eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

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

free vibration analysis of rectangular plates with variously shaped holes an approximate method for analyzing the free vibration of rectangular plates with a hole of different shapes is proposed the shapes of the holes are circular semi circular elliptic square rectangular triangular rhombic etc these rectangular plates with a hole can be considered ultimately as a kind of rectangular plates with non uniform thickness a hole in a plate can be considered as an extremely thin part of the plate therefore the free vibration problem of a plate with a hole can be translated into the free vibration problem of the equivalent rectangular plate with non uniform thickness for some plates with different shaped holes the convergency and accuracy of the numerical solutions calculated by the proposed method are investigated

an efficient method to determine the diagonal loading factor using the constant modulus feature the diagonal loading method is a simple and efficient method that improves the robustness of beamformers however determining an ideal diagonal loading factor dlf is not a trivial problem one that still has not been adequately addressed although beamformers are widely used in radar sonar and many other applications in this correspondence we consider a beamformer used only for digital communication applications in digital communications user information is coded into a sequence with the constant modulus cm in the baseband obviously if the beamformer can cancel interference sufficiently well the outputs of the beamformer should satisfy the cm condition more precisely therefore minimizing cm errors can act as a natural criterion for determining dlfs in this correspondence we present a cost function based on the criterion we also propose a direct search algorithm for dlf determination by minimizing the cost function numerical experiments show the effectiveness of the proposed method

high resolution viscous fingering simulation in miscible displacement using a p adaptive discontinuous galerkin method with algebraic multigrid preconditioner abstract high resolution simulation of viscous fingering can offer an accurate and detailed prediction for subsurface engineering processes involving fingering phenomena the fully implicit discontinuous galerkin dg method has been shown to be an accurate and stable method to model viscous fingering with high peclet number and mobility ratio in this paper we present two techniques to speedup large scale simulations of this kind the first technique relies on a simple p adaptive scheme in which high order basis functions are employed only in elements near the finger fronts where the concentration has a sharp change as a result the number of degrees of freedom is significantly reduced and the simulation yields almost identical results to the more expensive simulation with uniform high order elements throughout the mesh the second technique for speedup involves improving the solver efficiency we present an algebraic multigrid amg preconditioner which allows the dg matrix to leverage the robust amg preconditioner designed for the continuous galerkin cg finite element method the resulting preconditioner works effectively for fixed order dg as well as p adaptive dg problems with the improvements provided by the p adaptivity and amg preconditioning we can perform high resolution three dimensional viscous fingering simulations required for miscible displacement with high peclet number and mobility ratio in greater detail than before for well injection problems

least squares approach to blind channel equalization we present a least squares ls algorithm for blind channel equalization based on a reformulation of the godard algorithm a transformation for the equalizer parameters is considered to convert the nonlinear ls problem inherent in the godard algorithm to a linear ls problem unlike the godard 1980 algorithm the proposed ls approach does not suffer from ill convergence to closed eye local minima methods for extracting the equalizer parameters from their transformed version are developed offline and recursive implementations of the ls algorithm are presented the algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis a vis the godard algorithm the channel input correlation does not impose any restriction on the application of the algorithm as long as a weak sufficient excitation condition is satisfied simulation examples are presented to demonstrate the ls approach and to compare it with the godard algorithm

exact solutions for the buckling of rectangular plates having linearly varying in plane loading on two opposite simply supported edges abstract an exact solution procedure is formulated for the buckling analysis of rectangular plates having two opposite edges x 0 and a simply supported when these edges are subjected to linearly varying normal stresses x n0 1 y b h where h is the plate thickness the other two edges y 0 and b may be clamped simply supported or free or they may be elastically supported by assuming the transverse displacement w to vary as sin m x a the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients for which an exact solution is obtained as a power series i e the method of frobenius applying the boundary conditions at y 0 and b yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant care must be exercised to retain sufficient terms in the power series in calculating accurate buckling loads as is demonstrated by a convergence table for all nine possible combinations of unloaded clamped simply supported or free edges at y 0 and b buckling loads are presented for all nine possible edge combinations over the range of aspect ratios 0 5 a b 3 for loading parameters 0 0 5 1 1 5 2 for which 2 is a pure in plane bending moment some interesting contour plots of their mode shapes are presented for a variety of edge conditions and in plane moment loadings because the nondimensional buckling parameters depend upon the poisson s ratio for five of the nine edge combinations results are shown for them for the complete range 0 0 5 valid for isotropic materials comparisons are made with results available in the published literature

mesh free radial point interpolation method for the buckling analysis of mindlin plates subjected to in plane point loads in this paper a mesh free approach is employed for buckling analysis of mindlin plates that are subjected to in plane point loads the radial point interpolation method rpim is used to approximate displacements based on nodes variational forms of the system equations are established two step solution procedures are implemented the non uniform pre stress distribution of plate is first obtained using the rpim based on a two dimensional 2d elastic plane stress problem this predetermined non uniform pre stress distribution is then used to compute buckling loads of plate using the rpim based on mindlin s plate assumption the rpim can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads numerical examples considered here include circular and rectangular mindlin plates that are subjected to in plane uniform and point loads with different aspect ratios and boundary conditions the present results are validated against the available analytical and numerical solutions copyright 2004 john wiley sons ltd

robust smoothers for high order discontinuous galerkin discretizations of advection diffusion problems the multigrid method for discontinuous galerkin discretizations of advection diffusion problems is presented it is based on a block gauss seidel smoother with downwind ordering honoring the advection operator the cell matrices of the dg scheme are inverted in this smoother in order to obtain robustness for higher order elements employing a set of experiments we show that this technique actually yields an efficient preconditioner and that both ingredients downwind ordering and blocking of cell matrices are crucial for robustness discretizations of partial differential equations by higher order finite element methods or hp methods gained popularity during the last years after computing power and memory became readily available these methods yield much higher accuracy with similar degrees of freedom than standard schemes based on linear or bilinear polynomials nevertheless the utility of these schemes depends very much on the availability of efficient solvers for the discrete problems in this article we continue previous work and demonstrate that multilevel methods with suitably chosen smoothers can provide such solvers even in the presence of non self adjoint advection terms and locally refined meshes in 8 we devised a multilevel preconditioner for the symmetric interior penalty method and proved it s optimality these results were extended to other adjoint

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

two level additive schwarz methods for a discontinuous galerkin approximation of second order elliptic problems we present some two level nonoverlapping and overlapping additive schwarz methods for a discontinuous galerkin method for solving second order elliptic problems it is shown that the condition numbers of the preconditioned systems are of the order o frac h h for the nonoverlapping schwarz methods and of the order o frac h delta for the overlapping schwarz methods where h and h stand for the fine mesh size and the coarse mesh size respectively and delta denotes the size of the overlaps between subdomains numerical experiments are provided to gauge the efficiency of the methods and to validate the theory

performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest diagonal loading is one of the most popular techniques to improve robustness in this paper we present a theoretical analysis of the signal to interference plus noise ratio sinr for the class of beamformers based on generalized i e not necessarily diagonal loading of the covariance matrix in the presence of random steering vector errors a closed form expression for the sinr is derived that is shown to accurately predict the sinr obtained in simulations this theoretical formula is valid for any loading matrix it provides insights into the influence of the loading matrix and can serve as a helpful guide to select it finally the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal sinr

vibration of skew plates resting on point supports abstract this paper deals with the vibrations of skew plates resting on point supports the spline element method is used to demonstrate the accuracy of the method several examples are solved and results are compared with those obtained by other approximate methods the effects of skew angles and locations of point supports on natural frequencies of isotropic skew plates are also investigated

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method abstract a meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear deformable plates in this approach the first order mindlin reissner plate theory fsdt is used and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition the essential boundary conditions are enforced by a transformation method numerical examples considering various aspect ratios skew angles and boundary conditions are demonstrated to show the validity of the proposed method and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature

buckling of thick skew plates the paper considers the elastic buckling of thick skew plates up to now very little work has been done on this subject and the paper aspires to fill this gap based on the principle of stationary total potential energy and the recently developed pb 2 rayleigh ritz method as a solution procedure buckling solutions for skew plates of various aspect ratios skew angles and boundary conditions are determined the tabulation of these results not available thus far should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis

mesh free radial basis function method for buckling analysis of non uniformly loaded arbitrarily shaped shear deformable plates abstract a mesh free radial basis function rbf method is employed for the buckling analysis of non uniformly loaded thick plates the field variables are approximated using a set of scattered nodes in the problem domain the number of nodes and nodal distribution in the problem domain can be easily changed without a complex procedure for desired computational accuracy the shape functions possess the partition of unity properties based on the two dimensional 2d plane stress problem a variational form of the static system of equations is formulated in terms of displacements and is discretised the initial i e pre buckling stresses are obtained by solving the discrete system of equations based on the first order shear deformation plate theory a variational form of the plate problem with previously obtained initial stresses is established and discretised as the eigenvalue equation the buckling loads of circular trapezoidal and skew plates are presented the present results have good convergence and are in good agreement with the finite element solutions the present mesh free radial basis function method is effective for the buckling analysis of non uniformly loaded plates

analytical method for blind binary signal separation the blind separation of multiple co channel binary digital signals using an antenna array involves finding a factorization of a data matrix x into x as where all entries of s are 1 or 1 it is shown that this problem can be solved exactly and noniteratively via a certain generalized eigenvalue decomposition as indicated by simulations the algorithm is robust in the presence of noise an interesting implication is that certain cluster segmentation problems can be solved using eigenvalue techniques

a p type solution for the bending of rectangular circular elliptic and skew plates an energy method is presented in this paper for the linear static analysis of first order shear deformable plates of various shapes in this method the displacement fields are defined in terms of the shape functions which correspond to a set of predefined points and are composed of significantly high order polynomials the positions of these points are calculated by mapping the geometry using naturalized coordinates and the interpolating shape functions of second order to fourth order polynomials the displacement degrees of freedom are assigned to each of the displacement nodes the method is evaluated using the fully clamped and simply supported rectangular circular and elliptic plates subjected to uniformly distributed transverse load as examples for which the exact results are given in the monograph of timoshenko and woinowsky krieger also presented in this paper is the analysis of the above three types of plates subjected to eccentric square and circular patch loadings plates with eccentric square and circular openings are analyzed by this method using the full plate model and the results compare extremely well with those obtained by finite element methods the cutout part of the plate is accommodated in the solution by superposing negative stiffness and load over the area of the opening finally skew plates with simply supported and clamped boundaries are analyzed and discussed

free in plane vibration of isotropic non rectangular plates abstract a numerical study for the free in plane vibration of non rectangular plate is presented in this paper the plate is defined by four curved boundaries using eight points and natural co ordinates to map the geometry the displacement nodes are introduced at the boundary of the plate as well as inside the perimeter each displacement node has two degrees of freedom and much higher order polynomials than the ones used for the geometric representation are used to represent the displacement fields using the energy functional the matrix equation is obtained and solved for natural frequencies and associated mode shapes numerical results are calculated first for rectangular plates with three sets of boundary conditions and then compared with the data published in the literature by other researchers additional results are also presented and discussed in this paper for the in plane vibration of rhombic and circular annular sector plates

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

finite sample size effect on minimum variance beamformers optimum diagonal loading factor for large arrays minimum variance beamformers are usually complemented with diagonal loading techniques in order to provide robustness against several impairments such as imprecise knowledge of the steering vector or finite sample size effects this paper concentrates on this last application of diagonal loading techniques i e it is assumed that the steering vector is perfectly known and that diagonal loading is used to alleviate the finite sample size impairments the analysis herein is asymptotic in the sense that it is assumed that both the number of antennas and the number of samples are high but have the same order of magnitude borrowing some results of random matrix theory the authors first derive a deterministic expression that describes the asymptotic signal to noise plus interference ratio sinr at the output of the diagonally loaded beamformer then making use of the statistical theory of large observations also known as general statistical analysis or g analysis the authors derive an estimator of the optimum loading factor that is consistent when both the number of antennas and the sample size increase without bound at the same rate because of that the estimator has an excellent performance even in situations where the quotient between the number of observations is low relative to the number of elements of the array

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

higher order finite elements based on generalized eigenfunctions of the laplacian we present a new class of higher order finite elements based on generalized eigenfunctions of the laplace operator which are suitable for both product and simplicial geometries in d due to simultaneous orthogonality of the generalized eigenfunctions under both the h and l2 products and their almost negligible dependence on reference maps such finite elements are an excellent choice for the discretization of second order elliptic problems by the hp fem analysis is illustrated by numerical results and comparisons with other popular higher order finite elements are presented the new elements are used to compute efficiently the model of an electrostatic micromotor copyright 2007 john wiley sons ltd

equivalence of adaptive array diagonal loading and omnidirectional jamming diagonal loading where a diagonal matrix is added to the estimate of the covariance matrix is often used in adaptive arrays to minimize the array s responsiveness to random fluctuations in the estimate of the interference environment poor estimates of the covariance matrix often result in high random sidelobes in the sample matrix inversion smi adapted pattern it is shown in this communication that an omnidirectional spread of uniform jammers arriving at a linear array of half wavelength spaced elements with cosine element patterns also produces a diagonal matrix this equivalence of form is useful in visualizing the effects of diagonal loading and understanding the resulting patterns

moving least squares differential quadrature method and its application to the analysis of shear deformable plates a moving least squares differential quadrature mlsdq method is developed and employed for the analysis of moderately thick plates based on the first order shear deformation theory fsdt to carry out the analysis the governing equations in terms of the generalized displacements transverse deflection and two rotations of the plate are formulated by employing the moving least squares approximation the weighting coefficients used in the mlsdq approximation are computed through a fast computation of shape functions and their derivatives numerical examples illustrating the accuracy stability and convergence of the mlsdq method are presented effects of support size order of completeness and node irregularity on the numerical accuracy are investigated copyright 2003 john wiley sons ltd