for arbitrarily laminated skew plates the dynamic instability and nonlinear response of rectangular and skew laminated plates subjected to periodic in plane load are studied based on von karman plate theory the large amplitude dynamic equations of thin laminated plates are derived by applying the approach of generalized double fourier series on the assumed mode shape the governing equations are reduced to the mathieu equation using galerkin s method the incremental harmonic balance ihb method is applied to solve the nonlinear temporal equation of motion and the region of dynamic instability is determined in this work calculations are carried out for isotropic angle ply and arbitrarily laminated plates under two cases of boundary conditions the principal region of dynamic instability associated with the effect of the stacking sequence of lamination and the skew angle of plate are also investigated and discussed the results obtained indicated that the instability behavior of the system is determined by the several parameters such as the boundary condition number of the layers stacking sequence in plane load aspect ratio amplitude and the skew angle of plate

free vibration of continuous polar orthotropic annular and circular plates abstract the free vibration of a polar orthotropic annular plate supported on concentric circles is analyzed by the ritz method with use of lagrange multipliers a trial function for the deflection of the plate is expressed in terms of simple power series and a frequency equation for the plate is derived by the condition for minimizing the total potential energy with the constraint equations included in the numerical examples it is also shown that the method can directly yield quite accurate frequency values for a solid circular plate natural frequencies of annular and circular plates are calculated for wide ranges of the support location and orthotropic parameters

simplified method for solving problems of vibrating plates of doubly connected arbitrary shape part i derivation of the frequency equation abstract a simplified approximate method for solving problems of vibrating plates of doubly connected arbitrary shapes is presented in the analysis an arbitrarily shaped boundary is divided into small segments and general transformed expressions for the bending slope the bending moment and the shearing force of a segment are given under the assumption that the angle between the normal to the segment and the reference axis is constant the boundary conditions along the outer and the inner edges are satisfied by means of the fourier expansion collocation method the equation for finding the eigenfrequencies and mode shapes is obtained for arbitrarily shaped boundaries

exact vibration solutions for circular mindlin plates with multiple concentric ring supports this paper presents an analytical approach to investigate the vibration behaviour of circular mindlin plates with multiple concentric ring supports a circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports the governing differential equations and the solutions of these equations for the annular and circular segments based on the mindlin plate theory are presented a homogenous equation system governing the vibration of circular mindlin plates with ring supports is derived by imposing the essential and natural boundary and segment interface conditions the first known exact vibration frequencies for circular mindlin plates with multiple concentric ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented the influence of the ring support locations plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed

vibrational response of symmetrically laminated trapezoidal composite plates with point constraints abstract this paper presents the first known results for free vibrations of thin points supported symctrically laminated trapezoidal composite plates the solution method developed is based on the rayleigh ritz method and the admissible 2 d orthogonal polynomials to derive the governing eigenvalue equation the natural frequencies and mode shapes for the laminated plates are obtained by solving this governing eigenvalue equation several test problems are solved to demonstrate the accuracy and flexibility of the proposed method the effects of fibre orientations points location and the number of layers in the stacking sequences on the vibrational response for the plate problems are investigated variation of spring constants for the clastic points on the effect of the frequency parameters is also considered

the theory of toric manifolds toric manifolds the topological analogue of toric varieties are determined by an n dimensional simple convex polytope and a function from the set of codimensionone faces into the primitive vectors of an integer lattice their cohomology was determined by davis and januszkiewicz in 1991 and corresponds with the theorem of danilovjurkiewicz in the toric variety case we use the adams spectral sequence to compute the ko theory of all toric manifolds and certain toric varieties

a rayleigh ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions abstract to overcome the lack of a more general method for free vibration analysis of trapezoidal plates a computationally efficient and highly accurate rayleigh ritz approach with the newly developed orthogonal plate functions is proposed to solve these problems with any combination of clamped simply supported and free edge support conditions the deflection of the plate is approximated by a set of two dimensional orthogonal plate functions generated using the gram schmidt procedure which expresses the entire plate domain into two implicitly related variables in the present paper the effects of the fibre orientation on the vibrational behaviour of the plates are considered the numerical results for isotropic and anisotropic trapezoidal plates are presented where possible the numerical results are verified with other existing values in the literature

the fictitious foundation approach to vibration analysis of plates with interior point supports abstract a new approach to the continuum representation of interior point supports in the vibration analysis of plates is proposed the plate is assumed to be supported by a fictitious non uniform winkler foundation the flexibility distribution of the winkler foundation represented by a flexibility function is such that it has a zero value at the point support locations but assumes large values resulting in negligible restraint over the rest of the plate domain the improvization of the point supports as a special case of the flexibility distribution of the elastic foundation allows one to solve the problem in a single domain in contrast to the multiple domain solutions available in the literature the application of this approach namely the fictitious foundation approach is demonstrated by considering the free vibration of a simply supported rectangular plate with interior point supports also presented is a single domain application of the impulse function approach to plates with interior point supports involving the representation of the concentrated reactions at the point support locations by a double fourier series expansion of the impulse function the results obtained by using these single domain approaches are compared with those obtained by using the multiple domain flexibility function approach presented in an earlier study by the authors the new approach presented in this paper namely the fictitious foundation approach for the simulation of interior point supports in plates provides a method for absorbing the discrete discontinuities in the force field in the interior of the plate into the governing differential equation and obtaining a continuum representation of the solution in a single domain of the plate

a system identification algorithm using orthogonal functions an adaptive filter adf structure is proposed for applications in which large order adfs are required it is based on modeling the impulse response of the system to be identified as a linear combination of a set of discrete legendre orthogonal functions the proposed adaptive filter structure has desirable stability features and a unimodal mean square error surface as well as a modular structure that permits an easy increase of the filter order without changing the previous stages computer simulations in which the proposed structure is used to identify actual acoustic echo path impulse responses show that the legendre adf has better convergence performance than the transversal adf when identifying systems with long impulse response

the kernel adaptive autoregressive moving average algorithm in this paper we present a novel kernel adaptive recurrent filtering algorithm based on the autoregressive moving average arma model which is trained with recurrent stochastic gradient descent in the reproducing kernel hilbert spaces this kernelized recurrent system the kernel adaptive arma kaarma algorithm brings together the theories of adaptive signal processing and recurrent neural networks rnns extending the current theory of kernel adaptive filtering kaf using the representer theorem to include feedback compared with classical feedforward kaf methods the kaarma algorithm provides general nonlinear solutions for complex dynamical systems in a state space representation with a deferred teacher signal by propagating forward the hidden states we demonstrate its capabilities to provide exact solutions with compact structures by solving a set of benchmark nondeterministic polynomial complete problems involving grammatical inference simulation results show that the kaarma algorithm outperforms equivalent input space recurrent architectures using first and second order rnns demonstrating its potential as an effective learning solution for the identification and synthesis of deterministic finite automata

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

statical and dynamical behaviour of thin fibre reinforced composite laminates with different shapes abstract based on the classical laminated plate theory a variational approach for the study of the statical and dynamical behaviour of arbitrary quadrilateral anisotropic plates with various boundary conditions is developed the analytical formulation uses the ritz method in conjunction with natural coordinates to express the geometry of general plates in a simple form the deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the gram schmidt procedure the algorithm developed is quite general and can be used to study fibre reinforced composite laminates with symmetric lay ups which may have general anisotropy and any combinations of clamped simply supported and free edge support conditions various numerical applications are presented and some results are compared with existing values in the literature to demonstrate the accuracy and flexibility of the present method new results were also determined for plates with different geometrical shapes combinations of boundary conditions several stacking sequences and various angles of fibre orientation

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

application of a new differential quadrature methodology for free vibration analysis of plates a new methodology is introduced in the differential quadrature dq analysis of plate problems the proposed approach is distinct from other dq methods by employing the multiple boundary conditions in a different manner for structural and plate problems the methodology employs the displacement within the domain as the only degree of freedom whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently in order to demonstrate the capability of the new methodology all cases of free vibration analysis of rectangular isotropic plates in which the conventional dq methods have had some sort of difficulty to arrive at a converged or accurate solution are carried out excellent convergence behaviour and accuracy in comparison with exact results and or results obtained by other approximate methods were obtained the analogous dq formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised it must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods copyright 2002 john wiley sons ltd

an efficient differential quadrature methodology for free vibration analysis of arbitrary straight sided quadrilateral thin plates in this paper a new differential quadrature dq methodology is employed to study free vibration of irregular quadrilateral straight sided thin plates a four nodded super element is used to map the irregular physical domain into a square domain in the computational domain second order transformation schemes with relative ease and less computation are employed to transform the fourth order governing equation of thin plates between the two domains the only degree of freedom within the domain is the displacement whereas along the boundaries the displacement as well as the second order derivative of the displacement with respect to associated normal co ordinate variable in computational domain are the two degrees of freedom implementing the method the formulation for the dq method for the free vibration analysis of plates of straight sided shapes was presented together with the implementation procedure for the different boundary conditions to demonstrate the accuracy convergency and stability of the new methodology detail studies are made on isotropic plates at acute angles with different geometries boundary and loading conditions including dq free edge boundary condition implementations accurate results even with fewer degrees of freedom than for those of comparable numerical algorithms were achieved

vibration analysis of multi span plates having orthogonal straight edges abstract an accurate numerical technique is developed for flexural vibration of rectangular and l shaped plates continuous over rigid supports with arbitrary number of spans a set of orthogonally generated two dimensional plates function is used in the rayleigh ritz method to determine the natural frequencies of the plate systems several numerical examples are presented and the results obtained where possible are compared with the known solutions in the literature the present method is proven to be extremely versatile in solving a broad class of the aforementioned problems

use of two dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates abstract a general numerical method is developed to estimate the natural frequencies and the mode shapes for transverse vibration of circular and elliptical plates a set of orthogonal plate functions is used as the admissible functions in the rayleigh ritz approach to approximate the eigenvalues and eigenvectors new starting functions are proposed which are used in a recurrence formula to generate the higher terms in the set of orthogonal plate functions to approximate the mode shapes for circular and elliptical plates these functions are general and easily formed for circular and elliptical plates having classical boundary conditions several numerical examples are solved to demonstrate the applicability and the accuracy of the new proposed plate functions

free vibration analysis of conical shells via the element free kp ritz method in this paper we consider the free vibration analysis of thin conical shells under different boundary conditions the analysis is carried out using the element free kp ritz method the present study is based on the classical thin shell theory the kernel particle kp functions are employed in hybridized form with harmonic functions to approximate the two dimensional displacement field in order to examine the numerical stability of the present approach convergence studies are performed based on the influences of the support size and the number of nodes to verify the accuracy of this method comparisons of the present results are made with results available in the open literature this study also examines in detail the effects of semi vertex angles and boundary conditions on the frequency characteristics of the conical shells

treatments of over restrained boundaries for doubly connected plates of arbitrary shape in vibration analysis abstract the problem of the free flexural vibrations of plates of doubly connected arbitrary shape is investigated a hybrid energy approach which combines both the advantages of the rayleigh ritz method and the lagrange multiplier method is developed for analysing the aforementioned plate problems the rayleigh ritz method with a set of pb 2 shape functions is used to formulate the plates with classical boundary conditions as a single continuum element while the lagrange multipliers are imposed at discrete points in the inner plate boundaries for instance when the overrestrained boundary has occurred the admissible pb 2 shape function consists of the product of a two dimensional polynomial and a basic function the basic function is defined by the product of the equations of the prescribed piecewise continuous boundary shape each raised to the power of 0 1 or 2 corresponding respectively to a free simply supported or clamped edge this set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset numerical results for several examples of doubly connected plates of arbitrary shape are presented to demonstrate the applicability and accuracy of the present method

three dimensional vibration analysis of cantilevered skew plates three dimensional 3 d free vibration of cantilevered thick skew plates is analyzed based on the exact linear and small strain elasticity theory the skew domain of the plate is mapped onto a cubic domain a set of triplicate chebyshev polynomials multiplied by a boundary function is developed as the trial functions of each displacement components using the ritz method the eigenvalue equation is derived from the strain energy and kinetic energy of the plate the vibration modes are divided into the antisymmetric and symmetric ones in the thickness direction therefore can be studied individually the convergence study shows that the first eight frequency parameters for each mode categories can be obtained with an accuracy of at least four significant figures the effect of geometric parameters such as skew angle aspect ratio and span thickness ratio on frequency parameters is studied the results are compared with those obtained by using the algebraic polynomials as trial functions and the 3 d finite element solutions respectively it is shown that the chebyshev polynomials can provide better numerical stability than the algebraic polynomials especially for the plates with large skew angle the present results can serve as the benchmark data for the accuracy evaluation of other computational techniques

numerical study of grid distribution effect on accuracy of dq analysis of beams and plates by error estimation of derivative approximation the accuracy of global methods such as the differential quadrature dq approach is usually sensitive to the grid point distribution this paper is to numerically study the effect of grid point distribution on the accuracy of dq solution for beams and plates it was found that the stretching of grid towards the boundary can improve the accuracy of dq solution especially for coarse meshes the optimal grid point distribution corresponding to optimal stretching parameter depends on the order of derivatives in the boundary condition and the number of grid points used the optimal grid distribution may not be from the roots of orthogonal polynomials this differs somewhat from the conventional analysis this paper also proposes a simple and effective formulation for stretching the grid towards the boundary the error distribution of derivative approximation is also studied and used to analyze the effect of grid point distribution on accuracy of numerical solutions copyright 2001 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

free vibration of a solid plate of arbitrary shape lying on an arbitrarily shaped ring support this paper is concerned with a method for solving problems of vibrating plates of arbitrary shape lying on arbitrarily shaped inner ring supports to treat the inner ring support the reaction force of the support is assumed to be an external unknown force the exact solution of the equation of motion in polar co ordinates is applied the boundary conditions along the edge and the support are satisfied directly by means of the fourier expansion collocation method which has bee developed in the author s previous reports numerical calculations have been carried out for a solid polygonal plate on an annular ring support and a solid circular plate on a elliptical ring support

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

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

flexural vibration of shear deformable circular and annular plates on ring supports this paper presents an analysis of free flexural vibration of circular and annular mindlin plates lying on multiple internal concentric ring supports the rayleigh ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation the natural frequencies of circular and annular mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free simply supported and clamped conditions are determined a comprehensive set of vibration results is presented and where possible these have been verified with existing solutions published in the open literature no previous theoretical results for thick annular plates supported with internal rings are known to exist thus the study should be useful and valuable to engineers and researchers

t duality and homological mirror symmetry for toric varieties abstract let x be a complete toric variety the coherent constructible correspondence of fang et al 2011 14 equates p erf t x with a subcategory sh c c m r of constructible sheaves on a vector space m r the microlocalization equivalence of nadler and zaslow 2009 27 and nadler 2009 25 relates these sheaves to a subcategory fuk t m r of the fukaya category of the cotangent t m r when x is nonsingular taking the derived category yields an equivariant version of homological mirror symmetry dcoh t x dfuk t m r which is an equivalence of triangulated tensor categories the nonequivariant coherent constructible correspondence of treumann preprint 33 embeds p erf x into a subcategory s h c t r of constructible sheaves on a compact torus t r when x is nonsingular the composition of and microlocalization yields a version of homological mirror symmetry dcoh x dfuk t t r which is a full embedding of triangulated tensor categories when x is nonsingular and projective the composition is compatible with t duality in the following sense an equivariant ample line bundle l has a hermitian metric invariant under the real torus whose connection defines a family of flat line bundles over the real torus orbits this data produces a t dual lagrangian brane l on the universal cover t m r of the dual real torus fibration we prove l l in fuk t m r thus equivariant homological mirror symmetry is determined by t duality

target discrimination in synthetic aperture radar using artificial neural networks this paper addresses target discrimination in synthetic aperture radar sar imagery using linear and nonlinear adaptive networks neural networks are extensively used for pattern classification but here the goal is discrimination we show that the two applications require different cost functions we start by analyzing with a pattern recognition perspective the two parameter constant false alarm rate cfar detector which is widely utilized as a target detector in sar then we generalize its principle to construct the quadratic gamma discriminator qgd a nonparametrically trained classifier based on local image intensity the linear processing element of the qcd is further extended with nonlinearities yielding a multilayer perceptron mlp which we call the nl qgd nonlinear qgd mlps are normally trained based on the l sub 2 norm we experimentally show that the l sub 2 norm is not recommended to train mlps for discriminating targets in sar inspired by the neyman pearson criterion we create a cost function based on a mixed norm to weight the false alarms and the missed detections differently mixed norms can easily be incorporated into the backpropagation algorithm and lead to better performance several other norms l sub 8 cross entropy are applied to train the nl qgd and all outperformed the l sub 2 norm when validated by receiver operating characteristics roc curves the data sets are constructed from tabils 24 isar targets embedded in 7 km sub 2 of sar imagery mit ll mission 90

buckling and vibration of polar orthotropic circular plate resting on winkler foundation buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory the plate is resting on winkler type foundation an approximate solution has been obtained by ritz method which employs basis functions based upon static deflection of polar orthotropic plates the effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter flexibility parameter in plane force and nodal diameter the critical buckling load for clamped and simply supported plates have been obtained a comparison of results with those available in literature has been presented

free vibration analysis of circular plates using generalized differential quadrature rule the free vibration of solid circular plates has been studied using the generalized differential quadrature rule gdqr the effects such as stepped thickness intermediate concentric ring supports and elastic restraints have been considered discrete system equations for natural frequency analysis were derived based on the gdqr issues related to the implementation of the boundary and compatibility conditions were addressed two regularity conditions at the solid circular plate center were formularized since they were not quite clear in the present literature some wrong applications in the implementation of both differential quadrature methods and regularity conditions at the solid circular plate center have been pointed out excellent results have been obtained with the presented examples

online optimization of the time scale in adaptive laguerre based filters a new online method to optimize the free parameter in adaptive laguerre based filters is presented it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error the proposed technique presents a fast convergence and a good robustness

vibration of shallow conical shells with shear flexibility a first order theory a formulation of shear deformation theory implemented numerically for the prediction of vibratory characteristics of shallow conical shell panels is presented the derivation of thickness shear is assumed in a linear approximation the lame parameter for the transverse shear strain component which has previously been neglected is considered this consideration accounts for the replacement of a term in transverse strain distribution through the shell thickness which results in linear transverse shear strain distribution in contrast to the constant distribution hitherto known to researchers in this field the energy integral which incorporates the shear deformation and rotary inertia is minimized to derive the governing eigen matrix equation a set of benchmark frequency solutions is presented for two exemplary conical shells the cantilever and the fully clamped shells some selected mode shapes in terms of mid surface contour plots and three dimensional meshes are also illustrated

vibration analysis of twisted plates using first order shear deformation theory abstract based on general shell theory and the first order shear deformation theory an accurate relationship between strains and displacements of a twisted plate is derived by the green strain tensor an equation of equilibrium for free vibration is given by the principle of virtual work and the governing equation is solved by using the rayleigh ritz method with sets of orthonormal polynomials in which only the first polynomials are defined according to the geometric boundary conditions of a plate and the others are generated by the gram schmidt process the numerical verification is carried out by comparing with previous results of cantilever plates vibration characteristics of cantilever twisted plates such as frequency parameters and corresponding mode shapes are obtained by the present numerical method and the effects of the twist angle the aspect ratio and the thickness ratio on them are studied

vibration of eccentric ring and line supported circular plates carrying concentrated masses abstract the vibration of circular plates supported by combinations of ring and line supports and which are carrying concentrated masses is investigated for the first time to the author s knowledge by using the newly developed pb 2 rayleigh ritz method a set of ritz functions consisting of the product of the boundary expressions is used as the admissible displacement function this set of pb 2 ritz functions can accurately approximate the mode shapes of these circular plates with any prescribed boundary conditions and interior supports such as eccentric annular and or line supports to validate the present method numerical calculations have been carried out for several simplified plate problems and these are compared with those results available in the literature excellent agreement is achieved in all cases

parametric least squares approximation using gamma bases we study the problem of linear approximation of a signal using the parametric gamma bases in l sup 2 space these bases have a time scale parameter which has the effect of modifying the relative angle between the signal and the projection space thereby yielding an extra degree of freedom in the approximation gamma bases have a simple analog implementation that is a cascade of identical lowpass filters we derive the normal equation for the optimum value of the time scale parameter and decouple it from that of the basis weights using statistical signal processing tools we further develop a numerical method for estimating the optimum time scale

flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables a set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the rayleigh ritz method the set of orthogonal polynomials is constructed by employing the gram schmidt orthogonalization procedure the first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted results are compared with those obtained previously by other methods