an interpretive method for moving force identification dynamic load data have been valuable for bridge and pavement design traditional ways to acquire truck axle and gross weight information are expensive and subject to bias and this has led to the development of weigh in motion wim techniques most of the existing wim systems have been developed to measure only the static axle loads this paper aims to introduce a method to identify moving dynamic loads on bridges using the bridge responses caused by such loads a closed form solution can be obtained to identify moving constant loads while numerical methods must be used to identify the time varying moving loads the set of equations that leads to the solution is based on euler s equation of beams a two axle vehicle model is developed to generate the theoretical responses and the corresponding interactive moving forces studies were carried out to check whether the proposed method could recover the original interactive moving forces and the method was found to be feasible

free vibration analysis of a uniform multi span beam carrying multiple spring mass systems abstract the literature regarding the free vibration analysis of single span beams carrying a number of spring mass systems is plenty but that of multi span beams carrying multiple spring mass systems is fewer thus this paper aims at determining the exact solutions for the natural frequencies and mode shapes of a uniform multi span beam carrying multiple spring mass systems firstly the coefficient matrices for an intermediate pinned support an intermediate spring mass system left end support and right end support of a uniform beam are derived next the numerical assembly technique for the conventional finite element method is used to establish the overall coefficient matrix for the whole vibrating system finally equating the last overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes in this paper the natural frequencies and associated mode shapes of the vibrating system are obtained directly from the differential equation of motion of the continuous beam and no other assumptions are made thus the last solutions are the exact ones the effects of attached spring mass systems on the free vibration characteristics of the 1 4 span beams are studied

rogue waves rational solutions the patterns of their zeros and integral relations the focusing nonlinear schrodinger equation which describes generic nonlinear phenomena including waves in the deep ocean and light pulses in optical fibres supports a whole hierarchy of recently discovered rational solutions we present recurrence relations for the hierarchy the pattern of zeros for each solution and a set of integral relations which characterizes them

vibration analysis of non linear beams subjected to a moving load using the finite element method this paper is concerned with the non linear vibration of immovably supported variable beams in which the geometric non linearity due to the axial force generated by stretching the middle surface is taken into account when the beam is subjected to a moving load the dynamic deflections of the beam are computed by using a galerkin finite element formulation and the time differential terms are integrated by using the implicit direct integration method three types of approximations for solving the non linear problem are considered in the first of which both the longitudinal deflections and inertia are considered with only the longitudinal deflections being considered and in the second neither the longitudinal deflections nor inertia in the third the results obtained by using these non linear models are numerically compared with that obtained by the linear model

natural frequency changes of a cracked timoshenko beam by modified fourier series a new method is presented in this paper for computing the natural frequencies of a timoshenko beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is developed particularly for a timoshenko beam having an arbitrary number of transverse open cracks unlike the conventional fourier series the modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked timoshenko beam in the usual way and thus reduces the problem to a simple one by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form that renders the task of computer coding quite straightforward

dressing method and quadratic bundles related to symmetric spaces vanishing boundary conditions we consider quadratic bundles related to hermitian symmetric spaces of the type su m n s u m u n the simplest representative of the corresponding integrable hierarchy is given by a multi component kaup newell derivative nonlinear schrodinger equation which serves as a motivational example for our general considerations we extensively discuss how one can apply zakharov shabat s dressing procedure to derive reflectionless potentials obeying zero boundary conditions those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy one can distinguish between generic soliton type solutions and rational solutions

nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load this paper focuses on the geometrically nonlinear dynamic analysis of an eccentrically prestressed simply supported damped beam subjected to a concentrated moving harmonic load the nonlinear dynamic deflections of the beam are obtained by polynomial functions the kelvin voigt model for the material of the beam is used two coupled nonlinear systems of equations of motion are derived using lagrange s equations under the assumptions of the euler bernoulli beam theory with the von karman s nonlinear strain displacement relationships the rotary inertia axial displacement and axial inertia are included in the formulation the nonlinear equations of motion are solved by using the implicit time integration method of newmark in conjunction with the newton raphson iteration method in this study the effects of large deflections the internal damping of the beam the velocity of the moving harmonic load the prestress load the eccentricity of the prestress load and the excitation frequency on the dynamic response of the beam are discussed the obtained results are compared with the results based on the linear beam theory convergence studies are performed numerical results show that the above mentioned effects play a very important role in the deflections of the beam

vibration of multi span non uniform beams under moving loads by using modified beam vibration functions based on hamilton s principle the vibration of a multi span non uniform beam subjected to a moving load is analysed by using modified beam vibration functions as the assumed modes the modified beam vibration functions satisfy the zero deflection conditions at all the intermediate point supports as well as the boundary conditions at the two ends of the beam numerical results are presented for both uniform and non uniform beams under moving loads of various velocities examples show that this method converges very quickly and good results are obtained

regular operator mappings and multivariate geometric means we introduce the notion of regular operator mappings of several variables generalising the notion of spectral function this setting is convenient for studying maps more general than what can be obtained from the functional calculus and it allows for jensen type inequalities and multivariate non commutative perspectives as a main application of the theory we consider geometric means of k operator variables extending the geometric mean of k commuting operators and the geometric mean of two arbitrary positive definite matrices we propose dierent types of updating conditions that seems natural in many applications and prove that each of these conditions together with a few other natural axioms uniquely defines the geometric mean for any number of operator variables the means defined in this way are given by explicit formulas and are computationally tractable 1 msc2010 classification 26b25 47a64

on the eigenfrequencies for mass loaded beams under classical boundary conditions a frequency analysis of loaded beams is performed for ten classical beams involving guided fixed free an or pinned ends the explicit frequency equations are obtained by satisfying the differential equation of the eignvalue problem the boundary and comptatibility conditions a solution set of the transcendental expression will be compared with the experimental results and also with those obtained by using rayleigh s method

dynamic response of a rotating flexible arm carrying a moving mass abstract a clamped free flexible arm rotating in a horizontal plane and carrying a moving mass is studied in this paper the arm is modelled by the euler bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored the assumed mode method in conjunction with hamilton s principle is used to derive the equation of motion of the system which takes into account the effect of centrifugal stiffening due to the rotation of the beam the eigenfunctions of a cantilever beam which satisfy the prescribed geometric boundary conditions are used as basis functions in the assumed mode method the equation of motion is expressed in non dimensional matrix form pre designed transformed cosine profiles are used as trajectory inputs for the hub angle and the moving mass the equation of motion is solved numerically using the fourth order runge kutta method graphical results are presented to show the influence of centrifugal stiffening effect moving mass values mass travelling time hub angle and mass trajectory profile on the deflection of the beam

vibration and stability of cracked hollow sectional beams this paper presents simple tools for the vibration and stability analysis of cracked hollow sectional beams it comprises two parts in the first the influences of sectional cracks are expressed in terms of flexibility induced each crack is assigned with a local flexibility coefficient which is derived by virtue of theories of fracture mechanics the flexibility coefficient is a function of the depth of a crack the general formulae are derived and expressed in integral form it is then transformed to explicit form through 128 point gauss quadrature according to the depth of the crack the formulae are derived under two scenarios the first is for shallow cracks of which the penetration depth is contained within the top solid sectional region the second is for deeper penetration in which the crack goes into the middle hollow sectional region the explicit formulae are best fitted equations generated by the least squares method the best fitted curves are presented from the curves the flexibility coefficients can be read out easily while the explicit expressions facilitate easy implementation in computer analysis in the second part the flexibility coefficients are employed in the vibration and stability analysis of hollow sectional beams the cracked beam is treated as an assembly of sub segments linked up by rotational springs division of segments are made coincident with the location of cracks or any abrupt change of sectional property the crack s flexibility coefficient then serves as that of the rotational spring application of the hamilton s principle leads to the governing equations which are subsequently solved through employment of a simple technique it is a kind of modified fourier series which is able to represent any order of continuity of the vibration buckling modes illustrative numerical examples are included

the hierarchy of multi soliton solutions of the derivative nonlinear schrodinger equation we provide a relatively simple approach to backlund transformations for the derivative nonlinear schrodinger equation by iteration it leads to compact n soliton formulae both with asymptotically vanishing and non vanishing amplitudes the phenomenology of these solutions is discussed and illustrated in some detail

maximizing the natural frequency of a beam with an intermediate elastic support the minimum stiffness of a simple or point support that raises a natural frequency of a beam to its upper limit is investigated for different boundary conditions the approach produces the closed form solution for the minimum stiffness based on the derivative of a natural frequency with respect to the support position it is seen that when an intermediate elastic support is positioned properly the effect is similar to a rigid support the solution process also provides insight into the dynamics of a beam with an intermediate support for more general boundary conditions the resulting solutions can be used to guide the practical design of a support

natural frequencies and ope loop responses of an elastic beam fixed on a moving cart and carrying an intermediate lumped mass abstract in this paper the motion of a bernoulli euler cantilever beam clamped on a moving cart and carrying an intermediate lumped mass is considered the equations of motion of the beam mass cart system are analyzed through unconstrained modal analysis and a unified characteristic equation for calculating the natural frequencies of the system is established the changes of natural frequencies and the corresponding mode shapes with respect to the changes in the ratios between the beam mass the lumped mass and the cart mass and to the concentrated position of the lumped mass are investigated with the frequency equation which can be generally applied to this kind of system the exact and assumed mode solutions including the dynamics of the base cart are obtained and the open loop responses of the system by arbitrarily designed forcing functions are given by numerical simulations the results match well with physical phenomena even in the extreme cases where the mass is attached to the bottom and to the top of the beam

dynamic response of a beam with intermediate point constraints subject to a moving load abstract the transverse vibration of a beam with intermediate point constraints subject to a moving load is analyzed by using the euler beam theory and the assumed mode method the point constraints in the form of supports are assumed to be linear springs of large stiffness results of numerical simulations are presented for various combinations of constant axial velocity of the moving load and number of point constraints

a fixed point mean approximation to the cartan barycenter of positive definite matrices abstract in this paper we define a new weighted inductive geometric mean h n on the riemannian manifold of positive definite matrices of fixed size and present its fixed point mean approximation to the cartan barycenter karcher mean we show that for t 0 1 the weighted geometric mean equation x h n 1 t a 1 a n x where t t 1 t w 1 w n 1 t has a unique positive definite solution that approaches as t 0 to the weighted cartan mean of a 1 a n numerical computations for the stochastic convergence in terms of h n to derive a new contractive barycenter other than the cartan barycenter are presented

toeplitz lemma in geodesic metric space and convergence of inductive means abstract in this article we study the toeplitz lemma for inductive means in a geodesic metric space and by using the toeplitz lemma we prove the cesaro theorem for inductive means also we study an asymptotic property for hansen s inductive geometric mean and as an application of the toeplitz lemma we prove a convergence of hansen s inductive mean

free vibration analysis for tube in tube tall buildings an approximate solution procedure is formulated for free vibration analysis of tube in tube tall buildings in this paper the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients on the assumption that the transverse displacement is a harmonic vibration a power series solution which represents the mode shape function of tube in tube tall buildings is derived applying the boundary conditions yields the boundary value problem from which the frequency equation is established and solved through a numerical process to determine the natural frequencies two numerical examples are performed and compared with results available in the published literature to show the accuracy of the proposed method care has been exercised to retain sufficient terms in power series in evaluating natural frequencies of accepted accuracy the influences of the factors including flexural rigidity mass per unit length and building height to the natural frequency are discussed the method proposed herein enables one to calculate as an alternative the natural frequency of tube in tube tall buildings with good accuracy associated by calculators and hand prior to use of the complicated computer programs

natural frequencies of a non uniform beam with multiple cracks via modified fourier series abstract a new method is presented in this paper for computing the natural frequencies of a non uniform beam with an arbitrary number of transverse open cracks the essence of this new method lies in the use of a kind of modified fourier series mfs which is specially developed for a beam with transverse open cracks unlike conventional fourier series modified fourier series can approach a function with internal geometrical discontinuities based on the modified fourier series one can treat the cracked beam in the most usual way and thus reduce the problem to a simple one the beam can be of non uniform cross section and the number of cracks can be arbitrary by using the present method only standard linear eigenvalue equations rather than non linear algebraic equations need to be solved all the formulae are expressed in matrix form which renders the programming quite straightforward

derivative nonlinear schrodinger equations and hermitian symmetric spaces it is shown that to each hermitian symmetric space there corresponds an integrable system of generalised derivative nonlinear schrodinger equations nls the nonlinear terms are related to the curvature tensor of the associated symmetric space the hamiltonian form of the equations is presented the results are an extension of those presented in an earlier paper 1983 on generalised nls equations associated with symmetric and reductive homogeneous spaces

vibration of multi span timoshenko beams to a moving force abstract a method of modal analysis is proposed in this paper to investigate the forced vibration of multi span timoshenko beams the ratio of the radius of gyration of the cross section to one span length is defined as a parameterr the effect ofron the first modal frequency of a beam is studied a concentrated force traversing on the beam is used as an example the effects of span number rotary inertia and shear deformation on the maximum moment the maximum deflection and the critical velocity of a beam are examined the results are compared with those of a multi span bernoulli euler beam

rational solitons of wave resonant interaction models integrable models of resonant interaction of two or more waves in 1 1 dimensions are known to be of applicative interest in several areas here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear schrodinger equations and the equations describing the resonant interaction of three waves the darboux dressing construction of soliton solutions is applied under the condition that the solutions have rational or mixed rational exponential dependence on coordinates our algebraic construction relies on the use of nilpotent matrices and their jordan form we systematically search for all bounded rational mixed rational exponential solutions and find a broad family of such solutions of the three wave resonant interaction equations

crum transformation and rational solutions of the non focusing nonlinear schrodinger equation a crum transformation for the linear problem of the non focusing nonlinear schrodinger nls equation is used to construct the sequence of rational solutions given in terms of tau functions expressed as double wronskian determinants the rational solutions of the adler kaup newell segur akns hierarchy have already been obtained in the work of sachs using the equivalence with the classical boussinesq hierarchy however we find that sachs description of the restrictions that must be placed on the akns tau functions in order to obtain nls rational solutions is not entirely correct we briefly comment on the constrained calogero moser systems associated with the nls rational solutions and indicate how the calogero moser equations can be obtained from a trilinear equation for the tau function which arises by reduction of the kadomtsev petviashvili kp hierarchy

vibration frequencies of a rotating flexible arm carrying a moving mass abstract a clamped free flexible beam rotating in a horizontal plane and carrying a moving mass is modelled by the euler bernoulli beam theory the equation of motion is derived by hamilton s principle including the effects of centrifugal stiffening arising from the rotation of the beam the motion of the moving mass and the beam is coupled the equation of motion is a coupled non linear partial differential equation where the coupling terms have to be evaluated at the position of the moving mass in order to obtain the mode shapes which account for the motion of the moving mass the solution is discretized into space and time functions and the beam is divided into two separate regions with respect to the moving mass this results in two non homogeneous linear mode shape ordinary differential equations with four boundary one discontinuity and three continuity conditions the power series method is used to solve for the mode shape differential equations a frequency equation is derived giving the relationship between the non dimensional modal frequencies and the four non dimensional parameters i e the moving mass position the moving mass the beam angular velocity and the total moment of inertia about the hub the numerical bisection method is used to solve for the vibration frequencies under different parameters results are presented for the first three modes of vibration

non linear vibration of timoshenko beam due to a moving force and the weight of beam the large deflection theory is employed to derive the equations of motion of the timoshenko beam due to the coupling effect of an external force with the weight of the beam galerkin s method is employed to obtain the dynamic responses of the beam a set of two discrete moving forces is taken as an example to investigate the characteristics of these responses results show that the effect of weight of the beam decreases the fundamental period of the structure further both the dynamic deflection and the dynamic moment of the beam predicated by the theory including the effect of weight of the beam are less than those of the beam predicated either by the small deflection theory or by the large deflection theory without including the effect of weight of the beam

decay rate estimates for the quasi linear timoshenko system with nonlinear control and damping terms in this work we consider a class of quasi linear timoshenko systems with nonlinear control and damping terms we investigate the stabilization of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on control and damping terms

vibration of multi span non uniform bridges under moving vehicles and trains by using modified beam vibration functions abstract based on the lagrangian approach the vibration of a multi span non uniform bridge subjected to a moving vehicle is analyzed by using modified beam vibration functions as the assumed modes the vehicle is modelled as a two degree of freedom system the method is extended to the action of a moving train by modelling it as a series of two degree of freedom systems all the derived formulae are expressed in matrix form and therefore programming is quite straightforward the total number of unknowns for this method is very small compared with that of the finite element method convergence is very quick and in almost all cases 12 16 terms are sufficient to give satisfactory results

moving forces identification on a multi span continuous bridge abstract a continuous bridge is modelled as a multi span continuous timoshenko beam with non uniform cross section the vibration behaviour of this beam subjected to moving loads is analyzed by hamilton s principle with the intermediate point constraints represented by very stiff linear springs a method based on the modal superposition and optimization technique is developed to identify the moving forces in the time domain the damped least squares method is used in the identification to provide bounds to the results the errors in the moving force identification are discussed in the paper both computation simulations and laboratory tests show that the method is effective for identifying the moving loads using different combinations of measured responses

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations