vibration of rotationally periodic structures abstract the purpose of this paper is to determine eigensolutions of a rotationally periodic structure p of period n in terms of those of the i th substructure s i of p let y i be the generalized displacement vector and f i be the generalized force vector at interface i i where substructures s i and s i 1 are connected transfer function formulation of s i implies that there exists a linear operator g mapping y t and f i at interface i i to y i 1 and f i 1 at interface i i 1 in addition the operator g depends on transfer functions and therefore eigensolutions of s i the periodicity of p then requires that gn be an identity map this results in n self adjoint fredholm integral equations the non trivial solutions of which predict eigensolutions of p as a consequence a periodic structure p with period n will have exactly n eigenvalues lying between two consecutive eigenvalues of the substructure s i if the interface i i contains only one degree of freedom finally three examples are illustrated the first example considers anti plane strain vibration of a linear elastic solid containing four slots of infinitesimal width the second example derives exact eigensolutions of a string mass periodic structure the third example illustrates how eigensolutions of an axisymmetric structure can be recovered under the formulation of rotationally periodic structures

multi mode trimming of imperfect thin rings using masses at pre selected locations abstract this paper presents a practical method for trimming the natural frequencies of an initially imperfect ring to simultaneously eliminate certain of the frequency splits present compared with previous work the novel feature of this method is that the trimming masses are positioned at pre selected locations on the ring the basis for the proposed method is the concept of equivalent imperfection mass which allows any imperfect ring to be considered as a perfect ring with equivalent imperfection masses attached by considering this trimming problem it is deduced that it is possible to trim n pairs of modes simultaneously by removing a minimum of 2 n trimming masses at particular locations around the ring by positioning the trimming masses at pre selected locations it is shown that a simple set of trimming masses can be calculated easily and from this set an infinite number of solution sets can be found methods for generating these sets are outlined for the trimming of both a single and a dual pair of modes in practice it is likely that the trimming masses will be spaced regularly for this special case it is found that it is not possible to trim all single and dual mode pairs with any arrangement of masses validation of the derived simple solution set and the proposed procedure to generate further sets is achieved by studying a number of theoretical examples

the weighted hardy s inequality for nonincreasing functions the purpose of this paper is to give an alternative proof of recent results of m arino and b muckenhoupt 1 and e sawyer 8 concerning hardy s inequality for nonincreasing functions and related applications to the boundedness of some classical operators on general lorentz spaces our approach will extend the results of 1 8 to the values of the parameters which are inaccessible by the methods of these papers

free vibrations of elliptical rings with circumferentially variable thickness abstract this paper deals with the in plane free vibration of rings with a nominally elliptical centreline results are presented for rings of constant axial length that have a rectangular cross section the radial thickness of which is constant or has a simple analytically defined circumferential variation additionally and for the first time the effects of small variations in in plane profile such as those arising in practical rings due to manufacturing tolerances are considered the problem is tackled using an approach in which the true middle surface is determined numerically from the outer and inner surface profiles which can be defined either by exact analytical expressions or in a more general way using fourier series the rayleigh ritz method is used to obtain the natural frequencies and mode shapes results are presented for a range of cases including some that have previously been studied by other authors and some that have not the effects on frequency splitting due to profile variations and the aspect ratio of the ellipse are emphasized results obtained using the developed numerical approach show excellent agreement with finite element predictions

dynamic analysis of finite linear elastic solids containing small elastic imperfections theory with application to asymmetric circular plates abstract eigensolutions green s functions and steady state responses of three dimensional homogeneous isotropic finite linear elastic solids containing small linear elastic imperfections are presented in this paper the inhomogeneities are treated as perturbations to otherwise homogeneous solids the spectral eigensolutions of which are known the exact eigensolutions of the imperfect solid formulated through the betti reciprocal theorem satisfy a set of integral equations from which both analytic perturbation formulas and a numerical iteration scheme are developed special emphasis is given to analysis of perfect homogeneous elastic solids that are spectrally degenerate finally the vibration of circular plates with evenly spaced radial inclusions which cause splitting of some of the repeated vibration modes is analyzed both analytically and numerically for the eigensolutions

modeling fractal entrainment sets of tracers advected by chaotic temporally irregular fluid flows using random maps abstract we model a two dimensional open fluid flow that has temporally irregular time dependence by a random map n 1 m n n where on each iterate n the map m n is chosen from an ensemble we show that a tracer distribution advected through a chaotic region can be entrained on a set that becomes fractal as time increases theoretical and numerical results on the multifractal dimension spectrum are presented

vibration characteristics of systems with multiple blades abstract an interesting phenomenon can be observed when the state space dynamic substructural method is applied to the eigenproblem of bladed disk shaft systems whether or not the shaft is flexible each frequency of the single root fixed blade appears as a frequency of the whole structure with a multiplicity of at least n 3 wheren is the number of repetitive blades the presented result can be regarded as an extension of previous findings by the authors in the sense that the commonly interfaced repetitive substructures are allowed to be treated as a rigid body in modal analysis the defectiveness issue of the multiple eigenvalues arising from the repetitive substructures is also addressed examples of rotary wing models and a simplified turbine model are presented for validation together with attempting their physical explanations

linearly coupled shaft torsional and blade bending vibrations in multi stage rotor blade systems abstract in an attempt towards the understanding of coupling effects between shaft torsional and blade in plane bending vibrations in turbomachinery and other rotating bladed structures an idealized model is considered where the blades are represented by uniform euler bernouilli beams a synthetical multi frame and mixed consisting in a coalescence of finite element and galerkin methods approach is used to derive a linearized mathematical model for the system it is shown that the related eigenanalysis problem splits into two separate sub problems corresponding to two kinds of possible normal mode motions eigenanalyses are performed concerning single as well as multi stage rotor blade system examples parametric studies are presented on the variation of the eigenfrequencies with system parameters eigenvalue loci veering phenomena are shown to occur causing departure of the eigenvalues from those obtained through an uncoupled analysis mode shape examples are also presented

a lattice renorming theorem and applications to vector valued processes a norm 11 11 on a banach space e is said to be locally uniformly convex if iixnii lxii and iix xli 211xii implies that xn x in norm it is shown that a banach lattice has an order equivalent locally uniformly convex norm if and only if the lattice is order continuous this result is used to reduce convergence theorems for lattice valued positive martingales and submartingales to the scalar case 0 introduction a norm j on a banach space e is said to have the kadec klee property sometimes property h if whenever xn x weakly and llx ll lix ll then x0 x strongly the aim of this paper is to show that if e has an equivalent kadec klee norm then one may obtain convergence theorems for e valued random processes xj whenever j ixjj is a well known real valued convergent process and whenever the limit can be identified in the banach space for instance the classical kadec renorming theorem for separable banach spaces gives the convergence of vector valued martingales uniform amarts and additive processes ergodic theorem since their norms are real valued submartingales amarts and subadditive processes respectively while the identification of the limit requires the radonnikodym property on the space for the first two processes the limit of the third process exists in any banach space if now we consider positive submartingales and subadditive processes valued in a banach lattice one needs that the equivalent kadec klee norm be also a lattice norm in order to conclude that the norms of these processes are real valued submartingales and subadditive processes respectively 1 deals with the existence of such a lattice renorming while in 1i we show how this leads to a unified approach for proving the almost sure convergence of the processes mentioned above i renorming order continuous lattices a norm jj 1 on a banach space e is said to be locally uniformly convex if jjx jj i jjxii and iix xnjj 2j1xii imply that xn x strongly this notion is clearly stronger than the kadec klee property received by the editors october 15 1979 and in revised form february 11 1980 presented to the society san antonio january 1980 ams mos subject classifications 1970 primary 46b99 60g99

uniform k monotonicity and k order continuity in symmetric spaces with application to approximation theory abstract we investigate k order continuity in a symmetric space e using the fundamental function of e we also show a connection between reflexivity and k order continuity in symmetric spaces next we present several results devoted to a characterization of uniform k monotonicity and decreasing increasing uniform k monotonicity in symmetric spaces we also discuss a relationship between decreasing resp increasing uniform monotonicity and decreasing resp increasing uniform k monotonicity next we deliberate a correlation between uniform k monotonicity and uniform rotundity in symmetric spaces finally employing k monotonicity properties and k order continuity we provide solvability and stability of the best approximation problem in the sense of the hardy littlewood polya relation in symmetric spaces

relationships between k monotonicity and rotundity properties with application abstract in this paper we investigate a relationship between fully k rotundity properties uniform k monotonicity properties reflexivity and k order continuity in symmetric spaces e we also answer a crucial question whether fully k rotundity properties might be restricted in definition to e d the positive cone of all nonnegative and decreasing elements of e we present a complete characterization of decreasing uniform k monotonicity and k order continuity in e it is worth mentioning that we also establish several auxiliary results describing reflexivity in lorentz spaces p w and k order continuity in orlicz spaces l finally we show an application of discussed geometric properties to the approximation theory

points of monotonicity in orlicz lorentz function spaces abstract in orlicz lorentz function space m 0 points of upper monotonicity lower monotonicity upper local uniform monotonicity and lower local uniform monotonicity are characterized as the corollary we can easily obtain the criteria for strict monotonicity upper local uniform monotonicity and lower local uniform monotonicity of m 0

non squareness properties of orlicz lorentz sequence spaces abstract in this paper criteria for non squareness properties non squareness local uniform non squareness and uniform non squareness of orlicz lorentz sequence spaces and of their n dimensional subspaces n n 2 as well as of the subspaces a of all order continuous elements in are given since degenerate orlicz functions and degenerate weight sequences are also admitted these investigations concern the most possible wide class of orlicz lorentz sequence spaces finally as immediate consequences criteria for all non squareness properties of orlicz sequence spaces which complete the results of sundaresan 1966 53 hudzik 1985 23 hudzik 1985 24 are deduced it is worth recalling that uniform non squareness is an important property because it implies super reflexivity as well as the fixed point property see james 1964 31 james 1972 33 and garcia falset et al 2006 19

vibration of rings on a general elastic foundation the free vibration eigensolutions of a thin ring on a general elastic foundation are obtained by perturbation and galerkin analyses natural frequencies and vibration modes are determined as closed form expressions for a ring having a circumferentially varying foundation of very general description the elastic foundation consists of two orthogonal distributed springs oriented at an arbitrary inclination angle the foundation stiffnesses vary circumferentially the simple eigensolution expressions explicitly show the parameter dependencies lead to natural frequency splitting rules for degenerate unperturbed eigenvalues at both first and second orders of perturbation and identify which nodal diameter fourier components contaminate a given n nodal diameter base mode of the free ring discrete spring supports are treated as a special case where the natural frequencies are determined by five parameters nondimensional spring stiffness stiffness angle support angle number of springs and location of the springs the predicted effects of these parameters on the natural frequencies are verified numerically as an application and as the motivating problem for the study the natural frequencies and vibration modes of a ring gear used in helicopter planetary gears with unequally spaced planets are investigated

multi mode trimming of imperfect rings abstract this paper proposes a method for trimming the natural frequencies of an imperfect ring to simultaneously eliminate certain of the frequency splits present initially the effect of the addition of a number of imperfection masses on a perfect ring is considered this is achieved by using a rayleigh ritz approach in which it is assumed that the mode shapes are identical to those of a perfect ring by considering the inverse the so called trimming problem it is deduced that it is possible to trim n pairs of modes simultaneously by removing a minimum of n trimming masses at particular locations around the ring to calculate the trimming mass locations it is necessary to solve n non linear algebraic equations once this has been achieved the magnitude of the trimming masses can be calculated easily for the special case of trimming a single pair of modes analytic solutions for the magnitude and position of the single required trimming mass are available to trim two pairs of modes it is shown that a simple analytic relationship exists between the angular positions of the two required trimming masses and that the magnitude of these masses can be obtained easily to trim more pairs of modes numerical techniques are required and for this purpose a numerical procedure is proposed validation of the derived analytic results and the proposed numerical procedure is achieved by studying a number of theoretical examples

when weak and local measure convergence implies norm convergence abstract let m be a von neumann algebra of operators on a hilbert space h and be a faithful normal semifinite trace on m let t be the measure topology on the algebra s m of all measurable operators we prove that for b s m the sets i b a s m h b a b and k b a s m a a b are convex and t closed in s m in this case we have i b b t b t m h and t 1 and for invertible b we describe the set of extreme points of the set i b let m be an atomic von neumann algebra we prove that an operator b s m is compact if and only if the set i b is t compact the t compactness of i b for all compact operators b characterizes these algebras

stickiness in generic low dimensional hamiltonian systems a recurrence time statistics approach we analyze the structure and stickiness in the chaotic components of generic hamiltonian systems with divided phase space following the method proposed recently in lozej and robnik phys rev e 98 022220 2018 2470 004510 1103 physreve 98 022220 the sticky regions are identified using the statistics of recurrence times of a single chaotic orbit into cells dividing the phase space into a grid we perform extensive numerical studies of three example systems the chirikov standard map the family of robnik billiards and the family of lemon billiards the filling of the cells is compared to the random model of chaotic diffusion introduced in robnik et al j phys a math gen 30 l803 1997 jphac50305 447010 1088 0305 4470 30 23 003 for the description of transport in the phase spaces of ergodic systems the model is based on the assumption of completely uncorrelated cell visits because of the strongly chaotic dynamics of the orbit and the distribution of recurrence times is exponential in generic systems the stickiness induces correlations in the cell visits the distribution of recurrence times exhibits a separation of timescales because of the dynamical trapping we model the recurrence time distributions to cells inside sticky areas as a mixture of exponential distributions with different decay times we introduce the variable s which is the ratio between the standard deviation and the mean of the recurrence times as a measure of stickiness we use s to globally assess the distributions of recurrence times we find that in the bulk of the chaotic sea s 1 while s 1 in areas of stickiness we present the results in the form of animated grayscale plots of the variable s in the largest chaotic component for the three example systems included as supplemental material to this paper

dimension formula for random transformations we consider compositions of random diffeomorphisms and show that the dimension of sample measures equals lyapunov dimension as conjectured in the nonrandom case by yorke et al

vibration mode structure and simplified modelling of cyclically symmetric or rotationally periodic systems this paper proves the modal vibration properties of general rotating cyclically symmetric or rotationally periodic systems including those with central components to which cyclically symmetric

on some geometric properties of generalized orlicz lorentz function spaces in this article we continue investigations concerning generalized orlicz lorentz function spaces initiated in the papers foralewski 2011 29 30 cf also foralewski 2008 27 28 first it is shown that modular is orthogonally subadditive next monotonicity properties are considered in order to get sufficient conditions for uniform monotonicity of the space a strong condition of 2 type and the notion of regularity of the generated musielak orlicz function are introduced finally criteria for non squareness of are presented

fluctuations in the relaxation dynamics of mixed chaotic systems the relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space numerical studies however yield a variety of values for this exponent in order to reconcile these results we consider an ensemble of mixed chaotic systems approximated by rate equations and analyze the fluctuations in the distribution of poincare recurrence times our analysis shows that the behavior of these fluctuations as a function of time implies a very slow convergence of the decay exponent of the relaxation

fractal distribution of floaters on a fluid surface and the transition to chaos for random maps abstract the long time spatial distribution of particles floating on the surface of a confined fluid whose flow velocity has complicated time dependence is considered it is shown that this distribution can be either a fractal or else can clump at several or one discrete points the transition from the latter type of distribution to the former occurs when the lyapunov exponent characterizing the particle motion passes through zero from negative values to positive values the characteristic features of this type of transition are investigated using random maps it is shown that near the transition there are extremely intermittent temporal fluctuations in the particle cloud and their scaling with a parameter is elucidated

vibration of high speed rotating rings coupled to space fixed stiffnesses abstract this study investigates the vibration of high speed rotating rings coupled to space fixed discrete stiffnesses the ring radial and tangential deformations are defined using space fixed eulerian coordinates where material particles pass through fixed locations in space engineering strain is used in the strain energy expression the derived nonlinear equations from hamilton s principle are linearized about the steady non trivial configuration that results from constant ring rotation comparisons are made to other models in the literature that use different assumptions the governing equations are cast in terms of matrix differential operators that reveal the system s standard gyroscopic system structure the natural frequencies and vibration modes are calculated over a wide range of rotation speeds for axisymmetric free rings and a non axisymmetric ring with a space fixed discrete stiffness element

biased diffusion inside regular islands under random symplectic perturbations we study the random concatenation of slightly different two dimensional hamiltonian maps with a mixed phase space we consider a regular island whose fixed point is identical for all maps trajectories of the concatenated maps near this fixed point are no longer confined to invariant tori we derive a stochastic model for the distance from the fixed point which turns out to be a biased random walk with multiplicative noise we give an analytical prediction of the survival probability of trajectories inside the regular island which asymptotically is the product of a power law and an exponential we confirm these results numerically for the parametrically perturbed standard map

characterizations of kadec klee properties in symmetric spaces of measurable functions we present several characterizations of kadec klee properties in symmetric function spaces on the half line based on the k functional of j peetre in addition to the usual kadec klee property we study those symmetric spaces for which sequential convergence in measure respectively local convergence in measure on the unit sphere coincides with norm convergence

generalized solution of time dependent traveling load problem via moving finite element scheme abstract a finite element methodology is described which can handle the transient response of moving structures which are themselves subject to time dependent traveling load fields the generality of the approach is such that it can handle the overall transient response due to moving loads whose magnitude zone of application and trajectory are time dependent in addition to developing the overall transient solution methodology attention is also given to establishing the overall eigenvalue properties of the linear problem as well as developing a solution for the steady vibrating case to benchmark the overall procedure the results of several numerical experiments are included in the presentation

local monotonicity structure of symmetric spaces with applications abstract in this paper we discuss several monotonicity properties in banach lattices we start with several general results on local structure of symmetric banach function spaces discussing in particular whether a point x e has some local property if and only if its nonincreasing rearrangement x has the same property section 2 in that section we also prove some general facts for nonincreasing rearrangements which may be of independent interest next we apply these results to find complete criteria for local monotonicity structure of lorentz spaces p and orlicz lorentz spaces sections 3 local structure of lorentz spaces 4 1 local structure of orlicz lorentz spaces 4 2 local uniform structure of lorentz spaces we conclude with the description of global monotonicity structure of lorentz spaces p section 4 3 we finish with the applications of upper monotonicity and lower monotonicity points to local best dominated approximation problems in banach lattices section 5

random fluctuation leads to forbidden escape of particles a great number of physical processes are described within the context of hamiltonian scattering previous studies have rather been focused on trajectories starting outside invariant structures since the ones starting inside are expected to stay trapped there forever this is true though only for the deterministic case we show however that under finitely small random fluctuations of the field trajectories starting inside kolmogorov arnold moser kam islands escape within finite time the nonhyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field as a consequence trajectories which are started inside kam curves escape with hyperboliclike time decay distribution and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems we show a universal quadratic power law relating the exponential decay to the amplitude of noise we present a random walk model to relate this distribution to the amplitude of noise and investigate these phenomena with a numerical study applying random maps

forced response statistics of mistuned bladed disks a stochastic reduced basis approach this paper presents a stochastic reduced basis approach for predicting the forced response statistics of mistuned bladed disk assemblies in this approach the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors with undermined coefficients the terms of the preconditioned stochastic krylov subspace are used here as basis vectors two variants of the stochastic bubnov galerkin scheme are employed for computing the undetermined terms in the reduced basis representation which arise from how the condition for orthogonality between two random vectors is interpreted explicit expressions for the response quantities can then be derived in terms of the random system parameters which allow for the possibility of efficiently computing the response statistics in the post processing stage numerical studies are presented for mistuned cyclic assemblies of mono coupled single mode components it is demonstrated that the accuracy of the response statistical moments computed using stochastic reduced basis methods can be orders of magnitude better than classical perturbation methods

fractal snapshot components in chaos induced by strong noise in systems exhibiting transient chaos in coexistence with periodic attractors the inclusion of weak noise might give rise to noise induced chaotic attractors when the noise amplitude exceeds a critical value an extended attractor appears along the fractal unstable manifold of the underlying nonattracting chaotic set a further increase of noise leads to a fuzzy nonfractal pattern by means of the concept of snapshot attractors and random maps we point out that the fuzzy pattern can be decomposed into well defined fractal components the snapshot attractors belonging to a given realization of the noise and generated by following an ensemble of noisy trajectories the pattern of the snapshot attractor and its characteristic numbers such as the finite time lyapunov exponents and numerically evaluated fractal dimensions change continuously in time we find that this temporal fluctuation is a robust property of the system which hardly changes with increasing ensemble size the validity of the kaplan yorke formula is also investigated a superposition of about 100 snapshot attractors provides a good approximant to the fuzzy noise induced attractor at the same noise strength

measurement and analysis of modulated doublet mode response in mock bladed disks the steady state response of spatially modulated doublet modes that occur in low count flexible bladed disks is investigated for the case in which the structure is driven by a harmonic travelling wave excitation source finite element simulation and modal testing of prototypical bladed disk structures demonstrate the presence of particular wavenumbers beyond the base number of nodal diameters which contaminate and distort the appearance of certain doublet modes the manner in which the natural frequency and wavenumber content of such modes shift and split as functions of the number of blades and their span angle is discussed in the light of a companion perturbation analysis for rotationally periodic structures resonance conditions are established and verified through simultaneous measurements made with a spin test stand using sensors that are placed in the rotating structure and stationary excitation frames of reference the travelling wave response components of a repeated frequency doublet mode are shown to propagate either in the same or opposite direction as the excitation source depending on whether certain algebraic relationships between the excitation order the base number of nodal diameters and the contamination wavenumbers are satisfied to the extent that such components can travel at different phase speeds and directions relative to one another the placement of sensors on the structure can be optimized to best measure the response amplitude conversely other placements can result in submaximal measurement of peak vibration amplitude over the structure

diffusion for ensembles of standard maps two types of random evolution processes are studied for ensembles of the standard map with driving parameter k that determines its degree of stochasticity for one type of process the parameter k is chosen at random from a gaussian distribution and is then kept fixed while for the other type it varies from step to step in addition noise that can be arbitrarily weak is added the ensemble average and the average over noise of the diffusion coefficient are calculated for both types of processes these two types of processes are relevant for two types of experimental situations as explained in the paper both types of processes destroy fine details of the dynamics and the second process is found to be more effective in destroying the fine details we hope that this work is a step in the efforts for developing a statistical theory for systems with mixed phase space regular in some parts and chaotic in other parts

natural frequencies and modes of rings that deviate from perfect axisymmetry given the experimental or theoretical natural frequencies and modes of an axisymmetric ring an analytical method is presented that allows one to obtain the natural frequencies and modes when this ring is non axisymmetric due to a mass or stiffness non uniformity of the ring a ring is the simplest model of an axisymmetric structure and treatment of its non uniformities paves the way for treatment of more complicated structures such as tires for example the receptance method is employed to determine the natural frequencies and mode shapes of a circular ring which is deviating from axisymmetry due to a local mass of stiffness non uniformity the receptance of the ring is derived by utilizing the modal expansion method

response of rotating rings to harmonic and periodic loading and comparison with the inverted problem abstract the harmonic and periodic forced vibrations of rotating rings are derived and investigated the modal expansion technique yields the forced solution which is characterized by four generalized co ordinates associated with each n circumferential wave number the inextensional assumption is presumed when flexural vibration is the only important component to reduce the order of the system the closed form solutions to the harmonic load cases once concentrated once distributed are demonstrated and interpreted the approach is then extended to periodic loads where fourier sine and cosine series is applied examples depict the numerical responses to all the cases being derived the solutions of a stationary ring subjected to traveling loads are also solved for comparison their difference is investigated and interpreted from various viewpoints

local approach to kadec klee properties in symmetric function spaces abstract we prove several results concerning local approach to kadec klee properties with respect to global local convergence in measure in symmetric banach function spaces which may be of independent interest moreover we prove characterizations of these properties in the lorentz spaces finally we show applications of h g and h l points to the local best dominated approximation problems in banach lattices

local δ2e x condition as a crucial tool for local structure of calderon lozanovskiĭ spaces abstract we shall give a full criterion for a point x e to be a point of order continuity of calderon lozanovski spaces e in order to get that result we introduce the new local 2 e x condition which appears to be necessary and sufficient for this goal next we study the structure of points of lower local uniform monotonicity llum for short we give a result concerning general kothe sequence spaces and we present a characterization for llum points in calderon lozanovski spaces

rotundity structure of local nature for generalized orlicz lorentz function spaces abstract criteria for extreme points and rotund points in generalized orlicz lorentz function spaces which were introduced in foralewski 2011 27 are given some examples show that in these spaces the notion of rotund point is essentially stronger than the notion of extreme point finally the criteria obtained in this paper are interpreted in the case of classical orlicz lorentz spaces results of this paper are related to the results from carothers et al 1992 9 kaminska 1990 4 foralewski et al 2008 26

on the statistics of natural frequency splitting for rings with random mass imperfections abstract this paper considers the statistical distribution of natural frequency splits for an initially perfect ring with different types of random mass imperfection the analysis used to derive analytical expressions for the natural frequency splits is based on a rayleigh ritz approach in which it is assumed that the mode shapes of the imperfect rings are identical to those of a perfect ring the types of random mass imperfection investigated are i random harmonic variations in the mass per unit length around the circumference of the ring ii the attachment of random point masses at random locations on the ring and iii the attachment of random point masses at uniformly spaced positions on the ring for case i it is found that the frequency splits always have a rayleigh distribution for case ii an expression for the statistical distribution is deduced which tends to a rayleigh distribution as the number of attached masses increases for case iii it is found that the frequency split distribution is dependent upon the mode considered and the number of attached masses and that in some situations the frequency splits have a half gaussian i e non rayleigh distribution

the in plane vibration of thin rings with in plane profile variations part ii application to nominally circular rings abstract geometric profile variations always exist in nominally circular rings due to limitations in the manufacturing processes such profile variations are known to lead to frequency splitting between pairs of modes which are degenerate in a perfect ring in this paper the effects of circumferential profile variations on the in plane vibration characteristics of such rings are studied using a numerical method the inner and outer ring surfaces are described in a very general way by fourier series and the rayleigh ritz method is used to obtain the natural frequencies and mode shapes results are presented for a number of example cases which include single and multiple harmonic variations in profile the relationship between the patterns of frequency splitting and the harmonic content of the ring profile is investigated and the most important causes of frequency splitting are identified

on the performance of box counting estimators of fractal dimension summary box counting estimators are popular for estimating fractal dimension however very little is known of their stochastic properties despite increasing statistical interest in their application we show that if the irregular curve to which the estimators are applied is modelled by a gaussian process concise formulae may be developed for asymptotic bias and variance of box counting estimators these formulae point to critical differences between a naive form of the box counting estimator based directly on the capacity definition of fractal dimension and a regression inspired version of that estimator

free vibration analysis of an eccentric hollow cylinder using exact 3d elasticity theory abstract the translational addition theorem for cylindrical wave functions in conjunction with the appropriate orthogonal series expansions and the pertinent boundary conditions are employed to develop an exact 3d elasticity solution for free vibrations of a simply shear diaphragm supported elastic circular cylinder of finite length with an eccentrically located inner circular cavity the frequency spectrum plots of the first several eigenfrequencies are presented in a wide range of dimensionless eccentricities for selected length to radius and inner outer radius ratios also a detailed study on the 2d free vibration characteristics of an infinite eccentric cylinder is included the numerical results describe the imperative influence of cavity eccentricity mode type and radii and length ratios on the vibrational characteristics of the hollow cylinder it is observed that the introduction of bore eccentricity causes not only an increase in the number of resonant frequencies through the splitting of degenerate modes of the unperturbed problem but also changes the appearance order of natural vibration modes the accuracy of solutions is checked through appropriate convergence studies and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature

monotonicity and rotundity of lorentz spaces γp w abstract criteria for rotundity strict monotonicity and lower local uniform monotonicity of the lorentz spaces p w of maximal functions are given under arbitrary nonnegative weight function w necessary conditions are also established for uniform monotonicity of the spaces p w for 1 p moreover the spaces 1 w that are uniformly monotone are characterized

in plane free vibration of a single crystal silicon ring in this paper the natural frequencies and the associated mode shapes of in plane free vibration of a single crystal silicon ring are analyzed it is found that the si 1 1 1 ring is two dimensionally isotropic in the 1 1 1 plane for elastic constants but three dimensionally anisotropic while the si 1 0 0 ring is fully anisotropic hamilton s principle is used to derive the equations of vibration which is a set of partial differential equations with coefficients being periodic in polar variable expressing the radial and tangential displacements in sinusoidal form with non predetermined amplitudes and through the integration with respect to the circumferential variable the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form the exact expressions for frequencies and mode shapes are obtained it is found that for si 1 0 0 rings the frequencies of a pair of modes which are equal for an isotropic ring split due to the anisotropic effect only for the second in plane vibration mode the phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups when the single crystal silicon is replaced by the polycrystalline silicon which is isotropic in elastic constants the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting

the response of a non uniformly tensioned circular string to a moving load abstract a non uniformly tensioned circular string on a damped elastic foundation is acted upon by a moving concentrated load this configuration can be viewed as a very simplified representation of a spinning rectangularly orthotropic disk acted upon by a spatially fixed force or of a stationary orthotropic disk subjected to a circumferentially moving load the natural frequencies and normal modes of vibration of the string on elastic foundation are determined for a range of values of the tension inhomogeneity the response of the string to a moving load is then determined the results indicate that there are many speeds below the critical speed of the uniformly tensioned string for which the forced response is large it is anticipated that the response of this simple model to a moving load can provide insight into the behavior of the mathematically more complicated rectangularly orthotropic circular disk

excitation of rotating circumferentially periodic structures abstract a circumferentially periodic structure consists of a finite number of identical substructures coupled together in identical ways to form a closed ring type structure the vibrational behaviour of such structures when rotating about the axis of structural symmetry is considered especially the forced response due to forces fixed in space it is known that for a circumferentially symmetric structure rotating about its axis of structural symmetry and excited by a force fixed in space resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is n n where is the angular velocity of rotation the deformation at these resonances consists of waves travelling backwards in relation to the direction of the structure rotation this resonance condition also holds for a circumferentially periodic structure but then additional resonance possibilities exist given by n kn n where n is the number of sub structures and k 0 1 2 these results are known to hold true for a structure fixed in space and acted upon by a rotating force in this paper these results are shown to hold true also for a rotating structure acted upon by a force distribution fixed in space both backward and forward travelling waves can be excited in those cases when the rotating structure exhibits coriolis accelerations the natural frequencies for backward 1n and forward 2n rotating mode shapes are different this well known property has a pronounced effect on the forced response due to forces fixed in space in the absence of coriolis effects the magnification factor is essentially 1 n 2 2 where is the forcing frequency due to rotation but in the presence of coriolis effects the magnification factor has the characteristics 1 1n 2n

noisy one dimensional maps near a crisis ii general uncorrelated weak noise the escape rate for one dimensional noisy maps near a crisis is investigated a previously introduced perturbation theory is extended to very general kinds of weak uncorrelated noise including multiplicative white noise as a special case for single humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law for the rate is derived it predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum of the map is of sufficiently large order a simple heuristic explanation of this effect is given the escape rate is discussed in detail for noise distributions of levy dichotomous and exponential type in the latter case the rate is dominated by an exponentially leading arrhenius factor in the deep precritical regime however the preexponential factor may still depend more strongly than any power law on the noise strength

second dual projection characterizations of three classes of l0 closed convex bounded sets in l1 non commutative generalizations abstract we provide characterizations of convex compact for the topology of local convergence in measure subsets of non commutative l 1 spaces previously considered for classical l 1 spaces more precisely if m is a semifinite and finite von neumann algebra equipped with a distinguished semifinite faithful normal trace p m l 1 m is the non commutative yosida hewitt projection and c is a norm bounded subset of l 1 m that is convex and closed for the topology of local convergence in measure then we isolate the precise conditions on c for which p c w c is compactness preserving sequentially continuous or continuous when c w is equipped with the weak topology and c with the topology of local convergence in measure

on geometric structure of symmetric spaces abstract in this article we discuss local approach to strict k monotonicity and local uniform rotundity in symmetric spaces we prove several general results on local structure of symmetric spaces e showing relation between strict monotonicity and strict k monotonicity and the kadec klee property for global convergence in measure we also present the full criteria for points of upper k monotonicity in lorentz spaces p w for degenerated weight function w next we characterize local uniform rotundity in symmetric spaces e proving several correspondences between x e a point of local uniform rotundity and its decreasing rearrangement x and absolute value x finally we apply these results to find complete criteria for local uniform rotundity of lorentz spaces p w

pointwise products of some banach function spaces and factorization abstract the well known factorization theorem of lozanovski may be written in the form l 1 e e where means the pointwise product of banach ideal spaces a natural generalization of this problem would be the question when one can factorize f through e i e when f e m e f where m e f is the space of pointwise multipliers from e to f properties of m e f were investigated in our earlier paper 41 and here we collect and prove some properties of the construction e f the formulas for pointwise product of calderon lozanovski e spaces lorentz spaces and marcinkiewicz spaces are proved these results are then used to prove factorization theorems for such spaces finally it is proved in theorem 11 that under some natural assumptions a rearrangement invariant banach function space may be factorized through a marcinkiewicz space

local approach to order continuity in cesaro function spaces abstract the goal of this paper is to present a complete characterization of points of order continuity in abstract cesaro function spaces cx for x being a symmetric function space under some additional assumptions mentioned result takes the form c x a c x a we also find simple equivalent condition for this equality which in the case of i 0 1 comes to x l furthermore we prove that x is order continuous if and only if cx is under assumption that the cesaro operator is bounded on x this result is applied to particular spaces namely cesaro orlicz function spaces cesaro lorentz function spaces and cesaro marcinkiewicz function spaces to get criteria for oc points

response of modulated doublet modes to travelling wave excitation the forced vibration of a rotationally periodic structure when subjected to travelling wave excitation is discussed with emphasis placed on the steady state response of doublet modes having either repeated or split frequencies such vibration modes have spatially modulated shapes defined by 1 the number of nodal diameters present in the limiting case of axisymmetry and 2 certain additional fourier harmonics which contaminate and distort their appearances the natural frequency and mode structure of a model periodic structure is discussed in the context of an otherwise axisymmetric disk having evenly spaced sector shaped line distributions of stiffness and inertia through perturbation analysis the contamination wavenumbers present in a doublet having repeated frequency are shown to comprise two subsets the members of which have sine and cosine coefficients of the same or of differing signs for each wavenumber in the mode shape s fourier expansion the structure of the wavenumber content is explored further with respect to the response of repeated and split doublets to a harmonic travelling wave excitation the individual fourier components comprising a modulated doublet can respond and propagate in the same direction as the excitation or opposite to it depending on the wavenumber of the excitation and the subset to which the contamination wavenumber belongs the response of the split frequency doublets and the circumstances under which travelling or standing wave responses or a blend of the two can occur in the structure s reference frame are also examined in the context of the model periodic structure the qualitative character of the response the forward or backward propagation direction of each mode s constituent wavenumber components and the phase speeds of those components are discussed in illustrative case studies

sub trans and supercritical variable magnitude travelling loads on cylindrical rings abstract the problem of time dependent variable magnitude travelling loads in a closed symmetric structure is considered this includes the circumferential propagation in viscoelastically supported cylindrical rings which can rotate about their axes the main emphasis of the work is to establish the effects of time dependent load variability on the response characteristics when travelling velocities are in the sub trans and supercritical speed ranges this will enable the doppler like interactions among the propagating bending and in plane waves at the various travelling load speed ranges to be evaluated as an example simulation the model is tuned to define the dynamic response characteristics of tires rolling on bumpy surfaces this enables the sub trans and the supercritical response characteristics to be evaluated

the in plane vibration of thin rings with in plane profile variations part i general background and theoretical formulation abstract this paper presents a methodology for the analysis of the free in plane vibration of thin rings with profile variations in the circumferential direction the methodology is suitable for any thin ring which is bounded by closed curves which are single valued functions of circumferential position the inner and outer profiles are expressed as fourier series thus allowing any profile to be approximated with any degree of accuracy an iterative numerical procedure for determining the true middle surface and the corresponding thickness at each cross section around the circumference is established a reduced plane stress form of novozhilov s thin shell theory is used to model the deformation mechanics of the ring the eigenvalue problem is then formulated using the rayleigh ritz method in conjunction with a harmonic series description of the displacements general expressions are presented for the corresponding mass and stiffness matrices a companion paper presents a comprehensive set of results which illustrates application of the theory

a simple theory for the analysis and correction of frequency splitting in slightly imperfect rings abstract the flexural radial vibration of circular rings with imperfections represented by small attached masses and springs is considered the concept of an equivalent imperfection mass is introduced this is used to quantify the frequency splitting which occurs in slightly imperfect axisymmetric bodies the concept is used to estimate the trimming mass which must be added to or removed from the ring and at which point in order to reduce or eliminate the frequency split in a given pair of modes the method can be applied to any axisymmetric body for which the mode shapes can be measured or computed

kadec klee property for convergence in measure of noncommutative orlicz spaces abstract this paper studies the kadec klee property for convergence in measure of noncommutative orlicz spaces l m where m is the space of measurable operators and is an orlicz function we show that l m has the kadec klee property in measure if and only if the satisfies the 2 condition as a corollary the dual space and reflexivity of l m are given

free and forced response of mistuned linear cyclic systems a singular perturbation approach abstract the effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry is investigated the general methodology developed herein is applicable to any n degree of freedom strongly coupled cyclic system with two arbitrary and independent variations in system parameters that destroy the cyclic symmetry the specific system studied may be regarded as a simplified model of a strongly coupled bladed disk assembly singular perturbation methods along with modal expansion analysis are applied to gain a physical insight into the effects of parameter perturbations on the eigenvalues the eigenvectors as well as the forced response amplitudes the study shows that under appropriate conditions the splitting and veering of eigenvalues due to mistunings or small parameter variations increases the amplitude of vibration of some blades significantly compared to what would be predicted by an analysis of the perfectly tuned system furthermore modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs the variations in blade amplitudes are also found to be strongly dependent on damping and the type of engine order excitation applied to the system for the same set of mistuning parameters

local structure of symmetrizations e with applications abstract we study the local structure of the separated point x in the space e with respect to properties of its nonincreasing rearrangement x in the space e in particular we get the characterizations of local structure in the lorentz and marcinkiewicz spaces it is worth to mention that the local structure of a separated point can be applicable to the local best dominated approximation problems in banach lattices

advection in chaotically time dependent open flows the passive advection of tracer panicles is considered in open two dimensional incompressible flows with chaotic time dependence as illustrative examples we investigate flows produced by chaotically moving ideal point vortices the advection problem can be seen as a chaotic scattering process in a chaotically driven hamiltonian system studying the motion of tracer ensembles we present numerical evidence for the existence of a bounded chaotic set containing infinitely many aperiodic trajectories never leaving the mixing region of the flow these ensembles converge to filamental patterns which however do not follow self similar scaling nevertheless they possess a fractal dimension after averaging over several finite time realizations of the flow we propose random maps as simple models of the phenomenon

parametric instability of spinning elastic rings excited by fluctuating space fixed stiffnesses abstract this study investigates the vibration of rotating elastic rings that are dynamically excited by an arbitrary number of space fixed discrete stiffnesses with periodically fluctuating stiffnesses the rotating elastic ring is modeled using thin ring theory with radial and tangential deformations primary and combination instability regions are determined in closed form using the method of multiple scales the ratio of peak to peak fluctuation to average discrete stiffness is used as the perturbation parameter so the resulting perturbation analysis is not limited to small mean values of discrete stiffnesses the natural frequencies and vibration modes are determined by discretizing the governing equations using galerkin s method results are demonstrated for compliant gear applications the perturbation results are validated by direct numerical integration of the equations of motion and floquet theory the bandwidths of the instability regions correlate with the fractional strain energy stored in the discrete stiffnesses for rings with multiple discrete stiffnesses the phase differences between them can eliminate large amplitude response under certain conditions

logarithmic submajorisation and order preserving linear isometries abstract let e and f be noncommutative operator spaces affiliated with semifinite von neumann algebras m 1 and m 2 respectively we establish a noncommutative version of abramovich s theorem 1 which provides the general form of normal order preserving linear operators t e i n t o f having the disjointness preserving property as an application we obtain a noncommutative huijsmans wickstead theorem 44 by establishing the disjointness preserving property for an order preserving isometry t e f from a noncommutative symmetrically normed in particular quasi normed space into another we obtain the existence of a jordan monomorphism from m 1 into m 2 and the general form of this isometry which extends and complements a number of existing results such as 12 theorem 1 67 corollary 1 72 theorem 2 and 15 theorem 3 1 in particular we fully resolve the case when f is the predual of m 2 and other untreated cases in 78

parametric instability of a circular ring subjected to moving springs this work investigates parametric instabilities of in plane bending vibrations of a thin elastic ring subject to forces from discrete rotating springs of arbitrary number spacing and orientation several configurations are examined including systems with symmetric and asymmetric circumferential spring spacing and systems with and without fixed springs the method of multiple scales is applied to analytically identify principal and combination instability boundaries as closed form expressions two different numerical approaches are used to verify the analytical results the effects of different system parameters on the instability boundaries are studied analytically the bending stiffness of the ring the number of springs and their stiffness location orientation and rotation speed for several cases well defined properties for the occurrence or suppression of instabilities are obtained as simple relations in the system parameters

dynamic time responses of a flexible spinning disk misaligned with the axis of rotation using the finite element method this study investigates the dynamic time responses of a flexible spinning disk of which axis of rotation is misaligned with the axis of symmetry the misalignment between the axes of symmetry and rotation is one of major vibration sources in optical disk drives such as cd rom cd r cd rw and dvd drives based upon the kirchhoff plate theory and the von karman strain theory three coupled equations of motion for the misaligned disk are obtained two of the equations are for the in plane motion while the other is for the out of plane motion after transforming these equations into two weak forms for the in plane and out of plane motions the weak forms are discretized by using newly defined annular sector finite elements applying the generalized time integration method to the discretized equations the time responses and the displacement distributions are computed and then the effects of misalignment on the responses and the distributions are analyzed the computation results show that the misalignment has an influence on the magnitudes of the in plane displacements it is also found that the misalignment results in the amplitude modulation or the beat phenomenon in the time responses of the out of plane displacement

vibroacoustic response of an eccentric hollow cylinder abstract the linear 3d elasticity theory in conjunction with the classical method of separation of variables and the translational addition theorem for cylindrical wave functions are employed to investigate the three dimensional steady state sound radiation characteristics of an arbitrarily thick eccentric hollow cylinder of infinite length submerged in an unbounded ideal acoustic medium and subjected to arbitrary time harmonic on surface mechanical drives the spatial fourier transform along the shell axis and fourier series expansion in the circumferential direction are utilized to obtain a formal integral expression for the radiated pressure field in the frequency domain the method of stationary phase is subsequently implemented to evaluate the integral for an observation point in the far field the analytical results are illustrated with numerical examples in which air filled water submerged concentric and eccentric steel cylinders are driven by harmonic concentrated radial and transverse surface loads effects of excitation and cylinder eccentricity on the far field radiated pressure amplitudes directivities are discussed and contributions from pseudo rayleigh whispering gallery and axially guided waves are examined through selected spatial dispersion patterns limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature

repellers semi attractors and long lived chaotic transients abstract we study the chaotic transients observed in many deterministic systems in general they are related to strange repellers or semi attractors if they are repelling in some and attracting in other directions we propose formulas relating the average life time of the transient to dimensions of the repeller and to lyapunov exponents of the flow on it the formulas are tested numerically in a number of cases

a new method for in plane vibration analysis of circular rings with widely distributed deviation abstract a new analytical method was developed to predict the in plane mode shapes and the natural frequencies of a ring with widely distributed deviation the laplace transform was used to find the exact solution of eigenvalue problem without assuming any trial functions and finite elements the widely distributed deviation was effectively formulated in the theory using gauss legendre quadrature the validity of the proposed method was examined through finite element analysis and modal test the effects of partial change of the density the stiffness and the thickness on the natural frequencies of the ring were investigated

frequency split and vibration localization in imperfect rings abstract the dynamics of linearly elastic imperfect rings vibrating in their own plane is considered in this paper imperfections are modeled as perturbations of the uniform linear mass density and bending stiffness of a perfect ring a perturbation expansion and a spectral representation are employed and a variational formulation of the vibration problem is obtained a linear theory is deduced by retaining only the leading order terms in the variational formulation the linear theory yields simple closed form expressions for the eigenfrequencies and the modal shapes which are accurate when the imperfections are sufficiently small an enhanced nonlinear theory is also derived which is accurate even when the ring imperfections are not small in this case an iterative solution procedure is developed the proposed theories are validated by considering some case study problems and using the ritz rayleigh solution as a benchmark finally the linear theory is applied to the frequency trimming problem of an imperfect ring a simple closed form expression for the trimming masses is presented valid for trimming any selected number of eigenmodes

stochastic perturbations in open chaotic systems random versus noisy maps we investigate the effects of random perturbations on fully chaotic open systems perturbations can be applied to each trajectory independently white noise or simultaneously to all trajectories random map we compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time dependent conditionally map invariant measure for the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map in random maps we show that the escape rate ensuremath kappa and dimensions d of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation we discuss the accuracy bias and precision variance of finite size estimators of ensuremath kappa and d and show that the improvement of the precision of the estimations with the number of trajectories n is extremely slow ensuremath propto 1 mathrm ln n we also argue that the finite size d estimators are typically biased general theoretical results are combined with analytical calculations and numerical simulations in area preserving baker maps