the dimensional reduction approach for 2d non prismatic beam modelling a solution based on hellinger reissner principle abstract the present paper considers a non prismatic beam i e a beam with a cross section varying along the beam axis in particular we derive and discuss a model of a 2d linear elastic non prismatic beam and the corresponding finite element to derive the beam model we use the so called dimensional reduction approach from a suitable weak formulation of the 2d linear elastic problem we introduce a variable cross section approximation and perform a cross section integration the satisfaction of the boundary equilibrium on lateral surfaces is crucial in determining the model accuracy since it leads to consider correct stress distribution and coupling terms i e equation terms that allow to model the interaction between axial stretch and bending therefore we assume as a starting point the hellinger reissner functional in a formulation that privileges the satisfaction of equilibrium equations and we use a cross section approximation that exactly enforces the boundary equilibrium the obtained beam model is governed by linear ordinary differential equations odes with non constant coefficients for which an analytical solution cannot be found in general as a consequence starting from the beam model we develop the corresponding beam finite element approximation numerical results show that the proposed beam model and the corresponding finite element are capable to correctly predict displacement and stress distributions in non trivial cases like tapered and arch shaped beams

strong convergence theorems for a countable family of quasi ϕ asymptotically nonexpansive nonself mappings abstract the purpose of this article is to introduce a class of quasi asymptotically nonexpansive nonself mappings and to study the strong convergence under a limit condition only in the framework of banach spaces as an application we utilize our results to study the approximation problem of solution to a system of equilibrium problems the results presented in the paper improve and extend the corresponding results announced by some authors recently

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

dynamic stiffness analysis of follower force abstract the dynamic stiffness method can predict an infinite number of natural modes of a conservative structure by means of a finite number of co ordinates the method is extended to non conservative systems characterized by follower forces in this paper skeletal frame structures are taken as examples the resulting matrix equations are solved by the parametric inverse iteration method with the intensity of the follower forces as parameter the influences of shear deformation and rotatory inertia on the flutter instability are considered the higher order flutter mode critical follower forces for a slender cantilever are found to be 2n 0 5 2 2ei l2 approximately the flutter frequency and flutter load are calculated directly by a newtonian method with a romberg algorithm for the determinant derivatives it is found that flutter may occur by coalescence of non adjacent linear modes

multilevel dynamic substructures the dynamic substructure method is extended to multilevel recursive substructures the obvious distinction of the two approaches is that the stiffness and mass matrices before condensation are no longer frequency independent the dynamic stiffness matrix at any substructure level is proved to be a function of the vibrating frequency in terms of some constant matrices which are derivable from the dynamic stiffness matrix at one lower substructure level the method can accurately predict more modes than the number of degrees of freedom retained the computational procedure the generalized inverse iteration the stationary principle of the system natural frequency and the generalized rayleigh s quotient are derived for the frequency dependent matrices numerical examples are given to illustrate some engineering applications a transcendental dynamic stiffness matrix can be transformed to a more convenient algebraic form by the present method

strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces the purpose of the paper is to introduce modified halpern and ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in banach spaces we also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction

an orthogonal decomposition approach to modal synthesis modal synthesis is a method of formulating the equations of motion for complex vibratory systems this approach has many advantages in modelling systems that consist of an assembly of linear dynamic elements whose modal characteristics are given presented in the paper is a procedure for synthesizing linear dynamic models into one dynamic description in a numerically stable way this task is achieved by an orthogonal co ordinate transformation replacing the matrix inversions required when other procedures are used the modal synthesis approach is formulated as a problem of finding the equations of motion for a linear system subject to a set of linear constraints the numerical procedure to generate the equations of motion in terms of independent co ordinates is presented the paper concludes with several examples that demonstrate the properties of the proposed method and its application to the modelling of vibratory systems

non linear steady state vibration of frames by finite element method a finite element method based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced the axial and flexural deformations are coupled by mean of the induced axial force along the element the spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by fourier coefficients of the nodal displacements no unconventional element matrices are needed after applying the harmonic balance method a set of non linear algebraic equations of the fourier coefficients is obtained these equations are solved by the newtonian iteration method in terms of the fourier coefficient increments nodal damping can easily be included by a diagonal damping matrix the direct numerical determination of the fourier coefficient increments is difficult owing to the presence of peaks loops and discontinuities of slope along the amplitude frequency response curves parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase i e at resonance for undamped natural vibration the method of selective coefficients adopted numerical examples on the duffing equation a hinged hinged beam a clamped hinged beam a ring and a frame are given for reasonably accurate results it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability which are discussed in detail

coupled bending torsional dynamic stiffness matrix of an axially loaded timoshenko beam element abstract analytical expressions for the coupled bending torsional dynamic stiffness matrix terms of an axially loaded uniform timoshenko beam element are derived in an exact sense by solving the governing differential equations of motion of the element the symbolic computing package reduce has been used to generate an analytical expression for each of the dynamic stiffness terms in a concise form for check purposes numerical values of the dynamic stiffness matrix terms were obtained using the derived explicit expressions as well as by an alternative nonanalytical method based on matrix inversions and matrix multiplications stiffnesses obtained from both methods agreed with each other to machine accuracy application of the developed theory is discussed with particular reference to an established algorithm the influence of axial force shear deformation and rotatory inertia on the natural frequencies of a bending torsion coupled beam with cantilever end conditions is demonstrated by numerical results such results are not generally available in the literature therefore results obtained by partially restricting the present theory are compared with the existing literature wherever possible the results indicate that the method is accurate and efficient

flexural vibration of axially loaded beams with linear or parabolic taper abstract curves are presented which enable the first five natural frequencies to be found for axially loaded tapered members with an important family of cross sections previous curves have only included axial forces in a very limited number of cases whereas here axial forces within the range of greatest practical importance can always be allowed for the present curves cover 11 combinations of end conditions three types of taper all taper ratios between 0 2 and 1 and all axial forces between p c and 0 6 p c where p c is the critical buckling load for pure compression and can be found from curves provided a list of principal nomenclature is given in appendix 2 the cross sections covered include thin circular ones of constant thickness and thin walled cross sections consisting of constant thickness flat plates which all have their breadths tapering in the same way truncated wedges of varying depth and constant width are also covered the taper is linear between the ends or linear between a maximum value at the centre and equal values at the ends or parabolic with a maximum value at the centre simple examples show how the curves can be used to obtain natural frequencies or buckling loads to an accuracy which is almost always about 1 the curves also illustrate how natural frequencies and buckling loads of thin walled members are altered by changing the amount and type of a member s taper while keeping its wall thickness and mass constant finally it is shown that for the ranges covered by the curves frequencies which separate the first five natural frequencies can be found a priori the theory used to obtain the curves was simply to divide the tapered member into sufficient uniform members to ensure convergence to the tapered result to better than plotting accuracy exact bernoulli euler dynamic stiffnesses which allowed for axial force effects were used for these uniform components in appendix 1 the effects of using exact timoshenko stiffnesses instead of the bernoulli euler ones are illustrated

sequential monte carlo with kernel embedded mappings the mapping particle filter abstract in this work a novel sequential monte carlo filter is introduced which aims at an efficient sampling of the state space particles are pushed forward from the prediction to the posterior density using a sequence of mappings that minimizes the kullback leibler divergence between the posterior and the sequence of intermediate densities the sequence of mappings represents a gradient flow based on the principles of local optimal transport a key ingredient of the mappings is that they are embedded in a reproducing kernel hilbert space which allows for a practical and efficient monte carlo algorithm the kernel embedding provides a direct means to calculate the gradient of the kullback leibler divergence leading to quick convergence using well known gradient based stochastic optimization algorithms evaluation of the method is conducted in the chaotic lorenz 63 system the lorenz 96 system which is a coarse prototype of atmospheric dynamics and an epidemic model that describes cholera dynamics no resampling is required in the mapping particle filter even for long recursive sequences the number of effective particles remains close to the total number of particles in all the sequence hence the mapping particle filter does not suffer from sample impoverishment

dynamic substructure response abstract dynamic substructure methods enable one to analyze a large scale dynamic system by considering its constituents individually and the combined action afterwards steady state harmonic oscillation has been studied almost exclusively the methods are extended to general non steady state excitations the orthonormality condition of the modal vectors in terms of the masters is introduced a mixed mass matrix for initial conditions is derived the dynamic flexibility is expressed in spectral form for response calculation modal participation factors for both distributed and concentrated loads are given explicitly

a general dynamic synthesis for structures with discrete substructures abstract this paper presents a substructure synthesis method for the dynamic simulation of complex structures where the structures consist of an assemblage of discrete substructures an analogy between distributed and discrete structures is extensively invoked to stimulate the motion of discrete substructures the concept of admissible vectors is introduced where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures the individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures a numerical example illustrating the method is presented

damping in exact analysis of tapered beams abstract in this paper the free vibration frequencies of an euler bernoulli tapered beam are deduced in the presence of a concentrated mass at the end and of a concentrated linear damper at an arbitrary section along the beam the frequency equation is deduced and analytically solved in terms of bessel functions

the free vibration of a type of tapered beams this paper studies the vibrational characteristics of tapered beams with continuously varying rectangular cross section of depth and breadth proportional to xs and xt respectively where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co ordinate measured from the sharp end of the beam the bernoulli euler theory of bending is used to describe the motion of the beam a new set of beam functions are developed as the admissible functions which are the complete solution of the tapered beam under an arbitrary static load expanded into a taylor series the eigenfrequency equation is obtained by the rayleigh ritz method the accuracy is assured from the convergency and comparison studies the effect of the location of the taylor series expanding point on the convergency is discussed the analysis shows that the present approach is convergent for arbitrary truncation factor by taking the midpoint of the beam as the expanding point of the taylor series numerical results are tabulated for three different tapered beams with various boundary conditions and truncation factors it is shown that the eigenfrequencies can be obtained with high accuracy by using only a small number of terms of the static beam functions 2000 elsevier science s a all rights reserved

strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified mann method

linear non linear dynamic substructures the dynamic substructure method is extended to linear and non linear coupling systems only those master co ordinates with non linear nature non linear co ordinates are retained other slave co ordinates relating to the linear part linear co ordinates are eliminated by the dynamic substructure method the dynamic flexibility matrix associated with the linear co ordinates is first expanded in terms of the fixed interface natural modes the condensed dynamic stiffness matrix associated with the non linear co ordinates is formed subsequently the convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and taylor series expansion to find the steady state solutions the non linear responses are expanded into a fourier series responses of the linear co ordinates are related to the non linear co ordinates analytically to solve for the unknown fourier coefficients the harmonic balance method gives a set of non linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients a newtonian algorithm is adopted to solve for the unknown fourier coefficients iteratively the computational cost of a non linear analysis depends heavily on the number of degrees of freedom encountered in the method the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced

damped dynamic substructures the dynamic substructure method is extended to lightly or heavily damped systems both internal and external dampings are considered the damped dynamic flexibility associated with the slave co ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co ordinates is formed subsequently the convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices since the dynamic stiffness method is equivalent to the modal synthesis method the component mode method and kron s method the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

a modified halpern type iteration algorithm for totally quasi ϕ asymptotically nonexpansive mappings with applications abstract the purpose of this article is to modify the halpern type iteration algorithm for total quasi asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of banach spaces the results presented in the paper improve and extend the corresponding results of x l qin y j cho s m kang h y zhou convergence of a modified halpern type iterative algorithm for quasi nonexpansive mappings appl math lett 22 2009 1051 1055 z m wang y f su d x wang y c dong a modified halpern type iteration algorithm for a family of hemi relative nonexpansive mappings and systems of equilibrium problems in banach spaces j comput appl math 235 2011 2364 2371 y f su h k xu x zhang strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications nonlinear anal 73 2010 3890 3906 c martinez yanes h k xu strong convergence of the cq method for fixed point iteration processes nonlinear anal 64 2006 2400 2411 and others

elasticity solution for vibration of 2 d curved beams with variable curvatures using a spectral sampling surface method summary an accurate spectral sampling surface method for the vibration analysis of 2 d curved beams with variable curvatures and general boundary conditions is presented the method combines the advantages of the sampling surface method and spectral method the formulation is based on the 2 d elasticity theory which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced specifically a set of non equally spaced sampling surfaces parallel to the beam s middle surface are primarily collocated along the thickness direction and the displacements of these surfaces are chosen as fundamental beam unknowns this fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces each of the fundamental beam unknowns is then invariantly expanded as chebyshev polynomials of the first kind and the problems are stated in variational form with the aid of the penalty technique and lagrange multipliers which provide complete flexibility to describe any arbitrary boundary conditions finally the desired solutions are obtained by the variational operation copyright 2016 john wiley sons ltd

strong convergence theorems for solving equilibrium problems and fixed point problems of ξ strict pseudo contraction mappings by two hybrid projection methods in this paper we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a x strict pseudo contraction mapping in hilbert spaces we obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes the results presented in the paper extend and improve some recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 346 tada and takahashi a tada w takahashi weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem j optim theory appl 133 2007 359 370 and ceng et al l c ceng s al homidan q h ansari j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 and many others

coupled bending torsional dynamic stiffness matrix for beam elements explicit expressions for the coupled bending torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made the application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted the correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks

marginalized particle filters for mixed linear nonlinear state space models the particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non gaussian filtering problems while the particle filter is fairly easy to implement and tune its main drawback is that it is quite computer intensive with the computational complexity increasing quickly with the state dimension one remedy to this problem is to marginalize out the states appearing linearly in the dynamics the result is that one kalman filter is associated with each particle the main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state space model several important special cases occurring in typical signal processing applications will also be discussed the marginalized particle filter is applied to an integrated navigation system for aircraft it is demonstrated that the complete high dimensional system can be based on a particle filter using marginalization for all but three states excellent performance on real flight data is reported

superelement method for transient dynamic analysis of structural systems the method represents a generalization of existing static and dynamic superelement substructure algorithms natural frequencies and modal shapes of a fixed boundary substructure are used to obtain equations of motion of a superelement an implicit time stepping algorithm is presented for the numerical solution of a resulting superelement system of equations of motion the method is believed to be effective for large scale problems of structural analysis

prediction condensed models adapted to the nonlinear structures in time domain abstract this paper deals with a method to study closely the stationary solution of nonlinear dynamic systems in time domain this method is based on the exploitation of karhunen loeve decomposition with or without parametric modifications as well as on the characteristics of localized nonlinearities with the application of this method at first on linear models initially condensed by karhunen loeve the predictions of nonlinear responses can be obtained rapidly this method is adapted to a condensed linear model used in the first optimization procedure of the nonlinear dynamic behaviour this robust basis will be used as condensation basis of the modified model local per zone which leads to a prediction of vibratory responses of complex structures modified and affected by localized nonlinearities

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

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications abstract the purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems the monotone hybrid algorithms are presented and are used to approximate the common fixed points using this result we also discuss the problem of strong convergence concerning the maximal monotone operators in a banach space the results of this article modify and improve the results of matsushita and takahashi s matsushita w takahashi a strong convergence theorem for relatively nonexpansive mappings in a banach space j approx theory 134 2005 257 266 and the results of plubtieng and ungchittrakool s plubtieng k ungchittrakool strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a banach space j approx theory 149 2007 103 115 and the results of su et al y su z wang and h xu strong convergence theorems for a common fixed point of two hemi relatively nonexpansive mappings nonlinear anal 71 2009 5616 5628 and many others

on the analysis of laterally vibrating slender beams subject to various complicating effects the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain a simple analysis of the free vibration problem of slender beams subject to various complicating effects these effects are the presence of concentrated masses and or concentrated moments of inertia intermediate supports axial loading and non uniformity of cross section such may exist separately or in any combination numerical results are presented for several example beams illustrating the accuracy and versatility of the approach

modified block iterative algorithm for quasi ϕ asymptotically nonexpansive mappings and equilibrium problem in banach spaces abstract the purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi asymptotically nonexpansive mappings and the set of an equilibrium problem under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex banach space with the kadec klee property as an application at the end of the paper a numerical example is given the results presented in the paper improve and extend the corresponding results in qin et al convergence theorems of common elements for equilibrium problems and fixed point problem in banach spaces j comput appl math 225 2009 20 30 zhou et al convergence theorems of a modified hybrid algorithm for a family of quasi asymptotically nonexpansive mappings j appl math compt 17 march 2009 doi 10 1007 s12190 009 0263 4 takahashi and zembayshi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 wattanawitoon and kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid syst 3 2009 11 20 and matsushita and takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 and others

particle filtering with invertible particle flow a key challenge when designing particle filters in high dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution recent advances in particle flow filters provide a promising avenue to avoid weight degeneracy particles drawn from the prior distribution are migrated in the state space to the posterior distribution by solving partial differential equations numerous particle flow filters have been proposed based on different assumptions concerning the flow dynamics approximations are needed in the implementation of all of these filters as a result the particles do not exactly match a sample drawn from the desired posterior distribution past efforts to correct the discrepancies involve expensive calculations of importance weights in this paper we present new filters which incorporate deterministic particle flows into an encompassing particle filter framework the valuable theoretical guarantees concerning particle filter performance still apply but we can exploit the attractive performance of the particle flow methods the filters we describe involve a computationally efficient weight update step arising because the embedded particle flows we design possess an invertible mapping property we evaluate the proposed particle flow particle filters performance through numerical simulations of a challenging multitarget multisensor tracking scenario and complex high dimensional filtering examples

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

substructure synthesis and its iterative improvement for large nonconservative vibratory systems a general synthesis method is developed for the dynamic analysis of nonconservati ve vibratory systems composed of substructures the idea of the synthesis is to represent each substructure by a reduced order model and to couple the substructure models together to act as the whole system for general nonconservative systems a state space formulation is adopted for each substructure reduced order substructure models are obtained by approximating each state vector as a linear combination of a small number of real trial vectors the accuracy with which the synthesized model represents the whole system depends on the choices of trial vectors and the number of vectors used a procedure is developed for increasing the accuracy by iteratively generating improved substructure trial state vectors

exact bernoulli euler dynamic stiffness matrix for a range of tapered beams bernoulli euler theory and bessel functions are used to obtain explicit expressions for the exact dynamic stiffnesses for axial torsional and flexural vibrations of any beam which is tapered such that a varies as yn and gj and i both vary as y n 2 where a gj and i have their usual meanings y cx l 1 c is a constant such that c 1 l is the length of the beam and x is the distance from one end of the beam numerical checks give better than seven figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements a procedure is given for calculating the number of natural frequencies exceeded by any trial frequency when the ends of the member are clamped this enables an existing algorithm to be used to obtain the natural frequencies of structures which contain tapered members

component mode iteration for frequency calculations this paper presents component mode iteration a new method for carrying out a form of subspace iteration on the substructure level for structures composed of substructures in component mode iteration substructure displacement is in terms of component modes with the interface displacements as coefficients component modes are chosen such that exact compatibility is assured throughout the structure the reduced structure eigenvalue problem is assembled and solved for lower mode approximations the resulting estimates of lower mode interface motion are used to refine the component modes by approximating the dynamic response of substructures to interface motion with a vector iteration process for this step the substructures are independent and can be processed in parallel reassembly and solution of the reduced structure problem yields improved lower mode estimates further iterations of refinement and reassembly are performed until convergence takes place the initial component modes are generated automatically and at negligible expense and numerical examples show that convergence with these is excellent yielding very accurate results after only one iteration indeed convergence is shown to be significantly faster than in the standard subspace iteration method

exact static and dynamic stiffness matrices for general variable cross section members this paper concerns the formulation of a new finite element method for the solution of beams with variable cross section using only one element it is possible to derive the exact static and dynamic stiffness matrices up to the accuracy of the computer for any polynomial variation of axial torsional and bending stiffnesses along the beam examples are given for the accuracy and efficiency of the method

a modified halpern type iteration algorithm for a family of hemi relatively nonexpansive mappings and systems of equilibrium problems in banach spaces in this paper we prove strong convergence theorems by the hybrid method for a family of hemi relatively nonexpansive mappings in a banach space our results improve and extend the corresponding results given by qin et al xiaolong qin yeol je cho shin min kang haiyun zhou convergence of a modified halpern type iteration algorithm for quasi f nonexpansive mappings appl math lett 22 2009 1051 1055 and at the same time our iteration algorithm is different from the kimura and takahashi algorithm which is a modified mann type iteration algorithm yasunori kimura wataru takahashi on a hybrid method for a family of relatively nonexpansive mappings in banach space j math anal appl 357 2009 356 363 in addition we succeed in applying our algorithm to systems of equilibrium problems which contain a family of equilibrium problems

exact bernoulli euler static stiffness matrix for a range of tapered beam columns the static stiffnesses for torsional and flexural deformation of a tapered beam under axial loading are determined analytically extending the bernoulli euler bessel function approach of banerjee and williams 1985 the derivation of the expressions is explained in detail and numerical results for sample problems are presented in tables and shown to be in excellent agreement with those obtained using stepped beams of 400 or 500 elements

the exact explicit dynamic stiffness matrix of multi cracked euler bernoulli beam and applications to damaged frame structures abstract in this paper the closed form expression of the exact dynamic stiffness matrix of an euler bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived the procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi cracked beam derived by the same authors in a previous paper the knowledge of the exact explicit dynamic stiffness matrix of the multi cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes consistent with the distributed parameter model through the application of the well known wittrick williams algorithm some numerical applications relative to the evaluation of frequencies and the corresponding mode shapes of multi cracked framed structure are reported furthermore the closed form solution has been validated by comparing with some exact results available in the literature for a simple single cracked frame finally further new results for a multi cracked frame have been compared with those obtained by a finite element simulation

degree of convergence of modified averaged iterations for fixed points problems and operator equations abstract let h be a real hilbert space we propose a modification for averaged mappings to approximate the unique fixed point of a mapping t h h such that t is boundedly lipschitzian and t is monotone we not only prove strong convergence theorems but also determine the degree of convergence using this result an iteration process is given for finding the unique solution of the equation a x f where a h h is strongly monotone and boundedly lipschitzian

lambda matrix flexibility abstract to represent an harmonically vibrating continuous system having an infinite number of degrees of freedom by means of mathematical models of a finite number of co ordinates the relation between the excitation force vector and response displacement vector the dynamic stiffness matrix d is inevitably frequency dependent it is often required to compute the dynamic flexibility matrix z which is the inversion of d a new method is presented here to express z in terms of the eigensolutions of d it is similar to the classical format except that d is no longer required to be expressible as a matrix polynomial in with constant coefficient matrices in contrast to the state variables which tend to increase the order of the matrices only physical co ordinates are concerned d may be non symmetric and defective

approximating sample state vectors using the espt for computationally efficient particle filtering the extrapolated single propagation technique espt based particle filter is proposed instead of propagating all the sample state vectors using multiple numerical integrations only one sample state vector is propagated in the espt other sample states are computed at the next epoch with an accuracy of the second order taylor series expansion terms it is theoretically shown that the particle filter algorithm which uses the espt for state propagation requires up to text 90 reduced processing time than the conventional particle filter using a benchmark non linear estimation problem the performance of the modified algorithm is compared with the particle filter the experimental results confirm the theoretical analysis and demonstrate the effectiveness of the proposed method for non linear state estimation the proposed algorithm significantly reduces the processing time of the particle filter with a minor degradation in the estimation accuracy

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

recursive second order convergence method for natural frequencies and modes when using dynamic stiffness matrices when exact dynamic stiffness matrices are used to compute natural frequencies and vibration modes for skeletal and certain other structures a challenging transcendental eigenvalue problem results the present paper presents a newly developed mathematically elegant and computationally efficient method for accurate and reliable computation of both natural frequencies and vibration modes the method can also be applied to buckling problems the transcendental eigenvalue problem is first reduced to a generalized linear eigenvalue problem by using newton s method in the vicinity of an exact natural frequency identified by the wittrick williams algorithm then the generalized linear eigenvalue problem is effectively solved by using a standard inverse iteration or subspace iteration method the recursive use of the newton method employing the wittrick williams algorithm to guide and guard each newton correction gives secure second order convergence on both natural frequencies and mode vectors the second order mode accuracy is a major advantage over earlier transcendental eigenvalue solution methods which typically give modes of much lower accuracy than that of the natural frequencies the excellent performance of the method is demonstrated by numerical examples including some demanding problems e g with coincident natural frequencies with rigid body motions and large scale structures copyright 2003 john wiley sons ltd

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

on the substructure synthesis method substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures the motion of each of the substructures is represented by a series of admissible functions vectors and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures because the series of admissible functions vectors represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions the computed eigensolution is only an approximation of the actual one convergence of computed eigenvalues to actual eigenvalues requires two limiting processes one in which the number of admissible functions vectors is increased and the other in which the number of geometric compatibility conditions is increased

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

strong convergence theorems for relatively nonexpansive mappings in a banach space abstract in this paper we prove two strong convergence theorems of modified ishikawa iteration and modified halpern iteration for relatively nonexpansive mappings in a banach space our results extend and improve the recent ones announced by nakajo takahashi kim martinez yanes xu and some others

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

non prismatic beams a simple and effective timoshenko like model abstract the present paper discusses simple compatibility equilibrium and constitutive equations for a non prismatic planar beam specifically the proposed model is based on standard timoshenko kinematics i e planar cross section remain planar in consequence of a deformation but can rotate with respect to the beam center line an initial discussion of a 2d elastic problem highlights that the boundary equilibrium deeply influences the cross section stress distribution and all unknown fields are represented with respect to global cartesian coordinates a simple beam model i e a set of ordinary differential equations odes is derived describing accurately the effects of non prismatic geometry on the beam behavior and motivating equation s terms with both physical and mathematical arguments finally several analytical and numerical solutions are compared with results existing in literature the main conclusions can be summarized as follows i the stress distribution within the cross section is not trivial as in prismatic beams in particular the shear stress distribution depends on all generalized stresses and on the beam geometry ii the derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses iii axial and shear bending problems are strictly coupled iv the beam model is naturally expressed as an explicit system of six first order odes v the odes solution can be obtained through the iterative integration of the right hand side term of each equation vi the proposed simple model predicts the real behavior of non prismatic beams with a good accuracy reasonable for the most of practical applications

strong convergence theorem of an iterative method for variational inequalities and fixed point problems in hilbert spaces in this paper we introduce a new iteration method based on the hybrid method in mathematical programming and the descent like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in hilbert spaces our method modifies and improves some methods in literature

power series expansions of dynamic stiffness matrices for tapered bars and shafts summary stiffness and consistent mass matrices for tapered bars and shafts are derived with the aid of static displacement functions moreover the corresponding dynamic stiffness matrices are developed in the laplace transform domain from the exact solutions of axial torsional governing equations power series expansions of the bessel functions comprising the dynamic stiffness influence coefficients show that the stiffness and consistent mass matrices can be mathematically derived from the dynamic stiffness matrices a discussion on the convergence of the power series expansions is also presented the developments provide further insight into the approximations present in conventional consistent mass formulations of frameworks with tapered members

stability boundaries for parametrically excited systems by dynamic stiffness abstract the dynamic stability of skeletal systems subject to harmonic axial forces is of interest temporal discretization is achieved by fourier expansion the resulting differential equations in spatial co ordinates alone are solved by the exact frequency dependent shape functions the dynamic stability boundaries are determined by studying the free vibration behaviour with periods t and 2 t where t is the period of the harmonic axial force since spatial discretization is completely eliminated many stability boundaries can be determined accurately with the minimum number of elements

dynamic stiffness for structures with distributed deterministic or random loads abstract the dynamic stiffness method applies mainly to excitations of harmonic nodal forces for distributed loads modal analysis is generally required in the case of a clamped clamped beam the modal decomposition of a uniformly distributed load by the eigenbeam functions inherits slow convergence because the finite loads at the beam ends cannot be represented efficiently by the zero deflection and zero slope of the clamped clamped beam functions the computed reactions at the supports do not converge at all the problem is eliminated in this paper by using the finite element interpolation functions for the distributed load if the distributed load is adequately represented explicit exact solutions are found otherwise the residual load is expanded in the modal space as the residual modal force is much smaller and agrees well with the clamped clamped conditions fast convergence is achieved by means of the principle of superposition a structure with members having distributed loads can be analyzed by two systems one is associated with the individual members having distributed loads and the other is associated with resulting equivalent nodal forces the required frequency functions are given for all possible cases the results presented are exact if the load is interpolated adequately by finite element shape functions both deterministic and random loads are considered closed form solutions are obtained for the first time

exact natural frequencies of a three dimensional shear torsion beam with doubly asymmetric cross section using a two dimensional approach abstract this paper presents an exact analytical approach to the calculation of the natural frequencies of structures comprising contiguous three dimensional shear torsion beams with doubly asymmetric cross section such component members have the unusual theoretical property that they allow for coupled torsional and shearing deformation but not bending deformation initially exact dynamic member stiffness matrices exact finite elements are developed for planar shear and torsional motion these matrices can be combined in the usual way to model stepped and continuous beams whose uncoupled frequencies can then be determined exactly it is then shown how the corresponding coupled frequencies can be established easily from the uncoupled values through an exact relationship this enables coupled three dimensional vibration problems to be solved very efficiently using a two dimensional approach the paper is concluded with an example that clarifies the theory together with a parametric study that enables guidance to be given as to when lateral torsional coupling may safely be ignored

strong convergence of a proximal type algorithm in a banach space in this paper we study strong convergence of the proximal point algorithm it is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator but it fails to converge strongly then in math program 87 2000 pp 189 202 solodov and svaiter introduced the new proximal type algorithm to generate a strongly convergent sequence and established a convergence property for it in hilbert spaces our purpose is to extend solodov and svaiter s result to more general banach spaces using this we consider the problem of finding a minimizer of a convex function

strong convergence theorems of total quasi φ asymptotically nonexpansive semi groups in banach spaces the purpose of this article is first to introduce the concept of total quasi f asymptotically nonexpansive semigroups which contains many kinds of semi groups as its special cases and then to modify the halpern mann type iteration algorithm for this kind of semi groups to have the strong convergence under a limit condition only in the framework of banach spaces the results presented in the paper improve and extend the corresponding recent results announced by many authors

approximations of the optimal importance density using gaussian particle flow importance sampling abstractrecently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution and a number of particle filters based on this principle have been proposed samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo time such that their final values are distributed according to the desired posterior in practice implementing a particle flow sampler requires multiple layers of approximation with the result that the final samples do not in general have the correct posterior distribution in this article we consider using an approximate gaussian flow for sampling with a class of nonlinear gaussian models we use the particle flow within an importance sampler correcting for the discrepancy between the target and actual densities with importance weights we present a suitable numerical integration procedure for use with this flow and an accompanying step size control algorithm in a filtering co

an iterative method for total quasi φ asymptotically nonexpansive semi groups and generalized mixed equilibrium problems in banach spaces in this paper we introduce an iterative scheme by the modified halpern mann type for total quasi asymptotically nonexpansive semi groups and prove the strong convergence theorem using our new iterative process which converges strongly to a common element of the set of common fixed points for total quasi asymptotically nonexpansive semi groups and the set of solutions of generalized mixed equilibrium problem in a uniformly smooth and strictly convex banach space with the kadec klee property using the properties of the generalized f projection operator our results extend and improve the corresponding recent results in the literature

spectral element modeling for extended timoshenko beams periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension transverse shear bending coupled vibrations which can be well represented by the extended timoshenko beam theory in this paper the spectrally formulated finite element model simply spectral element model has been developed for extended timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube the periodic plane truss and the periodic space lattice beam

projection algorithms for solving nonmonotone equilibrium problems in hilbert space we propose two projection algorithms for solving an equilibrium problem where the bifunction is not required to be satisfied any monotone property under assumptions on the continuity convexity of the bifunction and the nonemptyness of the solution set of the minty equilibrium problem we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the primal equilibrium problem respectively

a new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in banach spaces with applications abstract the purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a banach space as applications we utilize our results to obtain some new results for finding a solution of an equilibrium problem a fixed point problem and a common zero point problem for maximal monotone mappings in banach spaces

asymptotically strict pseudocontractive mappings in the intermediate sense abstract it is proved that the modified mann iteration process x n 1 1 n x n n t n x n n n where n is a sequence in 0 1 with n 1 for some 0 1 converges weakly to a fixed point of an asymptotically strict pseudocontractive mapping t in the intermediate sense which is not necessarily lipschitzian we also develop cq method for this modified mann iteration process which generates a strongly convergent sequence