cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

the analysis of rates using poisson regression models models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters estimates of the parameters can be obtained by means of iteratively reweighted least squares irls when the events of interest follow the poisson distribution the irls algorithm is equivalent to using the method of scoring to obtain maximum likelihood ml estimates the general poisson regression models include log linear quasilinear and intrinsically nonlinear models the approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model standard statistical packages that support irls can then be used to obtain ml estimates their asymptotic covariance matrix and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space applications of these methods to epidemiologic follow up studies with the data organized into a life table type of format are discussed the method is illustrated by using a nonlinear model derived from the multistage theory of carcinogenesis to analyze lung cancer death rates among british physicians who were regular cigarette smokers

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

finding numerical derivatives for unstructured and noisy data by multiscale kernels the recently developed multiscale kernel of r opfer adv comput math 25 2006 pp 357 380 is applied to approximate numerical derivatives the proposed method is truly mesh free and can handle unstructured data with noise in any dimension the method of tikhonov and the method of l curve are employed for regularization no information about the noise level is required an error analysis is provided in a general setting for all dimensions numerical comparisons are given in two dimensions which show competitive results with recently published thin plate spline methods

moving least squares via orthogonal polynomials a method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points this yields a robust and efficient method which can avoid singularities and breakdowns in the moving least squares method caused by particular configurations of nodes in the system the method is tested by applying it to the estimation of first and second derivatives of test functions on random point distributions in two and three dimensions and by examining in detail the evaluation of second derivatives on one selected configuration the accuracy and convergence of the method are examined with respect to length scale point separation and the number of points used the method is found to be robust accurate and convergent

generalized linear models with random effects salamander mating revisited in recent years much effort has been devoted to extending regression methodology to non gaussian data where responses are not independent these methods for dependent responses are suitable for data from longitudinal studies or nested designs however use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution in this paper we cast the problem in a bayesian framework and use a monte carlo method the gibbs sampler to avoid current computational limitations the flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall

a bayesian space varying parameter model applied to estimating fertility schedules we propose a spatial generalized linear model glm to analyse the vital rates for small areas in each small area we have a response vector and covariates to explain its variability the statistical methodology is based on a spatial bayesian approach and it allows the covariates parameters of the generalized linear model to vary smoothly on space hence the effect of a covariate on the response varies depending on the random variables measurement location our model is an extension of disease mapping models allowing the space covariate interaction to be modelled in a natural way and giving space a position of intrinsic interest we introduce the model in the context of fertility curve estimation in each small area we have a curve describing the variation of fertility rates by age modelled by coale s fertility model which implies a glm in each area a simulation shows the advantages of our approach in addition the paper applies the procedure to census data used to study the diffusion of low fertility behaviour in brazil

the approximation power of moving least squares a general method for near best approximations to functionals on r d using scattered data information is discussed the method is actually the moving least squares method presented by the backus gilbert approach it is shown that the method works very well for interpolation smoothing and derivatives approximations for the interpolation problem this approach gives mclain s method the method is near best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation the interpolation approximation in r d is shown to be a c function and an approximation order result is proven for quasi uniform sets of data points

alternative models for the heterogeneity of mortality risks among the aged abstract to develop a model to estimate the degree of unobserved heterogeneity in morality risks in a population it is necessary to specify two types of functions one describing the age specific rate of increase of mortality risks for individuals and the other describing the distribution of mortality risks across individuals there has been considerable interest in the question of how sensitive the estimates of heterogeneity are to the choices of these functions to explore this question high quality data were obtained from published medicare mortality rates for the period 1968 1978 for analysis of total mortality among the aged in addition national vital statistics data for the period 1950 1977 were used to analyze adult lung cancer mortality for these data the estimates of structural parameters were less sensitive to reasonable choices of the heterogeneity distribution gamma vs inverse gaussian than to reasonable choices of the hazard rate function gompertz vs weibull

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

on derivative estimation and the solution of least squares problems surface interpolation finds application in many aspects of science and technology two specific areas of interest are surface reconstruction techniques for plant architecture and approximating cell face fluxes in the finite volume discretisation strategy for solving partial differential equations numerically an important requirement of both applications is accurate local gradient estimation in surface reconstruction this gradient information is used to increase the accuracy of the local interpolant while in the finite volume framework accurate gradient information is essential to ensure second order spatial accuracy of the discretisation in this work two different least squares strategies for approximating these local gradients are investigated and the errors associated with each analysed it is shown that although the two strategies appear different they produce the same least squares error some carefully chosen case studies are used to elucidate this finding

estimating average annual per cent change in trend analysis trends in incidence or mortality rates over a specified time interval are usually described by the conventional annual per cent change capc under the assumption of a constant rate of change when this assumption does not hold over the entire time interval the trend may be characterized using the annual per cent changes from segmented analysis sapcs this approach assumes that the change in rates is constant over each time partition defined by the transition points but varies among different time partitions different groups e g racial subgroups however may have different transition points and thus different time partitions over which they have constant rates of change making comparison of sapcs problematic across groups over a common time interval of interest e g the past 10 years we propose a new measure the average annual per cent change aapc which uses sapcs to summarize and compare trends for a specific time period the advantage of the proposed aapc is that it takes into account the trend transitions whereas capc does not and can lead to erroneous conclusions in addition when the trend is constant over the entire time interval of interest the aapc has the advantage of reducing to both capc and sapc moreover because the estimated aapc is based on the segmented analysis over the entire data series any selected subinterval within a single time partition will yield the same aapc estimate that is it will be equal to the estimated sapc for that time partition the capc however is re estimated using data only from that selected subinterval thus its estimate may be sensitive to the subinterval selected the aapc estimation has been incorporated into the segmented regression free software joinpoint which is used by many registries throughout the world for characterizing trends in cancer rates copyright 2009 john wiley sons ltd

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

analyzing multiple cross sectional samples with application to hospitalization time after surgeries repeated cross sectional sampling results in multiple biased samples with possibly different weight functions the standard non parametric maximum likelihood estimator for the lifetime distribution of interest solves a set of nonlinear equations and its variance has a very complicated form we suggest a simple closed form estimator for the case where entrances to the population of interest follow a poisson model the variance of the estimator and confidence intervals are easily calculated our motivating example concerns a series of cross sectional surveys conducted in israeli hospitals we discuss the bias mechanism in our data and suggest a simple design plan that provides valid estimators even when the weight functions are unknown the new method is applied to estimate the distribution of hospitalization time after bowel and hernia surgeries copyright 2015 john wiley sons ltd

testing goodness of fit for the poisson assumption when observations are not identically distributed abstract tests for detecting negative binomial departures from a poisson model are studied for the one way layout and regression through the origin cases approximations to the null and alternative distributions of these test statistics are presented locally optimal tests and tests suggested in the literature are compared in terms of asymptotic relative efficiency small sample comparisons are included

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

a statistical distribution with an unbounded hazard function and its application to a theory from demography we introduce a statistical distribution with hazard function mu t proportional to psi t beta 1 for 0 less than or equal to t less than psi and shape parameter beta satisfying 0 less than beta less than 1 this hazard function is suggested by a theory of aging in demography we discuss properties of this distribution and maximum likelihood estimates of its parameters mixture distributions are considered to account for pooling across dissimilar populations this model is compared with the gompertz and generalized pareto distributions and used to estimate a finite limit on human lifespan based on the survival of a group of female centenarians

empirical evaluation of statistical models for counts or rates we consider methods for selecting the joint specification of the mean and variance functions in statistical models for rates or counts based on analyses of diagnosis specific hospital discharge rates in michigan we show that a poisson model with an extra variance component for the systematic variation is superior to several other probability models with regard to specification of the error structure further the deviance residual appears superior to the pearson residual the proper specification of such variation is crucial for many types of analyses such as identification of outliers and regression analyses designed to explain the systematic component of the variation

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

multistate analysis from cross sectional and auxiliary samples this is the peer reviewed version of the following article leilei zeng richard j cook and jooyoung lee multistate analysis from cross sectional and auxiliary samples statistics in medicine 2019 39 4 387 408 which has been published in final form at https doi org 10 1002 sim 8411

improved approximate methods for calculating frequency response function matrix and response of mdof systems with viscoelastic hereditary terms as we know it is difficult and unnecessary to obtain all the eigenpairs of a large scaled viscoelastic nonviscous or hysteretic damping systems which means that the mode truncation scheme is generally used and the mode truncated error is therefore introduced this study is aimed at eliminating the influence of the unavailable modes on the dynamic response of mdof systems with viscoelastic hereditary terms the energy dissipation terms of the system depend on the past history of motion via convolution integrals over some kernel functions therefore the system is a nonviscously damped system which has been considered as the most generalized damping model within the scope of a linear mechanical analysis to approximate frequency response function frf matrix and response without using the unavailable modes we suggest two methods which attempt to approximate the influence of the unavailable modes in terms of the lower modes and system matrices by using the first one or two terms of neumann expansion of the contribution of the unavailable modes in contrast with the frf matrix approximated in terms of the first two terms of neumann expansion these procedures cannot be extended to further high order terms since all of them will be affected by the frequency dependent variation of damping matrix from previous terms finally an example is shown that the two presented methods can make the mode truncated error reduce and may be used to approximate the influence of nonviscous modes contributed to frf matrix due to the fact that the nonviscous modes are difficult to be obtained accurately even if a small scaled model is used for some eigensolution methods

the natural variability of vital rates and associated statistics the first concern of this work is the development of approximations to the distributions of crude mortality rates age specific mortality rates age standardized rates standardized mortality ratios and the like for the case of a closed population or period study it is found that assuming poisson birthtimes and independent lifetimes implies that the number of deaths and the corresponding midyear population have a bivariate poisson distribution it is suggested that situations in which explanatory variables are present may be modelled via a doubly stochastic poisson distribution for the number of deaths with mean proportional to the population size and an exponential function of a linear combination of the explanatories such a model is fit to mortality data for canadian females classified by age and year a dynamic variant of the model is further fit to the time series of total female deaths alone by year the models with extra poisson variation are found to lead to substantially improved fits excerpt

a variance components approach to categorical data models with heterogeneous cell populations analysis of spatial gradients in lung cancer mortality rates in north carolina counties a mixed categorical continuous variable model is proposed for the analysis of mortality rates this model differs from other available models such as weighted least squares and loglinear models in that the within cell populations are assumed to be heterogeneous in their levels of mortality risk heterogeneity implies that in addition to the sampling variance considered in other available models there will be a second component of variance due solely to within cell heterogeneity maximum likelihood procedures are presented for the estimation of the model parameters these procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function this assumption is shown to be equivalent to assuming a mixture of poisson processes with the differential risk levels among individuals within each cell being governed by a two parameter gamma distribution the model is applied to data on lung cancer mortality for 1970 1975 for the 100 counties of north carolina the analysis shows that though a gradient in lung cancer mortality rates exist in space the gradient is restricted to specific demographic categories identified by race age and sex

eliminating the modal truncation problem encountered in frequency responses of viscoelastic systems increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping the need to consider the modal truncation problem of viscoelastic systems is more than ever before the higher modes may be unnecessary to obtain in dynamic analysis for engineering applications for viscoelastic systems the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small scaled problem is considered for some eigensolution methods this study aims at eliminating the influence of the higher modes on the frequency responses of viscoelastically damped systems a method is presented by making the equilibrium equations of motion into a subspace equation spanned in terms of the columns of a projection basis obtained by considering the use of the contribution of the lower modes and the first two terms of the neumann expansion of the contribution of the unavailable modes finally three example studies are provided to illustrate the effectiveness of the derived results it is shown that the proposed method can reduce the modal truncation error significantly

new improved series expansion for solving the moving oscillator problem a new method able to evaluate the dynamic stress response of an elastic beam subject to moving oscillators is presented the proposed procedure improves the convergence and accuracy of the conventional eigenfunction series expansion of beam response taking into account the gravitational inertial and damping effects due to the moving oscillators the improvement of the conventional solution is obtained by means of an extension to continuous systems of the dynamic correction method originally proposed for discretized structures the proposed method is able to account for the truncated higher order eigenfunctions by adding a pseudo static term to the conventional series expansion numerical results are presented to demonstrate the capability of the method to accurately determine the discontinuity and jump in bending moment and shear force distributions respectively

multiplicative models and cohort analysis abstract three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age calendar year specific death rates the first method which assumes that the baseline rates are known from national vital statistics is a multiple regression analysis of the standardized mortality ratio the second method is a variant of cox s proportional hazards analysis in which the baseline rates are treated as unknown nuisance parameters the third method consists of case control sampling from the risk sets formed in the course of applying cox s model it requires substantially less computation than do the other two in illustrative analysis of respiratory cancer deaths among a cohort of smelter workers all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure the discussion centers on the tradeoff between efficiency and bias in the selection of a particular method of analysis and on practica

a comparison of frailty models for multivariate survival data this paper reviews some of the main approaches to the analysis of multivariate censored survival data such data typically have correlated failure times the correlation can be a consequence of the observational design for example with clustered sampling and matching or it can be a focus of interest as in genetic studies longitudinal studies of recurrent events and other studies involving multiple measurements we assume that the correlation between the failure or survival times can be accounted for by fixed or random frailty effects we then compare the performance of conditional and mixture likelihood approaches to estimating models with these frailty effects in censored bivariate survival data we find that the mixture methods are surprisingly robust to misspecification of the frailty distribution the paper also contains an illustrative example on the times to onset of chest pain brought on by three endurance exercise tests during a drug treatment trial of heart patients

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

estimating average annual percent change for disease rates without assuming constant change the annual percent change apc is often used to measure trends in disease and mortality rates and a common estimator of this parameter uses a linear model on the log of the age standardized rates under the assumption of linearity on the log scale which is equivalent to a constant change assumption apc can be equivalently defined in three ways as transformations of either 1 the slope of the line that runs through the log of each rate 2 the ratio of the last rate to the first rate in the series or 3 the geometric mean of the proportional changes in the rates over the series when the constant change assumption fails then the first definition cannot be applied as is while the second and third definitions unambiguously define the same parameter regardless of whether the assumption holds we call this parameter the percent change annualized pca and propose two new estimators of it the first the two point estimator uses only the first and last rates assuming nothing about the rates in between this estimator requires fewer assumptions and is asymptotically unbiased as the size of the population gets large but has more variability since it uses no information from the middle rates the second estimator is an adaptive one and equals the linear model estimator with a high probability when the rates are not significantly different from linear on the log scale but includes fewer points if there are significant departures from that linearity for the two point estimator we can use confidence intervals previously developed for ratios of directly standardized rates for the adaptive estimator we show through simulation that the bootstrap confidence intervals give appropriate coverage

a correction method for the analysis of continuous linear one dimensional systems under moving loads a new correction procedure for dynamic analysis of linear proportionally damped continuous systems under traveling concentrated loads is proposed both cases of non parametric moving forces and parametric moving mass loads are considered improvement in the evaluation of the dynamic response is obtained by separating the contribution of the low frequency lf modes from that of the high frequency hf modes the former is calculated as usual by classical modal analysis while the latter is taken into account using a new series expansion of the corresponding particular solution the advantage of the suggested method is immediately shown in the calculation of the stress distribution since it is able to capture the stress discontinuities due to the nature of the applied loads themselves numerical results are presented to discuss the convergence of the proposed series and to show the accuracy of the calculated response compared to the classical series expansion solution

revisiting the moving force problem abstract the problem of the vibration of a beam subject to a travelling force is considered the purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force it is shown that for given boundary conditions there exists a unique response velocity dependence function a technique to determine this function is suggested which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode to illustrate this the maximum response function is calculated analytically for a simply supported ss beam and constructed numerically for a clamped clamped beam the effect of the higher modes on the maximum response is investigated and the relative error of the one mode approximation for a ss beam is constructed the estimates obtained substantiate the assumption about adequacy of the one mode approximation in a wide range of velocities in particular the relative error in the neighborhood of the velocity that results in the largest response is less than one percent

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

calculating expected mortality the widely used person years method of calculating expected mortality has been discussed recently by several authors in studies where mortality is either lower or higher than the standard mortality of some reference population the use of exposure to death as an estimator of the expected number of deaths will generally lead to bias always exaggerating the difference between study and standard mortality this bias is examined in a proportional hazards model the recent suggestion by hartz et al of calculating the mortalities of individuals during their potential follow up time is claimed to be only rarely feasible in practice excerpt

approaches to fitting age period cohort models with unequal intervals age period cohort models have provided useful insights into the analysis of time trends for disease rates in spite of the well known identifiability problem unique parameter estimates that avoid arbitrary constraints are provided by estimable functions of the parameter estimates for data that are generated using equal interval widths for age and period the identifiability issue may be expressed in terms of the age period and cohort slopes however when the interval widths are not the same for age and period additional identifiability problems arise these may be represented in terms of macro trends which have the identical identifiability problem seen in the equal interval case and micro trends which are the source of the additional problems a framework for testing estimability is presented and a variety of potentially interesting functions of the parameters considered unlike the equal interval case drift is not estimable for unequal intervals but local drift may be in addition the available functions for forecasting are much more restrictive in the latter case this estimability problem induces cyclical patterns in the estimates of trend as is demonstrated using data on leukaemia in connecticut males but this can be avoided through the use of smoothing splines these methods of are illustrated for three year period and five year age intervals using data on lung cancer mortality in californian women

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

an approximate bivariate bayesian method for analyzing small frequencies an approximate bayesian method is developed to study the joint mortality rates of two cancer sites over several geographic areas a conditionally independent two stage hierarchical model is used to model the sources of variability in these data at the first stage conditional on area specific parameters the within area variation in the joint frequencies of death from two sites is modeled by a bivariate poisson distribution with means proportional to the populations at risk at the second stage conditional on parameters for the prior the between area variation in the joint logits of true mortality rates is modeled by a bivariate normal distribution the prior distribution in estimating area mortality rates of one site it is shown that the simultaneous use of data on both sites is superior to that based on a single site only the relation between two sites is studied using the correlation between the logits of true mortality rates a monte carlo simulation is conducted to investigate the performance of this method as a function of the prior correlation the method is applied to two data sets

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

a new family of mode superposition methods for response calculations abstract a new family of mode superposition methods for the computation of the forced response of proportionally damped systems with and without rigid body modes is investigated the method may be considered to be an extension of the mode acceleration method it allows response calculations to be done with a very small subset of the modes of the system numerical examples are given for systems of order 20 and 40 execution times and number of modes required for convergence are recorded the particular order of the method among the family which takes the shortest time is determined for the example systems time savings with the new method are realized compared to the existing mode displacement and mode acceleration methods the method is expected to be particularly suitable for large systems

dynamic response of a beam with a crack subject to a moving mass abstract an iterative modal analysis approach is developed to determine the effect of transverse cracks on the dynamic behavior of simply supported undamped bernoulli euler beams subject to a moving mass the presence of crack results in higher deflections and alters the beam response patterns in particular the largest deflection in the beam for a given speed takes longer to build up and a discontinuity appears in the slope of the beam deflected shape at the crack location crack effects become more noticeable as crack depth increases the effect of the inertia force due to the moving mass is in general qualitatively similar and additive to the effect of the crack the exact effect of crack and mass depends on the speed time crack size crack location and the moving mass level other approximate methods namely a stationary mass model and a single iteration technique are also evaluated the stationary mass approach is useful for light moving masses