a new exact approach for determining natural frequencies and mode shapes of non uniform shear beams with arbitrary distribution of mass or stiffness a new exact approach which combines the basic solutions with unit matrix property and recurrence formula for determining natural frequencies and mode shapes of non uniform shear beams is presented in this paper the function for describing the distribution of mass is arbitrary and the distribution of shear stiffness is expressed as a functional relation with the mass distribution and vice versa the governing equation for free vibration of a non uniform shear beam is reduced to a differential equation of the second order without the first order derivative by means of functional transformation then this kind of differential equation is reduced to bessel equations and other solvable equations for six cases the exact solutions of mode shape functions are thus found the basic solutions which have a unit matrix property are derived and used to obtain the frequency equations and mode shapes of multi step shear beams with varying cross sections numerical examples show that the calculated natural frequencies and mode shapes of two symmetric buildings are very close to the corresponding field measured data suggesting that the proposed methods are applicable to engineering application and practice

geometric significance of toeplitz kernels abstract let l 2 be the lebesgue space of square integrable functions on the unit circle we show that the injectivity problem for toeplitz operators is linked to the existence of geodesics in the grassmann manifold of l 2 we also investigate this connection in the context of restricted grassmann manifolds associated to p schatten ideals and essentially commuting projections

monitored heavy fuzzy measures and their role in decision making under uncertainty we discuss the fuzzy measure and the related idea of choquet aggregation we describe a prototypical application of the fuzzy measure in decision making under uncertainty we introduce an extension of the fuzzy measure called the monitored heavy fuzzy measure we give some examples of these new measures using these measures with the choquet integral we obtain a general class of aggregation operators that include both mean type operators and totaling type operators we consider the application of this measure to the problem of decision making under uncertainty in the case in which the uncertain variable can have multiple solutions

dynamic stiffness formulation and free vibration analysis of centrifugally stiffened timoshenko beams abstract the dynamic stiffness matrix of a centrifugally stiffened timoshenko beam has been developed and used to carry out a free vibration analysis the governing differential equations of motion of the beam in free vibration are derived using hamilton s principle and include the effect of an arbitrary hub radius for harmonic oscillation the derivation leads to two different but of similar form fourth order ordinary differential equations with variable coefficients that govern the amplitudes of bending displacement and bending rotation respectively an outboard force at the end of the beam is taken into account which makes possible the free vibration analysis of rotating non uniform or tapered timoshenko beams using the frobenius method of series solution and imposing boundary conditions the dynamic stiffness matrix which relates amplitudes of harmonically varying forces with the amplitudes of harmonically varying displacements at the ends of the element is formulated applying the wittrick williams algorithm to the resulting dynamic stiffness matrix the natural frequencies of a few carefully chosen illustrative examples are obtained the results are compared with those available in the literature

componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

the effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures part i simply supported and clamped clamped beams abstract a method for calculating the non linear mode shapes and natural frequencies of fully clamped beams at large vibration amplitudes is presented and results are compared with those of previous studies and of experimental measurements first the transverse displacement is assumed to be harmonic and is expanded in the form of a finite series of functions then the non linear deformation energy is expressed by taking into account the non linear terms due to the axial strain induced by large deflections a set of non linear algebraic equations which reduces to the classical linear eigenvalue problem when non linear terms are neglected is determined through hamilton s principle it is also shown that unless a condition is imposed on the contribution of one mode the solution of this set leads to the linear case consequently in order to obtain a numerical solution for the non linear problem in the neighbourhood of a given mode the contribution of this mode is chosen and those of other modes are calculated in this paper part i of a series of three papers this method is applied to obtain the first three non linear mode shapes of clamped clamped and simply supported beams the results obtained corresponding to the fundamental non linear mode shape are in good agreement with those of a previous theoretical and experimental study in particular high values of increase of beam curvatures are noticed near the clamps causing a highly non linear increase in bending strain with increasing deflection

quasicrystals and poisson s summation formula we characterize the measures on mathbb r which have both their support and spectrum uniformly discrete a similar result is obtained in mathbb r n for positive measures

on the flexural vibration of cylinders under axial loads numerical and experimental study abstract the flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the ritz method with terms of power series in the coordinate directions as approximating functions the effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory therefore geometrically nonlinear strain displacement relations with second order terms are considered here the natural frequencies of free free clamped clamped and sliding sliding cylinders subjected to axial loads are calculated using the proposed three dimensional ritz approach and are compared with those obtained with the finite element method and the bernoulli euler theory different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results an approach based on the ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression the results show that for low compressions the cylinder behaves similarly to a sliding sliding cylinder whereas for high compressions the cylinder vibrates as a clamped clamped one

a new approach for free vibration of axially functionally graded beams with non uniform cross section this paper studies free vibration of axially functionally graded beams with non uniform cross section a novel and simple approach is presented to solve natural frequencies of free vibration of beams with variable flexural rigidity and mass density for various end supports including simply supported clamped and free ends we transform the governing equation with varying coefficients to fredholm integral equations natural frequencies can be determined by requiring that the resulting fredholm integral equation has a non trivial solution our method has fast convergence and obtained numerical results have high accuracy the effectiveness of the method is confirmed by comparing numerical results with those available for tapered beams of linearly variable width or depth and graded beams of special polynomial non homogeneity moreover fundamental frequencies of a graded beam combined of aluminum and zirconia as two constituent phases under typical end supports are evaluated for axially varying material properties the effects of the geometrical and gradient parameters are elucidated the present results are of benefit to optimum design of non homogeneous tapered beam structures

free vibration of laminated cylindrical shells with a circular cutout a semi analytical solution method is presented for determining the natural frequencies and mode shapes of laminated cylindrical shells containing a circular cutout the method utilizes hamilton s principle to obtain the governing equations for the vibration response of the shell in the derivation of governing equations lagrange multipliers are employed to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints specifying appropriate stiffness values for the elastic extensional and rotational edge restraints springs allows the imposition of the kinematic boundary conditions in an indirect manner which enables the use of a broader set of functions for representing the displacement fields the natural frequencies and the corresponding modes of the shell are determined by transforming the governing equations into a matrix eigenvalue problem the present semi analytical solution method accurately predicts the natural frequency and vibration modes of the shells with a cutout the focus of this study is to investigate the effects of varying cutout size shell radius and laminate layup as well as the effects of two types of boundary conditions on the shell vibration response selected results of the parametric studies are presented for several geometric parameters to demonstrate that this semi analytical approach is a powerful means for optimizing design parameters

further results for modal characteristics of rotating tapered timoshenko beams the in plane and out of plane modes of free vibration of a tapered timoshenko beam mounted on the periphery of a rotating rigid hub are investigated the finite element method is used to discretize the beam this formulation permits unequal breadth and depth taper ratios as well as unequal element lengths the effects of shear deformation rotary inertia hub radius setting angle and spinning rotation are considered the generalized eigenvalue problem is defined using explicit expressions for the mass and stiffness matrices and numerical solutions are generated for a wide range of parameter variations explicit expressions of southwell coefficients are presented for the first time for the case of rotating uniform and tapered timoshenko beams comparisons are made wherever possible with exact solutions and other numerical results available in the literature extended results are obtained to serve as a benchmark solution for other numerical techniques and specialized applications

essentially commuting projections abstract let h h h be a fixed orthogonal decomposition of a hilbert space with both subspaces of infinite dimension and let e e be the projections onto h and h we study the set p c c of orthogonal projections p in h which essentially commute with e or equivalently with e i e p e p e e p is compact by means of the projection onto the calkin algebra one sees that these projections p p c c fall into nine classes four discrete classes which correspond to p being 0 1 e or e and five essential classes which we describe below the discrete classes are respectively the finite rank projections finite co rank projections the sato grassmannian of h and the sato grassmannian of h thus the connected components of each of these classes are parametrized by the integers via de rank the co rank or the fredholm index respectively the essential classes are shown to be connected we are interested in the geometric structure of p c c being the set of selfadjoint projections of the c algebra b c c of operators in b h which essentially commute with e in particular we study the problem of existence of minimal geodesics joining two given projections in the same component we show that the hopf rinow theorem holds in the discrete classes but not in the essential classes conditions for the existence and uniqueness of geodesics in these latter classes are found

the effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells part i coupled transverse circumferential mode shapes of isotropic circular cylindrical shells of infinite length the effects of large vibration amplitudes on the first and second coupled radial circumferential mode shapes of isotropic circular cylindrical shells of infinite length are examined a theoretical model based on hamilton s principle and spectral analysis developed previously for clamped clamped beams and fully clamped rectangular plates is extended to shell type structures reducing the large amplitude free vibration problem to the solution of a set of non linear algebraic equations the transverse and circumferential displacements are assumed to be harmonic and expanded in the form of a finite series of functions the donnel mushtarie shell theory taking into account the coupling between extensional and flexural deformations is used then the non linear deformation energy is expressed by taking into account the non linear term due to the considerable stretching of the middle surface of the shell induced by large deflections tables of numerical results are given for the first and second non linear modes for a wide range of the vibration amplitude which may be used for engineering purposes for each value of the vibration amplitude considered the corresponding contributions of the basic functions defining the non linear transverse and circumferential displacement shapes are given with the corresponding non linear frequencies selected plots of mode shapes and bending stress distributions are presented with an extensive discussion of the effects of non linearity on the dynamic behaviour of shells

asymptotic analysis of the dynamic problem of the theory of elasticity for a transverse isotropic hollow cylinder the forced vibrations of a transverse isotropic hollow cylinder loaded by an axisymmetric harmonic force at the butt ends are studied using the homogeneous solutions method a dispersion equation for the corresponding three dimensional elastic problem is derived that relates the wave number to the frequency of oscillations this equation is solved by an asymptotic method in the case of a thin wall and the possible waveforms of the tube are found

an analytical numerical and experimental study of the axisymmetric vibrations of a short cylinder this paper presents a study of standing axisymmetric waves in homogeneous isotropic linear and elastic cylinders whose length and diameter are of the same order of magnitude it is analytically demonstrated that only materials with a poisson s ratio equal to zero can vibrate in pure radial and longitudinal axisymmetric modes and hence the universal frequencies independent of poisson s ratio and the corresponding universal aspect ratios can be accurately calculated the ritz method is applied to numerically determine the natural frequencies and the mode shapes of finite cylinders vibration of a cylinder in the neighbourhood of the universal point is analysed both free and forced vibrations are experimentally detected by using a laser speckle interferometer that allows the determination of the natural frequencies and the mode shapes from the numerical calculations it is confirmed that for materials with poisson s ratio not equal to zero no crossings occur between the curves of non dimensional frequency versus aspect ratio neither for antisymmetric modes themselves nor for symmetric modes there is a good agreement between the analytical solutions the numerical results and the experimental measurements

on the natural frequencies of short cylinders and the universal point direct determination of the shear modulus this work presents a study of the relation between the lowest nondimensional natural frequencies of a short free cylinder vibrating in axisymmetric modes its slenderness ratio and its poisson s ratio ritz s method applied to the study of the symmetric vibration of cylinders confirms that all curves which show the dependence of frequency versus slenderness pass through a point called universal independently of poisson s ratio the lowest universal frequency is 2 6036 and corresponds to a cylinder whose quotient of its length and its diameter is 0 853 22 the rules leading to the identification of the first symmetric mode are inferred from the numerical results a cylinder with universal slenderness ratio is set into free vibration by applying an axial impact the lowest axisymmetric natural frequencies are obtained from measurement of the axial displacement by speckle interferometry a simple arithmetical operation permits calculation of the shear modulus from the value of the first symmetric frequency the diameter of the cylinder and its density the quotient of frequencies of two similar cylinders is studied as a function of their elastic properties and diameters

domain semantics of possibility computations the purpose of this paper is to introduce a kind of computational model called possibility computation to deal with non determinism both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified in this approach the denotational semantics will be set up by assigning to programs possibility state transformers i e scott continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states this possibility powerdomain of a dcpo will consist of all possibility valuations ordered pointwise of this dcpo the logical semantics will be given by fuzzy predicate transformers introduced by the first author and jung following dijkstra s predicate transformers two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations the categorical monad of the possibility powerdomain will be investigated

the symmetric sugeno integral we propose an extension of the sugeno integral for negative numbers in the spirit of the symmetric extension of choquet integral also called sipos integral our framework is purely ordinal since the sugeno integral has its interest when the underlying structure is ordinal we begin by defining negative numbers on a linearly ordered set and we endow this new structure with a suitable algebra very close to the ring of real numbers in a second step we introduce the mobius transform on this new structure lastly we define the symmetric sugeno integral and show its similarity with the symmetric choquet integral

the restricted grassmannian banach lie poisson spaces and coadjoint orbits we investigate some basic questions concerning the relationship between the restricted grassmannian and the theory of banach lie poisson spaces by using universal central extensions of lie algebras we find that the restricted grassmannian is symplectomorphic to symplectic leaves in certain banach lie poisson spaces and the underlying banach space can be chosen to be even a hilbert space smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established several pathological properties of the restricted algebra are pointed out

hopf rinow theorem in the sato grassmannian abstract let u 2 h be the banach lie group of unitary operators in the hilbert space h which are hilbert schmidt perturbations of the identity 1 in this paper we study the geometry of the unitary orbit u p u u u 2 h of an infinite projection p in h this orbit coincides with the connected component of p in the hilbert schmidt restricted grassmannian gr res p also known in the literature as the sato grassmannian corresponding to the polarization h p h p h it is known that the components of gr res p are differentiable manifolds here we give a simple proof of the fact that gr res 0 p is a smooth submanifold of the affine hilbert space p b 2 h where b 2 h denotes the space of hilbert schmidt operators of h also we show that gr res 0 p is a homogeneous reductive space we introduce a natural metric which consists in endowing every tangent space with the trace inner product and consider its levi civita connection this connection has been considered before for instance its sectional curvature has been computed we show that the levi civita connection coincides with a linear connection induced by the reductive structure a fact which allows for the easy computation of the geodesic curves we prove that the geodesics of the connection which are of the form t e t z p e t z for z a p co diagonal anti hermitic element of b 2 h have minimal length provided that z 2 note that the condition is given in terms of the usual operator norm a fact which implies that there exist minimal geodesics of arbitrary length also we show that any two points p 1 p 2 gr res 0 p are joined by a minimal geodesic if moreover p 1 p 2 1 the minimal geodesic is unique finally we replace the 2 norm by the k schatten norm k 2 and prove that the geodesics are also minimal for these norms up to a critical value of t which is estimated also in terms of the usual operator norm in the process minimality results in the k norms are also obtained for the group u 2 h

spectral gaps for sets and measures if x is a closed subset of the real line denote by gx the supremum of the size of the gap in the fourier spectrum of a measure taken over all non trivial finite complex measures supported on x in this paper we attempt to find gx in terms of x

classes of solutions in the problem of stability analysis in bars with varying cross section and axial distributed loading we construct classes of analytical solutions for the linear ordinary differential equation of variable coefficients governing the stability analysis of bars with varying cross section and axial distributed loading the analytical solutions obtained by li et al 1995 int j solids structures for two kinds of variable stiffness and axial loading in such types of bars result as special cases

convergence theorems for monotone measures in classical measure theory there are a number of convergence theorems such as the egorov the riesz and the lusin theorem among others we consider monotone measures i e monotone set functions vanishing in the empty set and defined on a measurable space and discuss how and to which extent classical convergence theorems can be carried over to this more general case

a power series solution for vibration of a rotating timoshenko beam abstract equations of motion for a rotating beam are developed based on the timoshenko beam theory which includes the effects of rotary inertia and shear deformation this leads to two variable coefficient differential equations for which only approximate solutions have been used in previous analyses this paper presents a convergent power series expression to solve analytically for the exact natural frequencies and modal shapes of rotating timoshenko beams first the results are presented for non rotating timoshenko beams and rotating euler bernoulli beams and compared with existing solutions some errors existing in a previous result are pointed out and corrected then the effects of rotary inertia and shear deformation on the dynamic characteristics of rotating beams are evaluated the exact solutions can be used both as a direct analytical solution for practical engineering problems and as a bench mark for approximate numerical models

free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method abstract starting from the governing differential equations of motion in free vibration the dynamic stiffness matrix of a uniform rotating bernoulli euler beam is derived using the frobenius method of solution in power series the derivation includes the presence of an axial force at the outboard end of the beam in addition to the existence of the usual centrifugal force arising from the rotational motion this makes the general assembly of dynamic stiffness matrices of several elements possible so that a non uniform or tapered rotating beam can be analyzed for its free vibration characteristics by idealizing it as an assemblage of many uniform rotating beams the application of the derived dynamic stiffness matrix is demonstrated by investigating the free vibration characteristics of uniform and non uniform tapered rotating beams with particular reference to the wittrick williams algorithm the results from the present theory are compared with published results it is shown that the proposed dynamic stiffness method offers an accurate and effective method of free vibration analysis of rotating beams

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

improvement of the semi analytical method based on hamilton s principle and spectral analysis for determination of the geometrically non linear response of thin straight structures part iii steady state periodic forced response of rectangular plates abstract in parts i and ii of this series of papers a practical simple multi mode theory based on the linearization of the non linear algebraic equations written on the modal basis in the neighbourhood of each resonance has been developed for beams and fully clamped rectangular plates 1 simple explicit formulae have been derived which allowed via the so called first formulation direct calculation of the basic function contributions to the first three non linear mode shapes of clamped clamped and clamped simply supported beams and the two first non linear mode shapes of fcrp also in part i of this series of papers this approach has been successively extended in order to determine the amplitude dependent deflection shapes associated with the non linear steady state periodic forced response 2 of clamped clamped beams excited by a concentrated or a distributed harmonic force in the neighbourhood of the first resonance this new approach has been applied in the present work to obtain the nlsspfr formulation for fcrp ssrp and cccssrp leading in each case to a non linear system of coupled differential equations which may be considered as a multi dimensional form of the well known duffing equation the single mode assumption and the harmonic balance method have been used for both harmonic concentrated and distributed excitation forces leading to one dimensional non linear frequency response functions of the plates considered comparisons have been made between the curves based on these functions and the results available in the literature showing a reasonable agreement for finite but relatively small vibration amplitudes a more accurate estimation of the fcrp non linear frequency response functions has been obtained by the extension of the improved version of the semi analytical model developed in part i for the nlsspfr of beams to the case of fcrp leading to explicit analytical expressions for the multi dimensional non linear frequency response function depending on the forcing level and the amplitude of the response induced in the range considered for the excitation frequency

the effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates part ii iterative and explicit analytical solution for non linear coupled transverse and in plane vibrations the objective of this paper is to present a more realistic and complete study of the geometrically non linear free vibrations of clamped immovable circular plates by taking into account the in plane deformation which has not been examined in part i of this series of papers j sound vibration 265 2003 123 the problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to twice the plate thickness the numerical results thus obtained are presented and compared with the available published results and with the ones calculated when neglecting the in plane displacement for the first two non linear axisymmetric mode shapes an explicit analytical solution is then presented and its range of validity for the fundamental non linear mode is determined via a detailed comparison with the solution based on the iterative procedure the results obtained by the explicit method show the usefulness of the new approach in comparison with the single mode approach solution frequently used in non linear vibration analysis of structures and are expected to be easy to implement in fatigue models in order to make more realistic and secure predictions of the structural fatigue life

accurate vibration frequencies of circular cylinders from three dimensional analysis a three dimensional 3 d method of analysis developed in a companion paper a w leissa and j so j acoust soc am 98 2122 2135 1995 is used to obtain free vibration frequencies of completely free elastic cylinders extensive accurate data are presented for the first 20 frequencies of each circumferential wave number 0 5 for free free cylinders having length to diameter ratios l d of 1 1 5 2 3 and 5 with a poisson s ratio of 0 3 an additional study for l d 1 over the full range 0 0 5 possible for isotropic materials shows that poisson s ratio effects can be quite important the first known values of frequencies from 3 d analysis of cylinders having one end fixed with all other boundaries free are also presented in considerable detail for free free cylinders comparisons are made with less accurate 3 d results published previously by other researchers

on chebyshev type inequalities for generalized sugeno integrals abstract we give the necessary and sufficient conditions guaranteeing the validity of chebyshev type inequalities for generalized sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions for several choices of operators we characterize the classes of functions for which the chebyshev type inequality for the classical sugeno integral is satisfied

optimization of the ritz method to calculate axisymmetric natural vibration frequencies of cylinders a straightforward accurate technique is presented for calculating natural frequencies for axisymmetric vibration of cylinders of any aspect ratio the ritz variational method is applied by using algebraic polynomials in the form of power series in the axial and radial coordinates the adequate choice of the maximum exponents for each coordinate is important factor in order to achieve better accuracy compatible with an admissible time of calculation a computational model is developed that provides the optimum selection of exponents by following an automatic iterative process this leads to a precise calculation of frequencies in a minimum time of calculation the method is tested by comparing numerical and experimental results and a good agreement is obtained the common hypothesis on the number of terms in the radial and axial coordinates is not sufficiently justified as is proved

an algorithm for identification of fuzzy measure in the paper the connection between fuzzy measures and lebesgue measure is discussed special attention is focused on fuzzy measures which satisfy the so called l rule a relation between such measures and probability measures is given basing on this relation a simple and fast algorithm for identification of a sugeno fuzzy measure is presented

hierarchy of hamilton equations on banach lie poisson spaces related to restricted grassmannian abstract we consider the banach lie poisson space i r u l res 1 and its complexification c l res 1 where the first one of them contains the restricted grassmannian gr res as a symplectic leaf using the magri method we define an involutive family of hamiltonians on these banach lie poisson spaces the hierarchy of hamilton equations given by these hamiltonians is investigated the operator equations of ricatti type are included in this hierarchy for a few particular cases we give the explicit solutions

generalized convergence theorems for monotone measures abstract in this paper we propose three types of absolute continuity for monotone measures and present some of their basic properties by means of these three types of absolute continuity we establish generalized egoroff s theorem generalized riesz s theorem and generalized lebesgue s theorem in the framework involving the ordered pair of monotone measures the egoroff theorem the riesz theorem and the lebesgue theorem in the traditional sense concerning a unique monotone measure are extended to the general case these three generalized convergence theorems include as special cases several previous versions of egoroff like theorem riesz like theorem and lebesgue like theorem for monotone measures respectively

a restricted shift completeness problem abstract we solve a problem about the orthogonal complement of the space spanned by restricted shifts of functions in l 2 0 1 posed by m carlsson and c sundberg

on egoroff s theorems on finite monotone non additive measure space in this note we give four versions of egoroff s theorem in non additive measure theory by using condition e the pseudo condition e of set function and the duality relations between the conditions these conditions offered are not only sufficient but also necessary for the four kinds of egoroff s theorems

free vibration of rotating tapered beams using the dynamic stiffness method abstract the free bending vibration of rotating tapered beams is investigated by using the dynamic stiffness method the range of problems considered includes beams for which the depth and or width of the cross section vary linearly along the length first the governing differential equation of motion of the rotating tapered beam in free flap bending vibration is derived for the most general case using hamilton s principle allowing for the effects of centrifugal stiffening an arbitrary outboard force and the hub radius term for harmonic oscillation the differential equation is solved for bending displacement by applying the frobenius method of series solution the expressions for bending rotation shear force and bending moment at any cross section of the beam are also obtained in explicit analytical form then the dynamic stiffness matrix is developed by relating the amplitudes of forces and moments to those of the displacements and rotations at the ends of the harmonically vibrating tapered beam next the wittrick williams algorithm is used as a solution technique to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of some illustrative examples a parametric study is carried out to demonstrate the effects of rotational speed taper ratio and hub radius on the results which are discussed and compared with the published ones finally some conclusions are drawn

comparisons of vibration frequencies for rods and beams from one dimensional and three dimensional analyses a method of three dimensional 3 d analysis is developed for the free vibration frequencies and mode shapes of solid circular cylinders of elastic material the method assumes for the three displacement components a fourier series in the circumferential direction and algebraic polynomials in the radial r and axial z directions all types of boundary conditions and arbitrary length to diameter ratios l d may be accommodated extensive convergence studies show that frequencies which are exact to five or six significant figures may be obtained for cylinders with free free ends and that three or four figure accuracy is achievable for fixed free ends these accurate frequencies are compared with ones determined from known elementary and improved 1 d theories for longitudinal torsional and bending modes for various l d ratios thereby establishing the ranges of accuracy of the 1 d analyses for circular cross sections

the effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells part ii a new approach for free transverse constrained vibration of cylindrical shells abstract the non linear dynamic behaviour of infinitely long circular cylindrical shells in the case of plane strains is examined and results are compared with previous studies a theoretical model based on hamilton s principle and spectral analysis previously developed for non linear vibration of thin straight structures beams and plates is extended here to shell type structures reducing the large amplitude free vibration problem to the solution of a set of non linear algebraic equations in the present work the transverse displacement is assumed to be harmonic and is expanded in the form of a finite series of functions corresponding to the constrained vibrations which exclude the axisymmetric displacements the non linear strain energy is expressed by taking into account the non linear terms due to the considerable stretching of the shell middle surface induced by large deflections it has been shown that the model presented here gives new results for infinitely long circular cylindrical shells and can lead to a good approximation for determining the fundamental longitudinal mode shape and the associated higher circumferencial mode shapes n 3 of simply supported circular cylindrical shells of finite length the non linear results at small vibration amplitudes are compared with linear experimental and theoretical results obtained by several authors for simply supported shells numerical results non linear frequencies vibration amplitudes and basic function contributions of infinite shells associated to the first four mode shapes of free vibrations are obtained using a multi mode approach and are summarized in tables good agreement is found with results from previous studies for both small and large amplitudes of vibration the non linear mode shapes are plotted and discussed for different thickness to radius ratios the distributions of the bending stresses associated with the mode shapes are given and compared with those obtained via the linear theory

axisymmetric free vibrations of finite anisotropic cylinders abstract a technique is presented for obtaining estimates for the natural frequencies of axisymmetric free vibration for anisotropic cylinders of finite length the weak forms of the governing differential equations are solved by using the ritz method with terms of power series in the co ordinate directions as the approximating functions the dimensions of the cylinder are arbitrary and a wide range of geometries can be considered the solution technique is applied to the example problems of an isotropic cylinder and a cylinder composed of a material with hexagonal symmetry the method gives natural frequencies and mode shapes that are in excellent agreement with existing solutions the condition of traction free faces of the cylinder is also accurately satisfied

weighted exponential approximation and non classical orthogonal spectral measures abstract a long standing open problem in harmonic analysis is given a non negative measure on r find the infimal width of frequencies needed to approximate any function in l 2 we consider this problem in the perturbative regime and characterize asymptotic smallness of perturbations of measures which do not change that infimal width then we apply this result to show that there are no local restrictions on the structure of orthogonal spectral measures of one dimensional schrodinger operators on a finite interval this answers a question raised by v a marchenko

three dimensional vibratory characteristics of solid cylinders and some remarks on simplified beam theories abstract a set of linear three dimensional frequency equations that describes the vibratory characteristics of elastic solid cylinders of different end supports is derived starting from the linear small strain three dimensional elasticity theory integral expressions for strain and kinetic energies are formulated the three dimensional mode shapes are expressed in terms of sets of one and two dimensional orthogonal polynomial functions which are to approximate the longitudinal and lateral surface variations of solid cylinders from the resulting displacement based energy expressions the variational form of the three dimensional energy functional is minimized to yield the linear eigen value equation frequency solutions for elastic solid cylinders of different lengths and end support conditions are determined the accuracy of solutions is validated through convergence tests and comparisons with the existing three dimensional analytical solutions and empirical data from the present three dimensional elasticity solutions some remarks on the existing simplified beam theories are made particular attention is drawn to timoshenko s shear deformable beam theory for transverse bending modes the validity of the one dimensional wave equation for longitudinal and torsional modes is also discussed

type alternative for frostman measures abstract for a finite positive borel measure on r its exponential type t is defined as the infimum of a 0 such that finite linear combinations of complex exponentials with frequencies between 0 and a are dense in l 2 the definition can be easily extended from finite to broader classes of measures in this paper we prove a new formula for t and use it to study growth and additivity properties of measures with finite positive type as one of the applications we show that frostman measures on r may only have type zero or infinity

three dimensional vibration analysis of solid cylinders of polygonal cross section using thep ritz method abstract theoretical and numerical analyses and some observations on the physical phenomena of free vibration of solid cylinders having square and hexagonal cross sections with combinations of fixed and free ends are reported the formulation is established based on the linear small strain three dimensional elasticity principle and thep ritz method is employed for computing the solution of the problem by expanding the displacements in spatial co ordinates integral expressions for strain and kinetic energies in a three dimensional setting are derived in cartesian form sets of one and two dimensional orthogonal polynomials are constructed to represent the three dimensional variations in the longitudinal and lateral surface directions a basic function is introduced in these polynomials to cater for the stress free lateral surfaces and the kinematic constraints at both ends several examples are solved to demonstrate the applicability of the method first known results in terms of vibration frequency parameters and mode shapes of cylinders having square and hexagonal cross sections for various symmetry classes and ends constraints are presented and the physics behind the results is highlighted these new results may serve as benchmark data for future research development in simplified beam theories

fuzzy measures and integrals we present fuzzy measures and fuzzy integrals as special poset homeomorphisms besides general fuzzy integrals regular fuzzy integrals are introduced and some of their properties are discussed state of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched

on free vibration of thin cylindrical shells with large circumferential wavenumber rayleigh s solution the method of matched asymptotic expansions is used to obtain the natural frequencies and mode shapes for thin ha 0 cylindrical shells corresponding to large circumferential wavenumbers n where n o ah 12 the deformation is nearly inextensional the frequency results are similar to rayleigh s result and are independent of end fixity through o 1n2 compared to unity

hyperkahler structures and infinite dimensional grassmannians abstract in this paper we describe an example of a hyperkahler quotient of a banach manifold by a banach lie group although the initial manifold is not diffeomorphic to a hilbert manifold not even to a manifold modelled on a reflexive banach space the quotient space obtained is a hilbert manifold which can be furthermore identified either with the cotangent space of a connected component gr res j j z of the restricted grassmannian or with a natural complexification of this connected component thus proving that these two manifolds are isomorphic hyperkahler manifolds moreover kahler potentials associated with the natural complex structure of the cotangent space of gr res j and with the natural complex structure of the complexification of gr res j are computed using kostant souriau s theory of prequantization

some notes on homogeneity property of semiconormed fuzzy integrals in this note we show that some results of homogeneity of semiconormed fuzzy integrals which are given by kim homogeneity properties of seminormed fuzzy integrals fuzzy sets and systems 157 2006 411 426 are not valid

free vibration analysis of rotating beams by a variable order finite element method the free vibration of rotating beams is analyzed by means of a finite element method of variable order this method entails displacement functions that are a complete power series of a variable number of terms the terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and additionally displacements at certain points within the element the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series numerical results are presented for uniform beams with zero and nonzero hub radii tapered beams and a nonuniform beam with discontinuities since the present method reduces to a conventional beam finite element method for a cubic displacement function the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom indeed essentially exact eigenvalues and eigenvectors are obtained with this technique which is far more rapidly convergent than other approaches in the literature

optimal paths for symmetric actions in the unitary group given a positive and unitarily invariant lagrangian mathcal l defined in the algebra of matrices and a fixed time interval 0 t 0 subset mathbb r we study the action defined in the lie group of n times n unitary matrices mathcal u n by mathcal s alpha int 0 t 0 mathcal l dot alpha t dt where alpha 0 t 0 to mathcal u n is a rectifiable curve we prove that the one parameter subgroups of mathcal u n are the optimal paths provided the spectrum of the exponent is bounded by moreover if mathcal l is strictly convex we prove that one parameter subgroups are the unique optimal curves joining given endpoints finally we also study the connection of these results with unitarily invariant metrics in mathcal u n as well as angular metrics in the grassmann manifold

hierarchical finite element method for rotating beams abstract the free vibration characteristics of rotating beams are analyzed by means of a finite element method of hierarchical form in which the displacement function for the element is taken to be a polynomial of variable degree the first four terms of the polynomial are expressed in terms of the displacements and slopes at the extremities of the elements and the rest of the terms are considered as internal degrees of freedom numerical results are presented for cantilever beams with uniform non uniform and discontinuous sectional properties a comparison of the present results with those in the published literature indicates that the present relatively simple formulation is as efficient as the other well established techniques finally some clarification is also provided of certain subtle issues concerning the accuracy of the finite element solution and monotonic convergence characteristics and their dependence on the arithmetic precision of the computer employed is indicated

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

dynamic characteristics of a beam and distributed spring mass system this paper studies dynamic characteristics of a beam with continuously distributed spring mass which may represent a structure occupied by a crowd of people dividing the coupled system into several segments and considering the distributed spring mass and the beam in each segment being uniform the equations of motion of the segment are established the transfer matrix method is applied to derive the eigenvalue equation of the coupled system it is interesting to note from the governing equations that the vibration mode shape of the uniformly distributed spring mass is proportional to that of the beam at the attached regions and can be discontinuous if the natural frequencies of the spring masses in two adjacent segments are different parametric studies demonstrate that the natural frequencies of the coupled system appear in groups in a group of frequencies all related modes have similar shapes the number of natural frequencies in each group depends on the number of segments having different natural frequencies with the increase of group order the largest natural frequency in a group monotonically approaches the natural frequency of corresponding order of the bare beam from the upper side whereas the others monotonically move towards those of the independent spring mass systems from the lower side numerical results show that the frequency coupling between the beam and the distributed spring mass mainly occurs in the low order of frequency groups especially in the first group in addition vibratory characteristics of the coupled system can be approximately represented by a series of discrete multi degrees of freedom system it also demonstrates that a beam on winkler elastic foundation and a beam with distributed solid mass are special cases of the proposed solution

polya sequences toeplitz kernels and gap theorems abstract a separated sequence on the real line is called a polya sequence if any entire function of zero exponential type bounded on is constant in this paper we solve the problem by polya and levinson that asks for a description of polya sets we also show that the polya levinson problem is equivalent to a version of the so called beurling gap problem on fourier transforms of measures the solution is obtained via a recently developed approach based on the use of toeplitz kernels and de branges spaces of entire functions

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

forced vibrations of solid elastic cylinders abstract a method is presented to determine the vibration response of a solid elastic isotropic cylinder with arbitrary length to radius ratio when subject to arbitrary distribution of axisymmetric excitation on its surfaces in this method the axial and radial components of displacement are expressed as a sum of two infinite series each term in both the series is an exact solution to the governing equations of motion and has a coefficient that is used to satisfy boundary conditions one series contains bessel functions that form a complete set in the radial direction and the other contains trigonometric functions that form a complete set in the axial direction the components of stress are also expressed in terms of complete sets of functions by using the expression for displacement the coefficients in the series are determined by using the orthogonal properties of the functions to satisfy the boundary conditions in a mean square error sense numerical results are presented to illustrate the broadband responses of cylinders to uniform and concentrated loads on the flat and curved surfaces they are in good agreement with results obtained using atila a commercial finite element software

beurling malliavin theory for toeplitz kernels we consider the family of toeplitz operators t j bar s a acting in the hardy space h2 in the upper halfplane j and s are given meromorphic inner functions and a is a real parameter in the case where the argument of s has a power law type behavior on the real line we compute the critical value c j s inf left a mathop mathrm ker t j bar s a ne0 right the formula for c j s generalizes the beurling malliavin theorem on the radius of completeness for a system of exponentials

operators which are the difference of two projections abstract we study the set d of differences d a p q p q p where p denotes the set of orthogonal projections in h we describe models and factorizations for elements in d which are related to the geometry of p the study of d throws new light on the geodesic structure of p we show that two projections in generic position are joined by a unique minimal geodesic the topology of d is examined particularly its connected components are studied also we study the subsets d c d f where d c are the compact elements in d and d f are the differences a p q such that the pair p q is a fredholm pair p q is a fredholm pair if q p r p r p r q is a fredholm operator

a problem on completeness of exponentials let be a nite positive measure on the real line for a 0 denote by ea the family of exponential functions ea fe ist j s2 0 a g

subspaces of c infty invariant under the differentiation let l be a proper differentiation invariant subspace of c infinity a b such that the restriction operator d dx vertical bar l has a discrete spectrum lambda counting with multiplicities we prove that l is spanned by functions vanishing outside some closed interval i subset of a b and monomial exponentials x k e lambda x corresponding to lambda if its density is strictly less than the critical value vertical bar i vertical bar 2 pi and moreover we show that the result is not necessarily true when the density of lambda equals the critical value this answers a question posed by the first author and b korenblum finally if the residual part of l is trivial then l is spanned by the monomial exponentials it contains c 2015 elsevier inc all rights reserved less

analysis of weak solution of euler bernoulli beam with axial force in this paper we discuss about the existence and uniqueness of the weak form of the non uniform cantilever euler bernoulli beam equation with variable axial tensile and compressive force we investigate the reason of the buckling from the coercivity analysis the frequencies of the beam with tensile force are found by the galerkin method in the sobolev space h2 with proper norm using this method a system of ordinary differential equations in time variable is formed and the corresponding mass and stiffness matrices are constructed a very general form of these matrices which is very simple and suitable for calculations is derived here with a standard basis numerical results for rotating beams with polynomial stiffness and mass variation typical of wind turbine and helicopter rotor blades are obtained these results match well with the published literature a new polynomial generating set is found using two elements of this set a formula to find the eigenfrequencies is derived the proposed approach is easy to implement in symbolic computing software

characterization of invariant aggregation operators abstract following the ideas of bartlomiejczyk and drewniak minimal invariant subsets of 0 1 n are investigated an equivalence relation on these subsets is introduced consequently invariant aggregation operators are characterized by means of choquet integral based representation there are exactly 68 binary invariant aggregation operators 4 among them are also continuous further there are 6 self dual invariant binary aggregation operators a recurrent method of constructing invariant aggregation operators for n 2 is proposed restriction of invariant aggregation operators to finite scales is also discussed

dynamic model for free vibration and response analysis of rotating beams abstract a new modeling method for the vibration analysis of a rotating cantilever beam is proposed and compared to the other modeling methods applying the hamilton principle the equations for the axial chordwise and flapwise motions are derived during the derivation of these equations the nonlinear von karman strain and the corresponding linear stress are used to consider the stiffening effect due to rotation the derived equations of motion obtained from the proposed method are analytically and numerically compared to equations from the previous modeling methods computations of the natural frequencies and time responses show that the described equations of motion are more reliable than the equations of the other modeling methods

on fuzzy number valued fuzzy measures defined by fuzzy number valued fuzzy integrals ii abstract in this paper we discuss some properties of a fuzzy number valued fuzzy set function defined by a fuzzy number valued fuzzy integral on the fuzzy set and give sufficient conditions that it is a fuzzy number valued fuzzy measure