a quasistatic contact problem for an elastoplastic rod abstract we consider a mathematical model which describes the quasistatic contact of an elastoplastic rod with an obstacle it is based on the prandtl reuss flow law and unilateral conditions imposed on the velocity two weak formulations are presented and existence and uniqueness results established the proofs are based on approximate problems with viscous regularization which have merit on their own and may be used as the basis for convergent numerical algorithms for the problem

a magnetic resonance imaging based articulatory and acoustic study of retroflex and bunched american english r speakers of rhotic dialects of north american english show a range of different tongue configurations for r these variants produce acoustic profiles that are indistinguishable for the first three formants delattre p and freeman d c 1968 a dialect study of american english r s by x ray motion picture linguistics 44 28 69 westbury j r et al 1998 differences among speakers in lingual articulation for american english r speech commun 26 203 206 it is puzzling why this should be so given the very different vocal tract configurations involved in this paper two subjects whose productions of retroflex r and bunched r show similar patterns of f1 f3 but very different spacing between f4 and f5 are contrasted using finite element analysis and area functions based on magnetic resonance images of the vocal tract for sustained productions the results of computer vocal tract models are compared to actual speech recordings in particular formant cavity affiliations are explored using formant sensitivity functions and vocal tract simple tube models the difference in f4 f5 patterns between the subjects is confirmed for several additional subjects with retroflex and bunched vocal tract configurations the results suggest that the f4 f5 differences between the variants can be largely explained by differences in whether the long cavity behind the palatal constriction acts as a half or a quarter wavelength resonator

identification of synthetic vowels based on a time varying model of the vocal tract area function the purpose of this study was to conduct an identification experiment with synthetic vowels based on the same sets of speaker dependent area functions as in bunton and story 2009 j acoust soc am 125 19 22 but with additional time varying characteristics that are more representative of natural speech the results indicated that vowels synthesized using an area function model that allows for time variation of the vocal tract shape and includes natural vowel durations were more accurately identified for 7 of 11 english vowels than those based on static area functions

formant frequency estimation of high pitched vowels using weighted linear prediction all pole modeling is a widely used formant estimation method but its performance is known to deteriorate for high pitched voices in order to address this problem several all pole modeling methods robust to fundamental frequency have been proposed this study compares five such previously known methods and introduces a technique weighted linear prediction with attenuated main excitation wlp ame wlp ame utilizes temporally weighted linear prediction lp in which the square of the prediction error is multiplied by a given parametric weighting function the weighting downgrades the contribution of the main excitation of the vocal tract in optimizing the filter coefficients consequently the resulting all pole model is affected more by the characteristics of the vocal tract leading to less biased formant estimates by using synthetic vowels created with a physical modeling approach the results showed that wlp ame yields improved formant frequencies for high pitched sounds in comparison to the previously known methods e g relative error in the first formant of the vowel a decreased from 11 to 3 when conventional lp was replaced with wlp ame experiments conducted on natural vowels indicate that the formants detected by wlp ame changed in a more regular manner between repetitions of different pitch than those computed by conventional lp

time integration schemes for the finite element dynamic signorini problem a large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic signorini problem we classify the different discretizations into four groups the first three groups correspond to different ways of enforcing the contact condition exact enforcement enforcement with penalty and enforcement with contact condition in velocity the fourth approach is based on a modification of the mass matrix numerical simulations on two one dimensional benchmark problems with analytical solutions illustrate the properties of representative methods within each class focusing first on spurious oscillations triggered by contact and then on energy behavior after multiple impacts selected schemes are also tested on a two dimensional benchmark

on the computation of fourier transforms of singular functions abstract in this paper we consider a method for the computation of finite fourier transforms of functions having endpoint singularities of algebraic or logarithmic type this method may be considered as a modification of clenshaw curtis quadrature the nonoscillatory and nonsingular part of the integrand is replaced by a truncated chebyshev series approximation and the integral is then evaluated using recurrence relations the numerical stability of these recurrence relations is investigated

the abc of hyper recursions each member of the family of gauss hypergeometric functions fn 2f1 a e1n b e2n c e3n z where a b c and z do not depend on n and ej 0 1 not all ej equal to zero satisfies a second order linear difference equation of the form anfn 1 bnfn cnfn 1 0 because of symmetry relations and functional relations for the gauss functions the set of 26 cases for different ej values can be reduced to a set of 5 basic forms of difference equations in this paper the coefficients an bn and cn of these basic forms are given in addition domains in the complex z plane are given where a pair of minimal and dominant solutions of the difference equation have to be identified the determination of such a pair asks for a detailed study of the asymptotic properties of the gauss functions fn for large values of n and of other gauss functions outside this group this will be done in a later paper

projected event capturing time stepping schemes for nonsmooth mechanical systems with unilateral contact and coulomb s friction this work addresses the problem of the numerical time integration of nonsmooth mechanical systems subjected to unilateral contacts impacts and coulomb s friction the considered systems are the space discretized continuous systems obtained by using a finite element method fem approach or the multi body systems or a mix of them as in flexible multibody dynamics up to now two main numerical schemes are available for this purpose the moreau jean scheme which solves the constraints at the velocity level together with a newton impact law and the schatzman paoli scheme which directly considers the constraints at the position level in both schemes the position and velocity constraints are not both satisfied in discrete time a first attempt is made by directly using the gear gupta leimkuhler ggl approach for differential algebraic equations dae that solves in discrete time the constraints on both position and velocity levels the obtained direct projection scheme succeeds in solving in discrete time both position and velocity constraints but introduces some chattering at contact after a finite accumulation of impacts the proposed scheme improves the direct projected scheme by combining several steps of activation and projection to avoid the chattering effect the stability and the local order of the scheme will be discussed the usefulness of the scheme is demonstrated on several academic examples and is illustrated on an industrial application the modeling and simulation of an electrical circuit breaker

on the numerical approximation of a viscoelastodynamic problem with unilateral constraints abstract the present work is dedicated to the study of numerical schemes for a viscoelastic valve vibrating longitudinally and having its motion limited by rigid obstacles at both ends fully discretized and finite difference schemes are presented and their convergence is proved finally some numerical examples are reported and analyzed

identification of synthetic vowels based on selected vocal tract area functions the purpose of this study was to determine the degree to which synthetic vowel samples based on previously reported vocal tract area functions of eight speakers could be accurately identified by listeners vowels were synthesized with a wave reflection type of vocal tract model coupled to a voice source a particular vowel was generated by specifying an area function that had been derived from previous magnetic resonance imaging based measurements the vowel samples were presented to ten listeners in a forced choice paradigm in which they were asked to identify the vowel results indicated that the vowels i ae and u were identified most accurately for all of speakers the identification errors of the other vowels were typically due to confusions with adjacent vowels

convergence acceleration for the numerical solution of second order linear recurrence relations the concept of modification used for accelerating the convergence of ordinary continued fractions is adapted to the case of the gautschi aggarwal burgmeier algorithm for the computation of nondominant solutions of nonhomogeneous second order linear recurrence relations

technique for tuning vocal tract area functions based on acoustic sensitivity functions a technique for modifying vocal tract area functions is developed by using sum and difference combinations of acoustic sensitivity functions to perturb an initial vocal tract configuration first sensitivity functions e g fant and pauli proc speech comm sem 74 1975 are calculated for a given area function at its specific formant frequencies the sensitivity functions are then multiplied by scaling coefficients that are determined from the difference between a desired set of formant frequencies and those supported by the current area function the scaled sensitivity functions are then summed together to generate a perturbation of the area function this produces a new area function whose associated formant frequencies are closer to the desired values than the previous one this process is repeated iteratively until the coefficients are equal to zero or are below a threshold value

a comparison of vocal tract perturbation patterns based on statistical and acoustic considerations the purpose of this study was to investigate the relation between vocal tract deformation patterns obtained from statistical analyses of a set of area functions representative of a vowel repertoire and the acoustic properties of a neutral vocal tract shape acoustic sensitivity functions were calculated for a mean area function based on seven different speakers specific linear combinations of the sensitivity functions corresponding to the first two formant frequencies were shown to possess essentially the same amplitude variation along the vocal tract length as the statistically derived deformation patterns reported in previous studies

a weighted finite element mass redistribution method for dynamic contact problems abstract this paper deals with a one dimensional wave equation being subjected to a unilateral boundary condition an approximation of this problem combining the finite element and mass redistribution methods is proposed the mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes the convergence as well as an error estimate in time is proved the analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution however some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact to overcome this difficulty a new unconditionally stable and a very lightly dissipative scheme is proposed

a nonsmooth generalized α scheme for flexible multibody systems with unilateral constraints summary mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints inspired by the generalized time integration method for smooth flexible multibody dynamics this paper presents a nonsmooth generalized method which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions both the algorithm and the implementation are illustrated in detail numerical example tests are given in the scope of both rigid and flexible body models taking account for both linear and nonlinear systems and comprising both unilateral and bilateral constraints the extended nonsmooth generalized method is verified through comparison to the traditional moreau jean method and the fully implicit newmark method results show that the nonsmooth generalized method benefits from the accuracy and stability property of the classical generalized method with controllable numerical damping in particular when it comes to the analysis of flexible systems the nonsmooth generalized method shows much better accuracy property than the other two methods copyright 2013 john wiley sons ltd

resurrecting the asymptotics of linear recurrences abstract once on the forefront of mathematical research in america the asymptotics of the solutions of linear recurrence equations is now almost forgotten especially by the people who need it most namely combinatorists and computer scientists here we present this theory in a concise form and give a number of examples that should enable the practicing combinatorist and computer scientist to include this important technique in her or his asymptotics tool kit

a new algorithm for computing orthogonal polynomials the aim of this paper is to present an algorithm for computing orthogonal polynomials the fast fourier transform completes the connection given by draux between the three term recurrence relationship and the euclidian algorithm applications to hankel systems and numerical examples illustrate our purpose

two dimensional vocal tracts with three dimensional behavior in the numerical generation of vowels two dimensional 2d numerical simulations of vocal tract acoustics may provide a good balance between the high quality of three dimensional 3d finite element approaches and the low computational cost of one dimensional 1d techniques however 2d models are usually generated by considering the 2d vocal tract as a midsagittal cut of a 3d version i e using the same radius function wall impedance glottal flow and radiation losses as in 3d which leads to strong discrepancies in the resulting vocal tract transfer functions in this work a four step methodology is proposed to match the behavior of 2d simulations with that of 3d vocal tracts with circular cross sections first the 2d vocal tract profile becomes modified to tune the formant locations second the 2d wall impedance is adjusted to fit the formant bandwidths third the 2d glottal flow gets scaled to recover 3d pressure levels fourth and last the 2d radiation model is tuned to match the 3d model following an optimization process the procedure is tested for vowels a i and u and the obtained results are compared with those of a full 3d simulation a conventional 2d approach and a 1d chain matrix model

numerical simulation of the dynamics of an impacting bar we calculate numerically the motion of a slender bar dropped on a rigid foundation for the computation the bar is discretized by a system of rigid bodies linked by spiral springs or by a pair of linear springs we assume that the impact is frictionless and we model it by newton s law we compute the motion by using either an event driven method based on the detection of impacts or a time stepping scheme avoiding the detection of impacts we calculate also the apparent restitution coefficient and we compare our results with the experimental and numerical results of stoianovici and hurmuzlu

conservative discretization of contact impact problems for nearly rigid bodies abstract a discretization scheme for contact impact problems related to modeling of gears is proposed the problem is first discretized in time and then a variational formulation for the resulted one step problem is developed a finite element discretization completes the discretization process the scheme is a reinterpretation of the general simo laursen chavla algorithm in the context of the rigid body motion superimposed with small elastic deformation it conserves precisely the linear momentum and total energy and approximately the angular momentum the discretization method is illustrated with two numerical examples the standard 1d impact problem for an elastic rod and a 2d model problem of an elastic wheel bouncing within a constraining box

improving a method for computing non dominant solutions of certain second order recurrence relations of poincare type in this paper we present a method of convergence acceleration for the calculation of non dominant solutions of second order linear recurrence relations for which the coefficients satisfy certain asymptotic conditions it represents an improvement of the method recently proposed by jacobsen and waadeland 3 4 for limit periodic continued fractions for continued fractions the method corresponds to a repeated application of the bauer muir transformation some examples and a generalization to non homogeneous recurrence relations are given

a wave problem in a half space with a unilateral constraint at the boundary in this paper we study the following problem let omega be a half space of mathbb r n defined by omega x x x n in mathbb r x n where x x ldots x n 1 is the usual notation and let there be given functions u 0 in h 1 omega and u 1 in l 2 omega we assume that u 0 x n 0 is nonnegative and similarly partial u 0 partial x n x n 0 which is a priori an element of h 1 2 mathbb r n 1 is nonnegative

an algorithm for nondominant solutions of linear second order inhomogeneous difference equations an algorithm is given for computing a weighted sum of a nondominant solution of a linear second order inhomogeneous difference equation to a prescribed accuracy by estimating the truncation error the present method is an extension of both the stable numerical method due to olver and sookne and a summation technique due to deuflhard for computing minimal solutions of a homogeneous difference equation the method is illustrated by numerical examples

numerical approximation of a wave equation with unilateral constraints the system u tt u xx ni f x in 0 l times 0 t with initial data u x 0 u 0 x u t x 0 u 1 x almost everywhere on 0 l and boundary conditions u 0 t 0 for all t geq 0 and the unilateral condition u x l t geq 0 u l t geq k 0 u l t k 0 u x l t 0 models the longitudinal vibrations of a rod whose motion is limited by a rigid obstacle at one end a new variational formulation is given existence and uniqueness are proved finite elements and finite difference schemes are given and their convergence is proved numerical experiments are reported the characteristic schemes perform better in terms of accuracy and the subcharacteristic schemes look better