isophoric arrays massively thinned phased arrays with well controlled sidelobes traditional filled phased arrays have an element placed in every location of a uniform lattice with half wavelength spacing between the lattice points massively thinned arrays have fewer than half the elements of their filled counterparts such drastic thinning is normally accompanied by loss of sidelobe control this paper describes a class of massively thinned linear and planar arrays that show well behaved sidelobes in spite of the thinning the term isophoric is derived from greek roots to denote uniform weight in isophoric arrays element placement based on difference sets forces uniformly weighted spatial coverage this constraint forces the array power pattern to pass through v uniformly spaced equal and constant values that are less than 1 k times the main beam peak where v is the aperture size in half wavelengths and k is the number of elements in the array the net result is reduced peak sidelobes especially when compared to cut and try random placement approaches an isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that k is approximately the square root of v where more than one beam must be generated at a time isophoric array designs may be used to advantage even within a traditional filled array by interweaving two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time two independent antenna power patterns can be generated each with a sidelobe region that is approximately a constant value of 1 2k relative to the main beam where k is the number of elements in the subarray

fast pencil beam pattern synthesis of large unequally spaced antenna arrays reducing the computational cost of large array pattern synthesis is attractive in many applications in this paper a fast pencil beam pattern synthesis method for large nonuniform antenna arrays is proposed this method is based on an interpolation in a least square sense and iterative fast fourier transform fft i e interpolate the nonuniform distributed elements into uniform virtual elements and then apply fft to synthesis the uniform array thanks to the efficiency of fft the proposed method is much faster and can handle much larger arrays than the existing methods to guarantee the interpolation accuracy the choice of the interpolation parameters is discussed both linear and planar nonuniform array examples are shown to validate the advantages of the proposed method

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

on the asymptotic boundary conditions of an anisotropic beam via virtual work principle in this research an efficient and effective method is proposed to derive the boundary conditions of an anisotropic beam in the asymptotic sense we first set up the constrained virtual work by introducing the lagrange multiplier on the displacement prescribed boundary the macroscopic beam and microscopic cross section equations with the boundary conditions are simultaneously obtained by taking the asymptotic expansion on the displacement vector in this way the three dimensional characteristics of the beam are asymptotically smeared into the macroscopic beam equations and the beam boundary conditions the boundary conditions obtained are then compared to those from the decay analysis method the beam bending slope boundary condition obtained in the frame work of variational principle is different from the well known average condition this new boundary condition is more accurate than the average one for a sandwich beam this is further demonstrated and discussed via the examples of a cantilever beam loaded at the end

another second order beam vibration theory explicit bending warping flexibility and restraint abstract a new symmetric beam bending vibration theory which explicitly includes bending warping is presented the governing differential equations are of sixth order and the boundary conditions allow enforcement of total fixity of the end of a beam the motivation for the study was the desire to determine if consideration of bending warping restraint in bending theory is as important as is torsion warping restraint in torsion theory natural frequency predictions are given and compared with other theories for constant cross section cantilevered beams of two types short deep rectangular beams and short thin shallow circular cylindrical shells the accuracy of the new theory is comparable with murty s levinson s bickford s and rehfield s theories for beams with rectangular cross sections it is also comparable with cowper s theory for general symmetric cross sections

hybrid ads based techniques for radio astronomy array design a set of techniques are presented that are based on the exploitation of low correlation sequences called almost difference sets adss to design correlator arrays for radio astronomy applications three approaches are discussed with different objectives and performances ads based analytical designs ga optimized arrangements and pso optimized arrays are presented and applied to the synthesis of open ended y and cross array configurations to maximize the u v coverage or to minimize the peak sidelobe level psl representative numerical results are illustrated to point out the features and performances of the proposed approaches and to assess their effectiveness in comparison with state of the art design methodologies as well the presented analysis indicates that the proposed approaches overcome existing pso based correlator arrays in terms of psl control e g 1 0 db reduction and tracking u v coverage e g up to 2 enhancement also improving the speed of convergence of the synthesis process

upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations abstract by introducing a new class of sequences involving iterates of the delay we are able to derive a sharper estimate on the ratio x t x t based on this we get some new upper bounds for the distance between consecutive zeros of solutions of the first order delay differential equation x t p t x t 0 in particular our results are not covered by previously known results some examples and a table are given to illustrate our results

rectangular thinned arrays based on mcfarland difference sets a new class of analytical rectangular thinned arrays with low peak sidelobe level psl is introduced the proposed synthesis technique exploits binary sequences derived from mcfarland difference sets to design thinned layouts on a lattice of p p p 2 positions for any prime p the pattern features of the arising massively thinned arrangements characterized by only p p 1 active elements are discussed and the results of an extensive numerical analysis are presented to assess advantages and limitations of the mcfarland based arrays

on the analysis of prismatic beams using first order warping functions abstract a one dimensional theory for isotropic homogeneous beams with a general cross section is developed that utilizes both deformations in the cross section plane and warping out of the cross section plane where these deformation functions are known from saint venant s elasticity solutions for bending and flexure of a prismatic beam first order warping functions in contrast to existing technical beam theories which assume that local cross section deformations and some stresses can be neglected the present theory makes no assumption the finite element model is developed using the resulting differential equations along with a partially weak form formulation full three dimensional constitutive equations are used solutions are found using the finite element method numerical results which are presented for a wide variety of loadings and boundary conditions show that the calculated stresses and displacements are in excellent agreement with existing elasticity solutions

higher order effective modeling of periodic heterogeneous beams i asymptotic expansion method this paper is concerned with the elastostatic behavior of heterogeneous beams with a cross section and elastic moduli varying periodically along the beam axis by using the two scale asymptotic expansion method the interior solution is formally derived up to an arbitrary desired order in particular this method is shown to constitute a systematic way of improving bernoulli s theory by including higher order terms without any assumption in contrast to timoshenko s theory or other refined beam models moreover the incompatibility between the interior asymptotic expansions and the real boundary conditions is emphasized and the necessity of a specific treatment of edge effects is thus underlined

on locking free shear deformable beam finite elements abstract this is an elementary exposition of beam finite element models an overview of existing and new displacement finite element models of the euler bernoulli and shear deformation beam theories is presented a locking free finite element model using the form of the exact solution of the timoshenko beam theory is developed the element contains the euler bernoulli beam element as a special case and yields exact nodal values for the generalized displacements for constant material and geometric properties of beams the procedure is extended to develop a locking free finite element model of the simplified third order theory of beams the element contains the euler bernoulli and the locking free timoshenko beam finite elements as special cases the element stiffness matrix of the unified beam bending element is 4 4 and yet has the superconvergence character the advantage of this element is that it can be used to obtain exact nodal displacements and forces from the equilibrium equations of the element in a frame structural analysis using one finite element per a structural member this cannot be achieved with the traditional equal interpolation reduced integration element because the element exhibits shear locking for thin members unless two or more elements per a structural member are used

sparse array beampattern synthesis via alternating direction method of multipliers in this paper we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers admm unlike the usual weighted l 1 norm we utilize the l p norm of the array weight vector where 0 as the objective function to enhance its sparsity for arbitrary array configurations to solve the resultant nonconvex and nonlinear optimization problem we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes and then the array weight vector and auxiliary variables are updated alternately via admm to determine the array weight vector with the l p norm we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives on the other hand we divide the objective function of auxiliary variables into multiple nonlinear subfunctions each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two sided constraints furthermore we extend our methodology to the symmetric excitation case with symmetric array configurations numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

relationships between bending solutions of classical and shear deformation beam theories the exact relationships between the deflections slopes rotations shear forces and bending moments of a third order beam theory and those of the euler bernoulli theory and the timoshenko beam theory are developed the relationships enable one to obtain the solutions of the third order beam theory from any known euler bernoulli or timoshenko beam theory solutions of beams for any set of boundary conditions and transverse loads the relationships can also be used to develop finite element models of the timoshenko and third order beam theories and determine numerical solutions from the finite element model of the euler bernoulli beam theory the finite element models are free of the shear locking that is found in the conventional shear deformable finite elements

on applications of generalized functions to beam bending problems using a mathematical approach this paper seeks an eacient solution to the problem of beams bending under singular loading conditions and having various jump discontinuities for two instances the boundary value problem that describes beam bending cannot be written in the space of classical functions in the first instance the beam is under singular loading conditions such as point forces and moments and in the second instance the dependent variable s and its derivatives have jump discontinuities in the most general case we consider both instances first we study singular loading conditions and present a theorem by which the equivalent distributed force of a general class of singular loading conditions can be found as a consequence of obtaining the equivalent distributed force of a distributed moment we find a mathematical explanation for the corner condition in classical plate theory while plate theory is not the focus of this paper this explanation is interesting then beams with various jump discontinuities are considered when beams have jump discontinuities the form of the governing diaerential equations changes we find the governing diaerential equations in the space of generalized functions it is shown that for euler bernoulli beams with jump discontinuities the operator of the diaerential equation remains unchanged only the force term changes so that delta function and its distributional derivatives appear within it but for timoshenko beams with jump discontinuities in addition to changes in the force terms the operator of one of the governing diaerential equations changes we then propose a new method for solving these equations this method which we term the auxiliary beam method is to solve the governing diaerential equations not in the space of generalized functions but rather to solve them by means of solving equivalent boundary value problems in the space of classical functions the auxiliary beam method reduces the number of diaerential equations and at the same time obviates the need to solve these diaerential equations in the space of generalized functions which can be more diacult 7 2000 elsevier science ltd all rights reserved

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations an iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented the algorithm consists in solving a sequence of weighted l1 convex optimization problems the method can thus be readily implemented and efficiently solved in the optimization procedure the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements the method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach whose computation time is several orders of magnitude below those of so called global optimization algorithms

ads based guidelines for thinned planar arrays we propose an analytical technique based on almost difference sets adss for thinning planar arrays with well controlled sidelobes the method allows one to synthesize bidimensional arrangements with peak sidelobe levels psls predictable and deducible from the knowledge of the array aperture the filling factor and the autocorrelation function of the ads at hand the numerical validation concerned with both small and very large apertures points out that the expected psl values are significantly below those of random arrays and comparable with those from different sets dss although obtainable in a wider range of configurations

the distribution of zeros of solutions for a class of neutral delay differential equations abstract in this paper the distribution of zeros of solutions of neutral differential equations x t cx t p t x t 0 where c 0 0 and p c t0 r are studied and some estimates for the distance between adjacent zeros of the oscillatory solutions of the above equation are obtained

square array antennas based on hadamard difference sets a regular method for synthesizing a planar aperiodic thinned array antenna aa with a low peak sidelobe level is suggested it is based on using specific combinatorial constructions noncyclic difference sets dss the method uses the fact that when the elements of an equiamplitude aa are arranged according to a ds law its power pattern takes constant value in the net of uniformly located space points in the sidelobe region and this value is less than where is the element number in distinction to the method using cyclic dss see leeper 1999 which enables one to build planar aas only on rectangular grids with co prime sidelengths the represented method omits such a constraint the most important class of the noncyclic 2 d dss is represented by the sets of hadamard type sets based on such sets rectangular and square aperiodic roughly half filled aas can be built here the numerical results obtained for the square aas with the element number in the array up to 300 are presented

nondestructive determination of buckling for plates and bars including shear it will be shown that the generic integral equation for nondestructive determination of the buckling loads obtained previously baruch m integral equations for nondestructive determination of buckling loads for elastic bars and plates israel journal of technology vol 11 no 1 2 1973 pp 1 8 includes the influence of the transverse shear strains on the buckling load this can not be said for the integral equations obtained by differentiation of the generic integral equation

hybrid design of non regular linear arrays with accurate control of the pattern sidelobes the hybridization of an analytical thinning technique based on almost difference sets adss and a convex programming cp strategy is proposed for designing non regular linear arrays over a half wavelength lattice that fit arbitrary upper bounds on the far field pattern the proposed approach combines the efficiency of the ads procedure in defining a low sidelobe thinned arrangement with the effectiveness of the cp approach in deducing the optimal tapering to control the beam shape a set of numerical results is presented to assess features and potentialities of the ads cp method

regular articlethe distribution of zeros of solutions of differential equations with a variable delay in this paper the distribution of zeros of solutions of the first order differential equation with a variable delayx t ptx t 0is studied the estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained

the distribution of zeros of solutions of differential equations with a variable delay this paper is concerned with the distribution of zeros of solutions of the first order linear differential equations with a variable delay of the form begin aligned x t p t x left tau t right 0 quad t ge t 0 nonumber end aligned where p tau in c t 0 infty 0 infty tau t le t tau t is nondecreasing and lim limits t rightarrow infty tau t infty by introducing a class of new series we are able to derive sharper upper bounds on the distance between zeros of solutions of the above delay differential equations some examples and a table are given to support our accomplishment

on the distance between consecutive zeros of solutions of first order delay differential equations this paper is concerned with the distribution of zeros of solutions of first order linear delay differential equations with variable coefficients of the formx t p t x email protected 0 t t where t 0 p t c t 0 by introducing a class of polynomial functions we are able to derive new estimates for the lower and upper bounds of the distance between consecutive zeros of solutions of the above equations we illustrate the obtained results with several examples

on the distribution of zeros of solutions of first order delay differential equations abstract this paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation x t p t x t 0 where p is a nonnegative continuous function our results are new and improve some known criteria illustrative examples are given to show the strength of some obtained results over the known ones

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

high order theory of homogeneous plate flexure the need for higher order models to obtain accurate estimates to transverse shear and normal stresses and strains is well known in this paper a higher order shear deformation theory with provision for cubic variation of in plane displacements and parabolic variation of the normal displacement has been considered for detailed study numerical results have been obtained for infinite plate strip simply supported on opposite edges and infinitely long in the other direction subjected to sinusoidal static load displacements strains and stresses are compared with the exact solution results by the classical plate theory levinson s theory and a higher order theory based on partial deflections are also included this study shows that the present model can predict all displacements strains and stresses reasonably accurately further it is also noted that the statically equivalent estimates to transverse stresses from classical theory and the corresponding strains also agree closely with the exact solution

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

a new family of almost difference sets and some necessary conditions almost difference sets have important applications in cryptography and coding theory in this paper new families of almost difference sets are constructed some necessary conditions for the existence of v k spl lambda t almost difference sets in z sub v are derived

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

peak sidelobe level reduction with a hybrid approach based on gas and difference sets this paper presents an approach for the optimization of the beam pattern produced by massively thinned arrays the method which combines the most attractive features of a genetic algorithm and those of a combinatorial technique namely the difference sets method is aimed at synthesizing massively thinned antenna arrays in order to suitably reduce the peak sidelobe level selected numerical results are presented in order to assess the effectiveness and reliability of the proposed approach

warping displacement of timoshenko beam model abstract a refined timoshenko beam model which takes into account warping of the cross sections is presented the model extends saint venant s theory of uniform torsion to the generic loading of a beam in a coherent manner the use of kinetic and kinematic assumptions virtual work expression of full elasticity problem and the principle of virtual work in derivation brings the presentation to the usual context of engineering models a new definition of the warping displacement in terms of a variational problem is one of the outcomes boundary value problems for the stretch shear bending and torsion loading modes are also given analytic and numeric solutions to warping displacements refined constitutive equations and correction factors for circular rectangle triangle and open annular cross sections of isotropic material are compared with expressions in literature as an interesting detail shear correction factors are found to be purely geometrical quantities which contradicts many findings in literature

on the robustness to element failures of linear ads thinned arrays the robustness of the analytical thinning based on almost difference sets adss is analyzed when faulty elements are present in linear arrays peak sidelobe level psl statistics of the damaged layouts are numerically inferred from representative simulations dealing with different aperture sizes and element failure rates

the estimate for number of zeros of solutions of second order functional differential equations in this paper by extending the maximum principle we study the number of zeros of solutions of second order functional differential equations we obtain a sufficient condition for the existence of at most one zero of solutions on an interval on this basis we estimate the maximal number of zeros of solutions on a large interval for illustrating the theoretical analysis we also give two numerical simulation examples

the distribution of zeros of solutions of first order delay differential equations abstract we give two estimates of the distance between adjacent zeros of the solutions of the first order delay differential equation x t p t x t 0

a generalization of shear deformation theories for axisymmetric multilayered shells a generalization of geometrically linear shear deformation theories for small elastic strains is presented for multilayered axisymmetric shells of general shape without any assumption other than neglecting the transverse normal strain the shear is taken into account by using a function f which is introduced in the assumed kinematics the boundary value problem is derived from the principle of virtual power with the shear function f in the kinematics all equations are directly applicable to kirchhoff love first order shear deformation third order shear deformation theories and obviously the proposed generalized shear deformation theory by using a certain sine shear function no shear correction factors are needed with the proposed generalization of shear deformation theories a numerical evaluation of the new theory is presented and compared with the above classic theories for a simply supported thick laminated cylindrical shell under an internal pressure

refined one dimensional formulations for laminated structure analysis this paper proposes one dimensional formulations based on hierarchical expansions of the unknown displacement variables for the analysis of multilayered structures made of anisotropic composite layers the hierarchical technique shows variable kinematic properties and it is based on the carrera unified formulation two different classes of refined theories are proposed the first expands the unknown variables in terms of power polynomials of the cross sectional coordinates it consists of a taylor like expansion the second class of onedimensional theories uses lagrange polynomials lagrange expansion and subdomain discretizations of the cross section and it leads to only pure displacements as the unknown variables taylor like expansion is used to develop equivalent single layer formulations and lagrange expansion is used to construct both equivalent single layer and layerwise descriptions the finite element method is employed to develop numerical applications using the carrera unified formulation finite element matrices are obtained in terms of a few fundamental nuclei that are formally independent of all the considered one dimensional formulations a number of numerical examples are given concerning on beams plates and more complex structures comparisons with results from plate and solid models are provided the following has been concluded 1 the proposed formulation represents a reliable compact and accurate method to develop refined one dimensional models 2 the present one dimensional models are very effective at detecting both global and local responses of composite structures 3 shell and solidlike results are obtained with a significant reduction in the computational costs

dynamics of transversely vibrating beams using four engineering theories abstract in this paper the full development and analysis of four models for the transversely vibrating uniform beam are presented the four theories are the euler bernoulli rayleigh shear and timoshenko first a brief history of the development of each beam model is presented second the equation of motion for each model and the expressions for boundary conditions are obtained using hamilton s variational principle third the frequency equations are obtained for four sets of end conditions free free clamped clamped hinged hinged and clamped free the roots of the frequency equations are presented in terms of normalized wave numbers the normalized wave numbers for the other six sets of end conditions are obtained using the analysis of symmetric and antisymmetric modes fourth the orthogonality conditions of the eigenfunctions or mode shape and the procedure to obtain the forced response using the method of eigenfunction expansion is presented finally a numerical example is shown for a non slender beam to signify the differences among the four beam models

a simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method a size dependent finite element model is developed nonlocal elasticity theory is used finite element solution is presented for buckling of microtubules the effect of elastic matrix surrounded by microtubules is modeled a simple nonlocal beam model is proposed to study buckling response of protein microtubules the size effect for buckling model of microtubules is considered by using the nonlocal continuum theory finite element procedure is used for solution of nonlocal differential equation of microtubules for elastic stability the influence of the small length scale on the buckling value is examined for different geometric parameters the effect of elastic matrix surrounded of microtubules is also examined and some benchmark results are presented

non uniform warping including the effects of torsion and shear forces part i a general beam theory this two part contribution presents a beam theory with a non uniform warping including the effects of torsion and shear forces and valid for any homogeneous cross section made of isotropic elastic material part i is devoted to the theoretical developments and part ii discusses analytical and numerical results obtained for torsion and shear bending of cantilever beams made of different kinds of cross section the theory is based on a kinematics assuming that the cross section maintains its shape and including three independent warping parameters associated to the three warping functions corresponding to torsion and shear forces starting from this displacement model and using the principle of virtual work the corresponding beam theory is derived for this theory closed form results are obtained for the cross sectional constants and the three dimensional expressions of the normal and shear stresses comparison with classical beam theories is carried out and additional effects due to the non uniformity of the warping are highlighted in particular the contributions of primary and secondary internal forces and the effect of the non symmetry of the cross section on the structural behavior of the beam are specified simplified versions of this theory wherein the number of degrees of freedom is reduced are also presented the analytical and numerical analyzes presented in part ii give responses on the quality of this non uniform beam theory and indicate also when its simplified versions could be applied

relationships between classical and shear deformation theories of axisymmetric circular plates the exact relationships between the deflections slopes rotations shear forces and bending moments of a third order theory and those of the classical theory and the first order shear deformation theory for axisymmetric bending of isotropic circular plates are developed the relationships enable one to obtain the solutions of the third order theory from any known classical or first order theory solutions of axisymmetric circular plates for any set of boundary conditions and transverse loads the relationships may also be used to develop finite element models of axisymmetric bending of circular plates according to the first order and third order theories

vibration and buckling of deep beam columns on two parameter elastic foundations natural frequencies and buckling stresses of a deep beam column on two parameter elastic foundations are analyzed by taking into account the effect of shear deformation depth change the transverse displacement w can vary in the depth direction of beam columns and rotatory inertia by using the method of power series expansion of displacement components a set of fundamental dynamic equations of a one dimensional higher order theory for thin rectangular beam columns subjected to axial stress is derived through hamilton s principle several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported deep elastic beam column in order to assure the accuracy of the present theory convergence properties of the minimum natural frequency and the buckling stress are examined in detail it is noted that the present approximate theories can predict the natural frequencies and buckling stress of deep beam columns on elastic foundations accurately compared with the timoshenko beam theory and the classical beam theory

bending solutions of levinson beams and plates in terms of the classical theories using the mathematical similarity of the governing equations of the classical beam and plate theories and the levinson beam and plate theories and the basis of load equivalence exact relationships between the bending solutions of the two theories for beams and plates are derived these relationships enable the conversion of the well known classical euler bernoulli beam and kirchhoff plate solutions to their shear deformable counterparts using the levinson beam and plate theories examples are given to illustrate the use of these relationships

vibration of a rectangular beam with a deforming cross section abstract levinson recently proposed a new theory for rectangular beam vibrations in which an inherent contradiction in conventional timoshenko beam theory is avoided by relaxing the assumption that plane sections remain plane in this paper this theory is reformulated in energy minimization terms it is found that the energy expressions are similar to those found for a timoshenko beam with a shear coefficient of 5 6 but they are not identical the two theories are therefore not equivalent at variance with levinson s conclusion it is shown that considerable care is needed to deal with a clamped boundary

distribution of zeros of solutions of functional differential equations abstract by improving the bracketing techniques for a functional differential inequality in a previous paper h w wu y t xu the distribution of zeros of solutions of neutral differential equations appl math comput 156 3 2004 665 677 we are able to derive sharper upper bounds on the distance between zeros of solutions of a class of neutral functional differential equations with delays and hence improve many known bounds in the literature

deformation of short composite beam using refined theories high order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented the formulation allows for warping of the cross section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories based on higher order shear deformation theories the governing equations are obtained using the principle of virtual work pvw the justification for use of higher order shear deformation theories is established for short and composite beams where cross sectional warping is predominant

free vibrations of a simply supported rectangular plate an exact elasticity solution abstract an exact three dimensional solution for the free vibrations of simply supported rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper the solution obtained in a semi inverse fashion as was the solution of the elastostatic problem for such plates satisfies all of the boundary conditions of the problem in a pointwise manner it is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi inverse solution other modes of oscillation may exist in the three dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes the two types of modes found are analogous to the flexural modes of classical plate theory and the thickness twist modes here called breathing modes of mindlin plate theory some numerical results are given which indicate that the predictions of mindlin plates are uncannily good approximations to the flexural frequencies given by the present three dimensional analysis even for very thick plates however the predictions of mindlin plate theory for the thickness twist or breathing frequencies are not nearly so good these discrepancies are discussed briefly in an appendix

the distribution of zeros of solutions of neutral differential equations in this paper the distribution of zeros of solutions of the first order neutral differential equation with two variable delays x t p t x g t q t x h t 0is studied the estimate for the distance between adjacent zeros of oscillatory solutions of the above equation is obtained

dynamic response of thin walled structures by variable kinematic one dimensional models abstract this paper investigates the accuracy capabilities of using variable kinematic modeling in compact and thin walled beam like structures with dynamic loadings carrera unified formulation cuf is employed to introduce refined one dimensional 1d models with a variable order of expansion for the displacement unknowns over the beam cross section classical euler bernoulli and timoshenko beam theories are obtained as particular cases of these variable kinematic models while a higher order expansion permits the detection of in plane cross section deformation since it leads to shell like solutions finite element fe method is used to provide numerical results and the newmark method is implemented as a time integration scheme some assessments with closed form solutions are discussed and comparisons with shell type results obtained with commercial fe software are made further analyses address both compact and thin walled cross sections in particular the case of a deformable thin walled cylinder loaded by time dependent internal forces is discussed the results clearly show that finite elements which are formulated in the cuf framework do not introduce additional numerical problems with respect to classical beam theories comparisons with elasticity solutions prove that the present 1d cuf model offers an accuracy in analyzing thin walled structures which is typical of shell or three dimensional models with a remarkable reduction in the computational cost required

beam theory for strongly orthotropic materials abstract this paper presents a displacement based model for orthotropic beams under plane linear elasticity based on the only kinematic assumption of transverse inextensibility any given axial and transverse loading as well as boundary conditions at the beam ends are considered the solution is decomposed into the principal and the residual part corresponding to the interior and the boundary problems which are obtained by series expansions of polynomial functions and eigenfunctions respectively it is proved that the proposed one dimensional theory gives both interior and boundary exact two dimensional elasticity solutions for strongly orthotropic materials i e for ratio between shear modulus and axial young modulus approaching zero for isotropic and orthotropic materials the accuracy of the beam model is also analysed and compared with that of other theories in particular the complementary energy error of the interior solution with respect to two dimensional elasticity is evaluated the asymptotic estimate of the characteristic decay length of end effects given in choi and horgan j appl mech asme 44 424 430 1977 by two dimensional analysis is reobtained and the range of validity of boundary solution is discussed the numerical results presented agree very well with exact and finite element solutions even in the neighbourhood of clamped cross sections where the solution is mainly governed by the boundary problem

on the two frequency spectra of timoshenko beams abstract this paper is concerned with the question of whether there are indeed two distinct spectra of frequencies for the transverse vibrations of timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and more recently for beams supported in an arbitrary manner elementary analysis leads to the conclusion that there is only a single frequency spectrum in the particular case of the simply supported beam the two frequency spectra viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex dynamical behavior of timoshenko beams

oscillation of first order delay equations we study the oscillation of first order delay equations using a method that parallels the use of riccati equations in the study of the oscillation of second order ordinary differential equations without delay we give an alternative proof of a comparison theorem first established by kwong and patula obtain some asymptotic behaviors of nonoscillatory solutions prove a new criterion that falls within a gap left open by established results and confirm a conjecture raised by hunt and yorke

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods

analogy between refined beam theories and the bernoulli euler theory abstract some refinements of the classical bernoulli euler theory of the bending of beams are shown to be completely analogous to the effects produced by sources of self stress in the bernoulli euler beam this is true for deflections bending moments and shearing forces they determine rotations stresses and strains according to the specific refined theory under consideration thus by analogy differences between the results of various refined theories having been the object of discussions in recent literature become accessible to a systematic classification in an appendix this strategy of treating refined theories from the point of view of the classical one is put into the more general context of the theory of science

upper bounds for the distances between adjacent zeros of solutions of delay differential equations abstract this paper is concerned with upper bounds for the distances between adjacent zeros of solutions of first order linear delay differential equations with variable coefficients of the form x t p t x t 0 t t where 0 and p t c t r by introducing a sequence of testing functions we are able to derive upper bounds that are better than those in the literature