a local level set method for paraxial geometrical optics we propose a local level set method for constructing the geometrical optics term in the paraxial formulation for the high frequency asymptotics of two dimensional 2 d acoustic wave equations the geometrical optics term consists of two multivalued functions a travel time function satisfying the eikonal equation locally and an amplitude function solving a transport equation locally the multivalued travel times are obtained by solving a level set equation and a travel time equation with a forcing term the multivalued amplitudes are computed by a neweulerian formula based on the gradients of travel times and takeoff angles as a byproduct the method is also able to capture the caustic locations the proposed eulerian method has complexity of o n 2 rm log n rather than o n 4 as typically seen in the lagrangian ray tracing method several examples including the well known marmousi synthetic model illustrate the accuracy and efficiency of the eulerian method

reflection of an acoustic line source by an impedance surface with uniform flow abstract an exact analytic solution is derived for the 2d acoustic pressure field generated by a time harmonic line mass source located above an impedance surface with uniform grazing flow closed form asymptotic solutions in the far field are also provided the analysis is valid for both locally reacting and nonlocally reacting impedances as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface the analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface the line source is found to excite surface waves on the impedance surface some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow the surface waves may be treated either correctly as unstable waves or artificially as stable waves enabling comparison with previous numerical or mathematical studies which make either of these assumptions the computer code for evaluating the analytic solution and far field asymptotics is provided in the supplementary material it is hoped this work will provide a useful benchmark solution for validating 2d numerical acoustic codes

feedback linearization and stabilization of second order non holonomic chained systems this paper presents a theoretical framework for non regular feedback linearization and stabilization of second order non holonomic chained systems by giving a new criterion for the problem of non smooth non regular feedback linearization it is proved that second order chained systems are non regular static state feedback linearizable a discontinuous control law is obtained based on linear system theory and the inversion technique the design mechanism is generalized to higher order non holonomic chained systems simulation studies are carried out to show the effectiveness of the approach

acoustic propagation over an impedance plane a new solution is obtained for the acoustic pressure field generated by a point source and scattered by a locally reacting impedance covered plane the new solution is obtained in the form of an asymptotic series which has been shown to agree well with other studies one of the most important features of this solution is that higher order terms can be calculated from preceding terms in the series by the use of recursion formulas comparing data predicted from this solution with that from a numerical integration of the exact expression shows the asymptotic series to be extremely accurate even for relatively low values of the parameter kr not surprisingly the plane wave solution often shows major deviations from the exact integral solution

ground effect over hard rough surfaces laboratory and outdoor measurements are reported of the relative sound pressure level spectrum over hard surfaces containing either random or periodically spaced arrays of 2 d roughnesses the resulting data have been compared with predictions obtained analytically and with numerical predictions of a boundary element code effective impedances of the rough surfaces have been calculated from the boss theory developed by twersky a classical asymptotic approximation for propagation near grazing incidence from a point source over an impedance boundary has been modified heuristically to allow for diffraction grating effects the resulting predictions are found to be in tolerable agreement with the data except for close and random packing the boundary element code is found to give superior results for larger roughnesses but computational restrictions on element size reduce its usefulness for roughnesses with small width or height

asymptotic evaluation of integrals related to time dependent fields near caustics integrals which arise in the theory of time dependent wave fields near caustics in nondispersive problems are much simpler than their time harmonic counterparts because they involve delta functions rather than exponentials fields near smooth caustics for instance involve solutions of cubic equations which can be expressed in elementary terms instead of the airy functions of the better known time harmonic theory the pearcey functions which arise in the theory of the cusped caustic are similarly replaced by expressions involving solutions of quartic equations etc as is well known each type of caustic is related to a particular type of catastrophe the theory presented here deals conveniently with fields reducible to single integrals since the delta function and the integral will annihilate each other leaving closed form expressions fields involving multiple integrals will be reduced somewhat in complexity but not in general to closed form and are not treated here

sound propagation above an impedance boundary an asymptotic solution of the scalar wave field due to a point source above a locally reacting plane surface is obtained by a modified saddle point method numerical calculation indicates that the relatively simple solution is more accurate than the thomasson asymptotic solution and the chien soroka solution furthermore it is shown that another solution simplified still more is also in good agreement with the exact solution

a hybrid bie ffp scheme for predicting barrier efficiency outdoors to assess the acoustical performance of noise screens in the presence of an arbitrary sound speed profile a numerical scheme based on a combination of the boundary integral and fast field program methods is developed the green s function required in the boundary integral is evaluated by a fast field formulation the procedure is validated by comparing its predictions with other numerical results for simple cases and with measurements for indoor model experiments simulating downward refracting conditions it is predicted that the performance of a noise screen placed 50 m from the source is reduced considerably by moderate downwind conditions

sound propagation above an inhomogeneous plane boundary integral equation methods abstract a boundary integral equation method is used to compute the sound pressure emitted by a harmonic source above an inhomogeneous plane first the theoretical aspects of the problem behaviour of the pressure around the discontinuities are studied then a comparison between theoretical levels and experimental levels obtained in an anechoic room is presented it shows that the boundary integral equation bie method is quite convenient for solving this kind of problem two interesting results are pointed out i if only a prediction of maximum sound levels is needed the attenuation is the same for a cylindrical source a spherical source and n spherical sources and so it is possible to transform some three dimensional problems into two dimensional ones ii a numerical method of computation of the sound field above an inhomogeneous plane does not provide a correct prediction if each part of the plane is not accurately described by the boundary condition chosen

a boundary element method for propagation over absorbing boundaries abstract two dimensional sound propagation over an arbitrarily shaped barrier situated on a locally reacting infinite plane in a homogeneous medium is treated using the boundary element method bem the boundary integral equation bie is formulated in terms of a half space green s function which is constructed to satisfy the impedance boundary condition on the ground plane the integral in the resulting green s function is transformed using the steepest descent method to a suitable form for effective numerical evaluation even for a relatively small distance between the image source and the receiving point comparison of the bem results with an available analytic solution and experimental results by kearns and by habault shows good agreement to the sound field using the bem

a fast two grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half plane we consider the numerical treatment of second kind integral equations on the real line of the form phi s psi s int infty infty k s t z t phi t dt s in mathbb r abbreviated k z in which l 1 z l and bc the space of bounded continuous functions on are assumed known and bc is to be determined we first derive sharp error estimates for the finite section approximation reducing the range of integration to a a via bounds on i k z 1 as an operator on spaces of weighted continuous functions numerical solution by a simple discrete collocation method on a uniform grid on is then analysed in the case whenz is compactly supported this leads to a coefficient matrix which allows a rapid matrix vector multiply via the fft to utilise this possibility we propose a modified two grid iteration a feature of which is that the coarse grid matrix is approximated by a banded matrix and analyse convergence and computational cost in cases wherez is not compactly supported a combined finite section and two grid algorithm can be applied and we extend the analysis to this case as an application we consider acoustic scattering in the half plane with a robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied our final result is that ifz related to the boundary impedance in the application takes values in an appropriate compact subsetq of the complex plane then the difference between s and its finite section approximation computed numerically using the iterative scheme proposed is c 1 khlog 1 kh 1 1 2 ka 1 2 in the interval a a 1 forkh sufficiently small wherek is the wavenumber andh the grid spacing moreover this numerical approximation can be computed in c 2 n logn operations wheren 2a h is the number of degrees of freedom the values of the constantsc 1 andc 2 depend only on the setq and not on the wavenumberk or the support ofz

sound radiation from ducts theory and experiment abstract the paper deals with a method of prediction of noise radiated from finite length ducts with arbitrary shape the computation of the internal and external acoustic field is based upon a new variational formulation by integral equations numerical results of far and near field radiation patterns are compared with experimental data for various higher order mode source conditions

extended sources radiation and laplace type integral representation application to wave propagation above and within layered media abstract in has been shown that the sound field reflected by the plane boundary of a layered ground can always be described by a specularly reflected wave and layer potentials despite its generality this representation is not quite suitable for numerical computation dealing with a very simple case weyl and later on ingard and thomasson proposed a representation of the solution in which the layer potential terms are replaced by the sum of surface wave and a laplace type integral such an integral is very convenient for numerical purposes in this paper it is shown that this kind of representation can be obtained for a very wide class of sound propagation problems above or within layered media a half space bounded by a locally reacting surface a finite layer of porous medium a porous medium with depth varying porosity a thin elastic plate wave propagation in shallow water with an impedance bottom many other applications could be developed

sound propagation above an inhomogeneous impedance plane abstract boundary integral equation bie methods are described for the prediction of sound propagation in particular from a line source over a flat plane of inhomogeneous impedance approximate methods which satisfy reciprocity for the calculation of the wave field over a two impedance plane are proposed these approximations applied to propagation from a line source give results agreeing well with those of the bie method when they are applied to propagation from a point source agreement with experiment is shown

sliding mode control of underactuated multibody systems and its application to shape change control in this article we introduce an approach based on sliding mode control to design full state feedback controllers for stabilisation of underactuated non linear multibody systems we define first order sliding surfaces as a linear combination of actuated and unactuated coordinate tracking errors lyapunov stability analysis guarantees that all system trajectories reach and remain on the sliding surfaces however stability of the sliding surfaces depends on the equilibrium manifold if the system has isolated equilibrium points it is linearly controllable and asymptotic stability can be guaranteed under certain conditions otherwise the control system fails brockett s necessary condition for existence of a smooth stabilising feedback in the latter case if the total momentum is conserved the closed loop control system will be marginally stable consequently a procedure is proposed to achieve an asymptotically stable discontinuous control law through sliding surface redefinition and shape changes it i

closed form solutions for the acoustical impulse response over a masslike or an absorbing plane the transient sound field caused by a dirac delta impulse function above an infinite locally reacting plane can be calculated by applying the inverse fourier transform of the corresponding half space green s function in frequency domain as a starting point the representation given by ochmann j acoust soc am 116 6 3304 3311 2004 is used which consists of discrete and continuous superposition of point sources for a locally reacting plane with masslike character and also with pure absorbing behavior it is possible to express the resulting impulse response in closed form such a result is surprising because corresponding formulations in the frequency domain are not available yet hence the first main result is the closed form solution eq 22 for an impulse response over an infinite plane with a pure imaginary impedance the second main result is the closed form solution eq 53 for an impulse response over an infinite plane with a pure real impedance as a particular application of both ma

variational formulation using integral equations to solve sound scattering above an absorbing plane the boundary element method is used to model two dimensional acoustic radiation and scattering from a body of arbitrary shape above an infinite plane of flat surface and homogeneous impedance the particularity of the study is the use of an indirect integral representation of the solution given in terms of the jumps of pressure and its normal derivative through the boundaries a variational formulation is associated with the boundary indirect integral equations modeling our problem the major difficulty in the formulation is the infinite feature of the plane which is avoided by introducing an appropriate green s function numerical results of the attenuation of sound by noise barriers are presented they show good agreement with other results in the literature

prediction of the attenuation of road traffic noise with distance abstract a method is described of calculating the sound pressure level received from single representative light and heavy vehicles after propagation over terrain composed of various combinations of hard ground and grass land these results are then used to derive correction contours for the attenuation with distance of the leq level received from streams of each class of vehicle the results apply to conditions where the boundary between the soft and hard areas is parallel to the traffic stream and the soft ground is on the receiver side various positions of the boundary are considered a simple prediction method for leq is developed incorporating the distance corrections similar calculations are carried out for the attenuation with distance of the l10 noise index for a representative stream of vehicles based on these results simple prediction equations for the excess attenuation are proposed in terms of the receiver position and the proportion of soft ground below the propagation path

on weight prioritized multitask control of humanoid robots we propose a formal analysis with some theoretical properties of weight prioritized multitask inverse dynamics like control of humanoid robots being a case of redundant manipulators with a nonactuated free floating base and multiple unilateral frictional contacts with the environment the controller builds on a weighted sum scalarization of a multiobjective optimization problem under equality and inequality constraints which appears as a straightforward solution to account for state and control input viability constraint characteristic of humanoid robots that were usually absent from early existing pseudoinverse and null space projection based prioritized multitask approaches we argue that our formulation is indeed well founded and justified from a theoretical standpoint and we propose an analysis of some stability properties of the approach lyapunov stability is demonstrated for the closed loop dynamical system that we analytically derive in the unconstrained multiobjective optimization case stability in terms of solution existence uniqueness continuity and robustness to perturbations is then formally demonstrated for the constrained quadratic program

long distance sound propagation over an impedance discontinuity abstract a calculation method is presented for sound propagation over an impedance discontinuity which is an improvement over previous methods being particularly efficient for long distances a homogeneous still atmosphere and flat ground are assumed the starting point is to make an approximation in a two dimensional boundary integral equation formulation of the problem this leads to an expression of the solution as the solution for homogeneous ground plus an integral over part of the boundary this integral is recognized as a generalized fourier integral to which standard techniques of asymptotic analysis can be applied an asymptotic approximation is found which can replace the part of the integral which is most expensive to evaluate by numerical quadrature the remaining integral is evaluated by numerical quadrature monofrequency excess attenuation results for propagation from a point source above rigid ground to a receiver above absorbing ground are discussed when the source and receiver are low enough very orderly trends are observed the results are applied with air attenuation and a weighting to a notional jet engine noise source simple trends are noted

wave arrival singularities at cuspidal points in the acoustic wave surfaces of anisotropic solids and their unfolding under weak spatial dispersion this paper is concerned with wave arrival singularities in the elastodynamic green9s functions of infinite anisotropic elastic solids and their unfolding into smooth wave trains known as quasi arrivals through spatial dispersion the wave arrivals treated here are those occurring in i the displacement response to a suddenly applied point force or three dimensional green9s function and ii the displacement response to an impulsive line force or two dimensional green9s function these arrivals take on various analytical forms including step function and logarithmic and power law divergences they travel outwards from the source at the group velocities in each direction and their locus defines the three and two dimensional acoustic wave surfaces respectively the main focus of this paper is on the form of the wave arrivals in the neighbourhood of cuspidal points in the wave surfaces and how these arrivals unfold into quasi arrivals under the first onset of spatial dispersion this regime of weak spatial dispersion where the acoustic wavelength begins to approach the natural length scale l of the medium is characterized by a correction to the phase velocity which is quadratic in the wavevector k and the presence of fourth order spatial derivatives of the displacement field in the wave equation integral expressions are established for the quasi arrivals near to cuspidal points involving the airy function in the case of and the scorer function in the case of numerical results are presented illustrating the oscillatory nature of the quasi arrivals and the interference effects that occur near to cuspidal points in the wave surface

a wavenumber independent boundary element method for an acoustic scattering problem in this paper we consider the impedance boundary value problem for the helmholtz equation in a half plane with piecewise constant boundary data a problem which models for example outdoor sound propagation over inhomogeneous flat terrain to achieve good approximation at high frequencies with a relatively low number of degrees of freedom we propose a novel galerkin boundary element method using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that on each element the approximation space contains polynomials of degree nu multiplied by traces of plane waves on the boundary we prove stability and convergence and show that the error in computing the total acoustic field is cal o n nu 1 log 1 2 n where the number of degrees of freedom is proportional to n log n this error estimate is independent of the wavenumber and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity

a novel boundary integral formulation for three dimensional analysis of thin acoustic barriers over an impedance plane this article presents a three dimensional formulation for the analysis of acoustic barriers over an impedance plane as infinitely thin structures the barriers are therefore modeled as simple surfaces rather than volumetric structures using this approach the problems caused by near singular integrations and near degenerate systems of equations are averted and mesh generation is made easier a dual boundary element method is used in the analysis involving the simultaneous solution of standard and hypersingular boundary integral equations an optimization procedure is used to speed up the assembling of the system of equations increasing the applicability of the method to a wider range of frequencies

ground effect analysis surface wave and layer potential representations abstract this paper presents two kinds of analytical exact expressions of the sound field reflected by a plane boundary as obtained by using either surface wave or layer potentials representations both solutions are first expressed as a sum of integrals which have a form suitable for numerical computation then these integrals are expanded into convergent series which provide analytical approximations of the solution numerical techniques are proposed for computing a the surface wave representation and b the approximation deduced from the layer potentials representation this approximation and the classical one sum of the surface wave and the first two terms of the asymptotic series are compared with the exact solution several examples show that the approximate formulas established here are valid on a range much wider than the validity domain of the classical ones

adaptive variable structure set point control of underactuated robots control of underactuated mechanical systems robots represents an important class of control problem in this correspondence a model based adaptive variable structure control scheme is introduced where the uncertainty bounds only depend on the inertia parameters of the system global asymptotic stability is established in the lyapunov sense numerical simulations are conducted to validate the theoretical analysis

the complex equivalent source method for sound propagation over an impedance plane the sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane originally such an approach for representing the half space green s function was described by sommerfeld at the beginning of the last century in order to treat half space problems of heat conduction however the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances the singular part of the line integral can be transformed into a hankel function which shows that surface waves are contained in the whole solution unfortunately this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence the main idea of the present method is to use also a superposition of equivalent point sources but to allow that these sources can be located at complex source points the corresponding form of the half space green s function is suitable for both masslike and springlike surface impedances and can be used as a cornerstone for a boundary element method

control problems in super articulated mechanical systems control of super articulated mechanical systems sams controlled mechanical system in which the dimension of the configuration space exceeds the dimension of the control input space is studied as a starting point a graphical characterization of general sams is developed in which a so called control flow diagram cfd is constructed to represent the interaction forces among the degrees of freedom of the system three types of structure namely the chain structure the tree structure and isolated points are identified degree of complexity of the system is defined based on the structure of the system a systematic backstepping type controller design is proposed for systems with a chain structure to achieve global asymptotic stability and trajectory tracking such a controller design itself illustrates the sufficient conditions for the existence of smooth feedback control such that the systems with a chain structure can be globally asymptotically stabilized the connection of the authors control algorithm with existing results is discussed