locating p poly optimally in the extended low hierarchy the low hierarchy in np and the extended low hierarchy have turned out to be very useful in classifying many interesting language classes and almost all of them could be located optimally therein however until now the exact location of p poly remained open

wavelet expansion based stochastic response of chain like mdof structures abstract this paper presents a wavelet expansion based approach for response determination of a chain like multi degree of freedom mdof structure subject to full non stationary stochastic excitations specifically the generalized harmonic wavelet ghw is first utilized as the expansion basis to solve the dynamic equation of structures via the galerkin treatment in this way a linear matrix relationship between the deterministic response and excitation can be derived further considering the ghw based representation of the stochastic processes a time varying power spectrum density psd relationship on a certain wavelet scale or frequency band between the excitation and response is derived finally pertinent numerical simulations including deterministic dynamic analysis and monte carlo simulations of both the response psd and the story drift based reliability are utilized to validate the proposed approach

on the dynamical axisymmetric stress field in a finite pre stretched bilayered slab resting on a rigid foundation the dynamic axisymmetric stress field in an initially finite pre stretched bilayered slab resting on a rigid foundation is studied within the framework of the piecewise homogeneous body model the three dimensional linearized theory of elastic waves in initially stressed bodies is used it is assumed that a time harmonic point located normal force acts on the free face plane of the slab the considered problem is solved by employing the hankel integral transformation the materials of the layers are assumed to be incompressible and the elastic relations are given through the treloar potential the formulation and solution to the problem coincide with the corresponding ones of classical linear theory of elasticity for an incompressible body in the case where there is no initial stretching in the layers numerical results are presented and these results involve stresses acting on the interface planes in particular it is established that stresses on the interface planes decrease as the pre stretching is increased

on a general model for damping when a structure exhibits a damped dynamic behavior that does not conform to the classical and well known viscous or hysteretic models a more general approach must be sought several questions may then be raised like i in which theoretical background should one base the investigation or ii can one apply common modal analysis tools to solve the problem recent works have shown that some types of materials and therefore structures demand a more rigorous behavior description and that it seems possible to address the problem by means of the theory of fractional derivatives leading to a model in terms of general damping parameters such an approach reveals itself somewhat complicated to implement in practice and some simplifications are necessary the authors discuss the use of a generalized damping concept for modeling the dynamic behavior of linear systems and show how this concept allows for a clearer interpretation and explanation of the behavior displayed by the common viscous and hysteretic models

bounded queries approximations and the boolean hierarchy this paper investigates nondeterministic bounded query classes in relation to the complexity of np hard approximation problems and the boolean hierarchy nondeterministic bounded query classes turn out be rather suitable for describing the complexity of np hard approximation problems the results in this paper take advantage of this machine based model to prove that in many cases np approximation problems have the upward collapse property that is a reduction between np approximation problems of apparently different complexity at a lower level results in a similar reduction at a higher level for example if maxclique reduces to log n approximating maxclique using many one reductions then the traveling salesman problem tsp is equivalent to maxclique under many one reductions several upward collapse theorems are presented in this paper the proofs of these theorems rely heavily on the machinery provided by the nondeterministic bounded query classes in fact these results depend on a surprising connection between the boolean hierarchy and nondeterministic bounded query classes

complexity restricted advice functions the authors consider uniform subclasses of the nonuniform complexity classes defined by karp and lipton l enseign math 28 1982 via the notion of advice functions these subclasses are obtained by restricting the complexity of computing correct advice also the effect of allowing advice functions of limited complexity to depend on the input rather than on the input s length is investigated among other results using the notions described above new characterizations of a np np cap sparse b np with a restricted access to an np oracle and c the odd levels of the boolean hierarchy are given as a consequence it is shown that every set that is nondeterministically truth table reducible to sat in the sense of rich j comput system sci 38 1989 pp 511 523 is already deterministically truth table reducible to sat furthermore it turns out that the np reduction classes of bounded versions of this reducibility coincide with the odd levels of the boolean hierarchy

free vibration analysis of microtubules based on an atomistic continuum model abstract analysis of free vibration of microtubules based on an atomistic continuum model is presented the theory bridges the polyatomic structure of microtubules with a macroscopic continuum approach under mesh free computing scheme a higher order gradient continuum constitutive relationship is developed and incorporated into a higher order cauchy born rule instead of considering the atomic interaction between every atom pair in such polyatomic bio composite textures interatomic energy between subcomponents in microtubules is evaluated by a homogenization technique represented by the fictitious bond material properties and stiffness matrix are determined depending on deformation of fictitious bonds since the mesh free approximation automatically satisfies the higher order continuity and possesses intrinsic nonlocal property the established quasicontinuum theory takes into consideration both atomic interaction and the size effect for modeling this microscale structure natural vibration frequencies of microtubules of different lengths and boundary restrictions are predicted and compared with existing solutions

modelling of floating slab tracks with continuous slabs under oscillating moving loads this paper discusses modelling of floating slab tracks on rigid foundations the model consists of an upper euler bernoulli beam to account for both the rails and a lower euler bernoulli beam to account for the slab there are two continuous resilient layers in the model one to account for railpads between the rails and the slab and one to account for slab bearings underneath the slab the fourier transformation method is used to calculate displacements of such a track under an oscillating moving load these results are used to calculate the cut on frequencies and critical velocity of the track the work in this paper also demonstrates some basic concepts in the context of vibration of infinite systems including dispersion curves critical velocities load velocity lines and coupling of systems in the wavenumber frequency domain the paper offers a complete treatment of the issues important to the analysis of a double beam system not elsewhere available in the published literature

predicting buckling behavior of microtubules based on an atomistic continuum model abstract an atomistic continuum model is proposed for microtubules a higher order gradient continuum constitutive relationship is established and elasticity and global buckling of microtubules are studied intensively as a typical macromolecular bio system atomic components and structures are much more complicated traditional atomistic simulation methods and classical continuum approaches have their own fundamental drawbacks in dealing with this large atomic system adopting a homogenization technique this paper proposes a concept of fictitious bonds for microtubules to link the large atomic structure with continuum description after selecting a representative unit the fictitious bond energy equals to the energy stored in the continuum model the higher order cauchy born rule is used to approximate the deformation of fictitious bonds under arbitrary loading conditions a mesh free numerical scheme is specifically developed for modeling computation the elastic modulus and critical compressive force are predicted representative case studies are presented and some results are obtained and discussed

stochastic modelling of traffic induced ground vibration abstract in this paper an entirely analytical method of calculating the power spectrum of ground vibration in the vicinity of a busy roadway is presented it is based on the assumption that vehicles are sufficiently closely spaced that ground vibration can be considered to be a random and statistically stationary process the assumption is valid at distances away from the road greater than or equal to the mean vehicle spacing random process theory is used to obtain expressions for the power spectra of horizontal and vertical vibration when given the power spectrum of road surface roughness a dynamic vehicle model and a model for vibration transmission through a half space a suitable two axle vehicle model is discussed in an accompanying paper 19 where allowances are made for the statistical variation of vehicle dimensions weight suspension characteristics and distribution along the road and in particular for the effect of wheelbase filtering calculated ground vibration power spectra compare favourably with measured vibration spectra in the vicinity of a busy road near cambridge

the vibration of a non prismatic beam on an inertial elastic half plane abstract the problem of vibration of a non prismatic beam resting on an inertial elastic half plane described by classical elastokinetics equations is solved using chebyshev series approximation as a result closed analytical formulae for the sought solution s coefficients the passive foundation pressure function and the system displacement function were obtained the method was applied to solve the problem of harmonically excited vibration

on the dynamics of a finite pre strained bi layered slab resting on a rigid foundation under the action of an oscillating moving load this paper investigates the dynamic response of a finitely pre strained bi layered slab resting on a rigid foundation to a time harmonic oscillating moving load within the scope of the piecewise homogeneous body model utilizing the 3d linearized wave propagation theory in the initially stressed body it is assumed that the materials of the layers are highly elastic ones and their elasticity relations are given in terms of the harmonic potential moreover it is also assumed that the velocity of the line located time harmonic oscillating moving load is constant as it acts on the free face of the upper layer of the slab our investigations were carried out for a 2d problem plane strain state under subsonic velocity for a moving load in complete contact conditions the corresponding numerical results were obtained for the stiff upper layer and soft lower layer system in which the constants of elasticity for the upper layer material are greater than those of the lower layer material numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters in particular it is established that with the oscillating frequency of the moving load the values of the critical velocity decrease moreover it is established that the initial stretching of the upper layer of the slab causes the critical velocity to increase and the absolute values of the normal stresses acting on the mid planes of the layers of the slab to decrease

universal analytical solution of the steady state response of an infinite beam on a pasternak elastic foundation under moving load abstract in this paper the steady state response of a uniform infinite euler bernoulli elastic beam resting on a pasternak elastic foundation and subjected to a concentrated load moving at a constant velocity along the beam is analytically investigated a universal closed form analytical solution is derived through fourier transform apt to represent the response for all possible beam foundation parameters a rigorous mathematical procedure is formulated for classifying the parametric behavior of the solution including for viscous damping depending on such a classification different types of bending wave shapes are shown to propagate within the beam ahead and behind the moving load position and crucial physical characteristics such as critical velocity and critical damping are reinterpreted into a wholly exact and complete mathematical framework mechanical features of the solution are revealed for the steady state response in terms of normalized deflection cross section rotation bending moment and shear force

convergence study of the truncated karhunen loeve expansion for simulation of stochastic processes a random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coefficients karhunen loeve k l series expansion is based on the eigen decomposition of the covariance function its applicability as a simulation tool for both stationary and non stationary gaussian random processes is examined numerically in this paper the study is based on five common covariance models the convergence and accuracy of the k l expansion are investigated by comparing the second order statistics of the simulated random process with that of the target process it is shown that the factors affecting convergence are a ratio of the length of the process over correlation parameter b form of the covariance function and c method of solving for the eigen solutions of the covariance function namely analytical or numerical comparison with the established and commonly used spectral representation method is made k l expansion has an edge over the spectral method for highly correlated processes for long stationary processes the spectral method is generally more efficient as the k l expansion method requires substantial computational effort to solve the integral equation the main advantage of the k l expansion method is that it can be easily generalized to simulate non stationary processes with little additional effort copyright 2001 john wiley sons ltd

a hybrid approach to analyse a beam soil structure under a moving random load abstract to study the stochastic response of a beam soil structure under a moving random load a hybrid approach based on the pseudo excitation method and the wavelet method is proposed using the pseudo excitation method the non stationary random vibration analysis is transformed into a conventional moving harmonic load problem analytical solutions of the power spectral density and standard deviation of vertical displacement are derived in an integral form however the integrand is singular and highly oscillatory and the computational time is an important consideration because a large number of frequency points must be computed to calculate the response accurately and efficiently a wavelet approach is introduced numerical results show that the frequency band which brings the most significant response is dependent on the load velocity the hybrid method provides a useful tool to estimate the ground vibration caused by traffic loads

non stationary random ground vibration due to loads moving along a railway track the pseudo excitation method pem and the precise integration algorithm are combined to compute the non stationary random ground vibration caused by loads moving along a railway track at constant speed the rails are modeled as a single infinite euler beam connected to sleepers and hence to ballast this ballast rests on the ground which is assumed to consist of layered transversely isotropic soil the equations of motion of the system are established in a cartesian coordinate system which moves with the loads the non stationary power spectral density and the time dependent standard deviation can be derived conveniently by means of pem while the precise integration algorithm for two point boundary value problems is applied to the solution of the equations of motion in the frequency wavenumber domain by virtue of the transverse isotropic property of the layered soils the threefold iteration process in the frequency wavenumber domain is reduced into a twofold iteration process hence the computational efficiency is improved considerably

general theory of small elastic deformations superposed on finite elastic deformations using tensor notations a general theory is developed for small elastic deformations of either a compressible or incompressible isotropic elastic body superposed on a known finite deformation without assuming special forms for the strain energy function the theory is specialized to the case when the finite deformation is pure homogeneous when two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials the potential functions are used to solve the problem of the infinitesimally small indentation by a spherical punch of the plane surface of a semi infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force free plane surface

polynomial chaos expansions for optimal control of nonlinear random oscillators the polynomial chaos decomposition of stochastic variables and processes is implemented in conjunction with optimal polynomial control of nonlinear dynamical systems the procedure is demonstrated on a base excited system whereby ground motion is modeled as a stochastic process with a specified correlation function and is approximated by its karhunen loeve expansion an adaptive scheme for stochastic approximation with polynomial chaos bases is proposed which is based on a displacement velocity norm and is applied to the identification of phase orbits of nonlinear oscillators this approximation is then integrated in the design of an optimal polynomial controller allowing for the efficient estimation of statistics and probability density functions of quantities of interest numerical investigations are carried out employing the polynomial chaos expansions and the lyapunov asymptotic stability condition based control policy the results reveal that the performance as gaged by probabilistic quantities of interest of the controlled oscillators is greatly improved a comparative study is also presented against the classical stochastic optimal control whereby statistical linearization based lqg is employed to design the optimal controller it is remarked that the proposed polynomial chaos expansion is a preferred approach to the optimal control of nonlinear random oscillators

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

nonlinear interaction between a moving vehicle and a plate elastically mounted on a tunnel abstract the paper presents a theoretical study of the interaction between a nonlinear model of a moving vehicle velocity v and a plate elastically mounted in a tunnel an efficient approach to the solution of the problem of vehicle slab track tunnel soil interaction is developed on the basis of a coupling of the finite element and integral transform methods fem and itm according to this approach the tunnel which may have an arbitrary shape and a portion of the surrounding soil is modelled by finite elements while the soil half space is described by the itm the corresponding solution is found using the solutions for the uniform half space and for the continuum with a cylindrical cavity to exploit the invariance of the structure in longitudinal direction x for this direction additionally to the time frequency transform t a space wavenumber transform x k x is used the case of a half space is analyzed using a fourier transform also in the second horizontal direction y k y and an analytical solution for the z direction on the basis of exponential functions in the case of the infinite continuum with the cavity a fourier series for the circumferential direction and a series of cylindrical functions for the radial direction are used for the solution regarding the cross sectional coordinates y z the tunnel structure that may have an arbitrary shape and a portion of the surrounding soil will be modelled by finite elements in a x k x t transformed domain in order to observe the boundary conditions at the surface of the half space as well as at the surface of the cavity the superposition of the two solutions has to be performed after an inverse fourier transform ift in the k x y z domain the solution for the complete system floating slab track tunnel half space is obtained in the k x y z domain once the system transfer function h with vk x for this complete coupled system is found the displacements of the plate can be calculated in time domain by the ift of the product p h i e the convolution of the loading p t with the impulse response function h t which completely represents the behavior of the coupled system in the context of the coupling of systems in a relative movement the problems of differential algebraic equations dae have to be observed

analysis of the critical velocity of a load moving on a beam supported by a finite depth foundation abstract a detailed analysis of the critical velocity of a uniformly moving load is carried out in this paper it is assumed that the load is traversing an infinite beam supported by a finite depth foundation under plane strain condition the problem is solved analytically in the fourier domain respecting two formulations of the interface condition the critical velocity is determined as the velocity under which the undamped beam deflection tends to infinity i e by identifying double poles in the fourier image of the beam deflection situated on the real fourier variable axis results obtained are compared with the previously published results of this author where simplifying assumptions were imposed on the shear contribution of the foundation based on the results an addition to the previous formula for critical velocity estimate is proposed it is confirmed that there are several critical velocities but the lowest one which is the dominating one smoothly changes from the classical value to the lowest wave velocity of propagation in the foundation according to the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass particular situations where the first double pole cannot be formed in this model are discussed in detail in such cases a significant increase of deflection is observed in the vicinity of the expected location defining thus a pseudo critical velocity attention is paid to the cases where there are two or more very close critical velocities which causes an increased risk for practical applications in addition several options of damping are compared

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

dimension reduction of karhunen loeve expansion for simulation of stochastic processes abstract conventional karhunen loeve expansions for simulation of stochastic processes often encounter the challenge of dealing with hundreds of random variables for breaking through the barrier a random function embedded karhunen loeve expansion method is proposed in this paper the updated scheme has a similar form to the conventional karhunen loeve expansion both involving a summation of a series of deterministic orthonormal basis and uncorrelated random variables while the difference from the updated scheme lies in the dimension reduction of karhunen loeve expansion through introducing random functions as a conditional constraint upon uncorrelated random variables the random function is expressed as a single elementary random variable orthogonal function in polynomial format non gaussian variables or trigonometric format non gaussian and gaussian variables for illustrative purposes the simulation of seismic ground motion is carried out using the updated scheme numerical investigations reveal that the karhunen loeve expansion with random functions could gain desirable simulation results in case of a moderate sample number except the hermite polynomials and the laguerre polynomials it has the sound applicability and efficiency in simulation of stochastic processes besides the updated scheme has the benefit of integrating with probability density evolution method readily for the stochastic analysis of nonlinear structures

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

surface ground vibration due to a moving train in a tunnel two dimensional model abstract vibration of a surface of a two dimensional 2d elastic layer generated by a point load moving uniformly along a beam which is located inside the layer is investigated theoretically it is supposed that the layer possesses a small viscosity is fixed along the bottom and has a traction free surface the beam is described by the euler bernoulli model and located parallel both to the surface and the bottom of the layer the surface vibration is analysed under three types of the load namely constant harmonically varying and a stationary random load for the deterministic loads the vector displacement of an observation point on the layer surface is analyzed along with the amplitude spectrum of vibration in this point for the random load main attention is paid to the variance of vibration at the observation point qualitative features of obtained results are discussed via kinematic analyses of the wave propagation in the structure

symplectic random vibration analysis of a vehicle moving on an infinitely long periodic track based on the pseudo excitation method pem symplectic mathematical scheme and schur decomposition the random responses of coupled vehicle track systems are analyzed the vehicle is modeled as a spring mass damper system and the track is regarded as an infinitely long substructural chain consisting of three layers i e the rails sleepers and ballast the vehicle and track are coupled via linear springs and the moving vehicle model is adopted the latter assumes that the vehicle moves along a static track for which the rail irregularity is further assumed to be a zero mean valued stationary gaussian random process the problem is then solved efficiently as follows initially pem is used to transform the rail random excitations into deterministic harmonic excitations the symplectic mathematical scheme is then applied to establish a low degree of freedom equation of motion with periodic coefficients in turn these are transformed into a linear equation set whose upper triangular coefficient matrix is established using the schur decomposition scheme finally the frequency dependent terms are separated from the load vector to avoid repeated computations for different frequencies associated with the pseudo excitations the proposed method is subsequently justified by comparison with a monte carlo simulation the fixed vehicle model and the moving vehicle model are compared and the influences of vehicle velocity and class of track on system responses are also discussed

the non stationary freefield response for a moving load with a random amplitude this paper presents a stochastic solution procedure for the calculation of the non stationary freefield response due to a moving load with a random amplitude in this case a non stationary autocorrelation function and a time dependent spectral density are required to characterize the response at a fixed point in the freefield the non stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude it is shown how the deterministic solution can be calculated in an efficient way by means of integral transformation methods if the problem geometry exhibits a translational invariance in the direction of the moving load a key ingredient is the transfer function between the source and the receiver that represents the fundamental response in the freefield due to an impulse load at a fixed location the solution in the case of a moving load with a random amplitude is formulated in terms of the double forward fourier transform of the non stationary autocorrelation function the solution procedure is illustrated with an example where the non stationary autocorrelation function and the time dependent standard deviation of the freefield response are computed for a moving harmonic load with a random phase shift the results are compared with the response in the deterministic case

accurate and highly efficient algorithms for structural stationary non stationary random responses abstract an accurate and highly efficient algorithm series for structural stationary non stationary random response analysis pseudo excitation method pem is presented the algorithm series which have been developed since early 1980s applies to the random vibration analyses of structures subjected to single multiple stationary non stationary random excitations including the very attractive issue the solution of the response to non uniformly modulated evolutionary random excitations each algorithm in this series is an accurate complete quadratic combination cqc method because the cross correlation quadratic terms between the participant modes and between the excitations have both been included such algorithms are easy to use because structural stationary random response analysis is reduced to the analysis of structural harmonic response while structural non stationary random responses can be readily computed in terms of any step by step integration scheme e g newmark scheme or the precise integration method

restricted information from nonadaptive queries to np we investigate classes of sets that can be decided by bounded truth table reductions to an np set in which evaluators donothave full access to the answers to the queries but get only restricted information such as the number of queries that are in the oracle set or even just this number modulom for somem 2 we also investigate the case in which evaluators are nondeterministic we show that when we vary the information that the evaluators get this can change the resulting power of the evaluators we locate all these classes within levels of the boolean hierarchy which allows us to compare the complexity of such classes