continuation of acoustic near fields this paper deals with the analytic continuation of a coherent pressure field specified on a finite sheet located close to and conformal to the surface of a vibrator this analytic continuation is an extension or extrapolation of the given measured field into a region outside and tangential to the original finite sheet and is based on the green s function the transfer function relating acoustic quantities on the two conformal surfaces the continuation of the measured pressure field is an inverse problem that requires the use or regularization theory especially when noise is present in the data an iteration algorithm is presented that is successful in continuing the pressure field into the tangential sheet the results are accurate close to the original boundary and taper decay toward zero with distance away from it the algorithm is tested on numerical and experimental data from a point driven rectangular plate results show the successful extrapolation continuation of this data into an area nearly double that of the original pressure field this algorithm is not limited to planar surfaces and can be applied to arbitrarily shaped surfaces

an inverse method to compute equivalent forces on a structure based on sound power measurements when modelling the dynamic response of an existing structure to predict the effects of design modifications many types of forces are difficult to characterize e g those due to unsteady flows or acoustic excitation to model the forcing function in such cases a method is presented which solves for an equivalent forcing function based on sound power measurements the method assumes that the equivalent forcing function may be represented with a superposition of force distributions on a mode by mode basis i e there is one force distribution per eigenvalue with the shape of the eigenvector the method is applied to cases where the structure is lightly damped and has low modal density experimental results show that the method accurately predicts the effect of design changes on the structure s radiated sound power the accuracy of the method is sensitive to small differences between the experimental and theoretical natural frequencies and thus it is important to match the damped natural frequencies of the physical structure as accurately as possible

3 d sound source reconstruction and field reprediction using the helmholtz integral equation abstract a method for reconstruction of the boundary conditions of an arbitrarily shaped three dimensional 3 d sound source from a finite number of field pressures is presented and the associated field is repredicted by using the helmholtz integral equation to minimize the reconstruction error due to noise in the field pressures a filtering method is proposed and it is verified that numerically singular values which correspond to the higher order modes of the evanescent like components of the source velocities are eliminated for arbitrarily shaped sources with complex boundary conditions the reconstruction is performed accurately when the size of each element is less than a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of a sphere in the vicinity of the source our technique can be used in computer aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from the finite number of field pressures and repredicts the variation of the sound field procuced by a redesigned loudspeaker cabinet on which the reconstructed diaphragm is mounted

singular value analysis of the jacobian matrix in microwave image reconstruction for non linear inverse scattering problems utilizing gauss newton methods the jacobian matrix encodes rich information concerning the system performance and algorithm efficiency in this paper we perform an analytical evaluation of a single iteration jacobian matrix based on a previously derived nodal adjoint representation concepts for studying linear ill posed problems such as the degree of ill posedness are used to assess the impact of important system parameters on the expected image quality analytical singular value decomposition svd of the jacobian matrix for a circular imaging domain is derived along with the numerical svd for optimizing imaging system configurations the results show significant reductions in the degree of ill posedness when signal frequency antenna array density and property parameter sampling are increased specifically the decay rate in the singular spectrum of the jacobian decreases monotonically with signal frequency being approximately 1 3 of its 0 1 ghz value at 3 ghz is improved with antenna array density up to about 35 equally spaced circumferentially positioned elements and drops significantly with increased property parameter sampling to more than twice the amount of measurement data these results should serve as useful guidelines in the development of design specifications for an optimized hardware installation

attractors for the 3d baroclinic quasi geostrophic equations of large scale atmosphere abstract the existence of absorbing sets and a compact connected global attractor to the 3d baroclinic quasi geostrophic equations of large scale atmosphere are obtained using cft theory an upper bound of the hausdorff and fractal dimensions of the global attractor in terms of the physically relevant parameters re the reynolds number ro the rossby number and f is derived moreover similar results are also established for the 2d vorticity equations of globe atmosphere

estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

uniqueness of the global weak solutions to 2d compressible primitive equations abstract in this paper we investigate an initial boundary value problem for 2d compressible primitive equations with some specific viscosities we will prove the uniqueness of the weak solutions obtained by b v gatapov and a v kazhikhov 12

an experimental comparison of various methods of nearfield acoustic holography abstract an experimental comparison of four different methods of nearfield acoustic holography nah for planar acoustic sources is presented in this study the four nah methods considered in this study are based on 1 spatial fourier transform 2 equivalent sources model 3 boundary element methods and 4 statistically optimized nah two dimensional measurements were obtained at distances ranging from one half to sixteen microphone spacings away from a sound source and the nah methods were used to reconstruct the sound field at the source surface reconstructed particle velocity and acoustic pressure fields presented in this study showed that the equivalent sources model based algorithm along with tikhonov regularization provided the best localization of the sources reconstruction errors were found to be smaller for the equivalent sources model based algorithm and the statistically optimized nah algorithm the effects of hologram distance on the performance of various algorithms are discussed in detail the study also compares the computational time required by each algorithm to calculate the reconstruction four different regularization parameter choice methods were compared the l curve method provided more accurate reconstructions than the generalized cross validation and the morozov discrepancy principle at larger measurement distances the performance of fixed parameter regularization was comparable to that of the l curve method

strong solutions to the 3d primitive equations with only horizontal dissipation near h 1 initial data abstract in this paper we consider the initial boundary value problem of the three dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal diffusivity we establish the local in time well posedness of strong solutions for any initial data v 0 t 0 h 1 by using the local in space type energy estimate we also establish the global well posedness of strong solutions for this system with any initial data v 0 t 0 h 1 l such that z v 0 l m for some m 2 by using the logarithmic type anisotropic sobolev inequality and a logarithmic type gronwall inequality this paper improves the previous results obtained in cao et al 2016 10 where the initial data v 0 t 0 was assumed to have h 2 regularity

ergodicity of eigenfunctions for ergodic billiards we give a simple proof of ergodicity of eigenfunctions of the laplacian with dirichlet boundary conditions on compact riemannian manifolds with piecewise smooth boundaries and ergodic billiards examples include the bunimovich stadium the sinai billiard and the generic polygonal billiard tables of kerckhoff masur and smillie

acoustic source property prediction based on near field measurements in planar coordinate abstract near field acoustical holography nah can be used to predict the acoustical properties of noise sources by starting from measurements of near field pressures in particular the sound pressure particle velocity and intensity can all be estimated on a source plane in the present work an equation relating acoustical source properties and the pressure radiated from a source is derived from the kirchoff helmholtz integral equation and is here referred to as the inverse rayleigh method the inverse rayleigh method reduces to the rayleigh integral when the source is located on an infinite rigid baffle however the same equation can also be used to predict the acoustic properties of a source in a more general environment i e without assuming the presence of an infinite rigid baffle in this article the inverse rayleigh method is described and then its relative accuracy is compared with other procedures that can be used to predict source particle velocity from near field pressure measurements on a planar hologram by comparing the accuracy of the present nah method with other procedures in the case of a large hologram it was found that the inverse rayleigh method is accurate and computationally efficient for predicting the source particle velocity from near field pressure measurements both with and without a rigid baffle

augmented hooke s law in frequency domain a three dimensional material damping formulation abstract an isothermal fully three dimensional material damping modelling technique to some extent alternative to classic viscoelasticity is proposed the method is formulated in the frequency domain as an augmented hooke s law ahl with a constitutive matrix in which material damping is introduced by adding frequency dependent complex valued terms to the classical material modulus matrix of hooke s generalized law the derivations are based on linear irreversible thermodynamics and the concept of hidden coordinates as introduced by biot 1955 phys rev 97 1463 1469 the one dimensional concept of multiple augmenting thermodynamic fields by lesieutre 1992 int j solids structures 29 1567 1579 is generalized to a suitable three dimensional continuum form through the introduction of a special type of hidden coordinate vectors with linear first order time domain relaxation equations consistent with the hidden coordinates a free energy density function assuming isothermal conditions is introduced as the time domain basis of the augmented hooke s law through a time domain model of the coupled evolution of the mechanical displacements and the thermodynamical variables issues of causality are avoided completely in the final frequency domain formulation the general time domain model used is shown to be equivalent to a three dimensional multiple anelastic displacement field model an isotropic augmented hooke s law with both dilatational and shearing damping has been implemented and tested using a 20 node volume element in the finite element code aska acoustics a close agreement between finite element calculations and the corresponding analytically exact results for the studied rod and beam cases is obtained

measurement of structural intensity using boundary element method based nearfield acoustical holography the regularization method for measurement of structural intensity si using boundary element method bem based nearfield acoustical holography nah is proposed spatial derivatives of normal displacement are necessary to obtain the structural intensity the derivative operations amplify high wavenumber component of measurement noise and contaminate the measurement result of si to overcome this difficulty regularization method for measurement of si using fast fourier transform based nah has been introduced in this paper this regularization method is modified for the bem based nah the bem based nah avoids the aperture replication problem therefore measurement aperture for bem based nah can be set smaller than that for fft based nah the effectiveness of the proposed method is demonstrated by experiments

polyhedral billiards eigenfunction concentration and almost periodic control we study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non smooth part of the boundary called pockets we prove there are only finitely many immersed periodic tubes missing the pockets and moreover establish a new quantitative estimate for the lengths of such tubes this extends well known results in dimension 2 we then apply these dynamical results to prove a quantitative laplace eigenfunction mass concentration near the pockets of convex polyhedral billiards as a technical tool for proving our concentration results on irrational polyhedra we establish a control theoretic estimate on a product space with an almost periodic boundary condition this extends previously known control estimates for periodic boundary conditions and seems to be of independent interest

enhanced nearfield acoustic holography for larger distances of reconstructions using fixed parameter tikhonov regularization this paper evaluates the performance of various regularization parameter choice methods applied to different approaches of nearfield acoustic holography when a very nearfield measurement is not possible for a fixed grid resolution the larger the hologram distance the larger the error in the naive nearfield acoustic holography reconstructions these errors can be smoothed out by using an appropriate order of regularization this study shows that by using a fixed manual choice of regularization parameter instead of automated parameter choice methods reasonably accurate reconstructions can be obtained even when the hologram distance is 16 times larger than the grid resolution

wavelet preprocessing for lessening truncation effects in nearfield acoustical holography the goal of planar nearfield acoustical holography nah is to recover the sound field at the sound source from pressure measurements made close to the source plane the theory requires the pressure to be measured over a complete plane because experimentation consists of acquiring only a finite measurement aperture of the pressure field it naturally causes erroneous values in the reconstructed field wavelet preprocessing applied to the pressure measurements in the nearfield provides a solution to lessen the effects due to the truncation of the hologram the approach is based on a multiresolution analysis of the field from different wave number bands followed by selective spatial filtering of effects highlighted by the first analysis experimental results show the relevance of the method by comparison to standard nah involving exponential filtering in the wave number domain the computation of objective indicators based on distance measurements between wave number spectra and comparisons between pattern

fast fourier transform and singular value decomposition formulations for patch nearfield acoustical holography nearfield acoustical holography nah requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface the latter generally coincident with a vibrator patch nah provides a major simplification by eliminating the need for complete surface pressure scans only a small area needs to be scanned to determine the normal velocity on the corresponding small area concentric patch on the vibrator the theory of patch nah is based on 1 an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and 2 a decomposition of the transfer function pressure to velocity and or pressure to pressure between the two surfaces using the singular value decomposition svd for general shapes and the fast fourier transform fft for planar surfaces inversion of the transfer function is stabilized using tikhonov regularization and the morozov discrepancy principle experimental results show that root mean square errors of the normal velocity reconstruction for a point driven vibrator over 200 2700 hz average less than 20 for two small concentric patch surfaces 0 4 cm apart reconstruction of the active normal acoustic intensity was also successful with less than 30 error over the frequency band

acoustic imaging using under determined inverse approaches frequency limitations and optimal regularization this paper presents an acoustic imaging technique based on an under determined inverse approach the principle is to quantify an elementary source distribution on a source surface from acoustic pressure measurements the acoustic transfer system between elementary sources and microphone positions very under determined is then reduced to a square system using singular value decomposition the high frequency limitation of this method is studied as well as the regularization techniques that have to be used at low frequency a monte carlo simulation is carried out to compare the efficiency of generalized cross validation and l curve validation to choose the tikhonov regularization parameter a combined validation criterion is finally proposed to take advantage of both approaches

local instability of orbits in polygonal and polyhedral billiards we classify when local instability of orbits of closeby points can occur for billiards in two dimensional polygons for billiards inside three dimensional polyhedra and for geodesic flows on surfaces of three dimensional polyhedra we sharpen a theorem of boldrighini keane and marchetti we show that polygonal and polyhedral billiards have zero topological entropy we also prove that billiards in polygons are positive expansive when restricted to the set of non periodic points the methods used are elementary geometry and symbolic dynamics

non periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons this paper proves the existence of non periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons for anyn 3 there exists a corresponding convexn agon forn 3 this will be a right triangle with a small acute angle while in three dimensional space it will be a prism then agon serving as the base

inverse problem with beamforming regularization matrix applied to sound source localization in closed wind tunnel using microphone array abstract microphone arrays have become a standard technique to localize and quantify source in aeroacoustics the simplest approach is the beamforming that provides noise source maps with large main lobe and strong side lobes at low frequency since a decade the focus is set on deconvolution techniques such as damas or clean sc while the source map is clearly improved these methods require a large computation time in this paper we propose a sound source localization technique based on an inverse problem with beamforming regularization matrix called hybrid method with synthetic data we show that the side lobes are removed and the main lobe is narrower moreover if the sound noise source map provided by this method is used as input in the damas process the number of damas iterations is highly reduced the hybrid method is applied to experimental data obtained in a closed wind tunnel in both cases of acoustic or aeroacoustic data the source is correctly detected the proposed hybrid method is found simple to implement and the computation time is low if the number of scan points is reasonable

inverse aeroacoustic problem for a streamlined body ii accuracy of solutions previously established methods for performing the aeroacoustic inversion for a fiat plate airfoil are tested to determine their sensitivity to errors in both the far field input data and the mean flow input parameters the results of the sensitivity analysis for the input data show that the magnification of input error due to ill posedness can be controlled by optimal choices of the regularization parameter and the input data locations a similar sensitivity analysis of the effect of mean flow parameters mach number and reduced frequency shows strong dependence of the inverse process on these parameters in this case improvements in the reconstructions can be obtained by using input data from the midfield

patch near field acoustic holography regularized extension and statistically optimized methods the patch holography method allows one to make measurements on an extended structure using a small microphone array increased attention has been paid to the two techniques which are quite different at first glance one is to extrapolate the pressure field measured on the hologram plane while the other is to use statistically optimized processing a singular value decomposition formulation of the latter is proposed in this paper the similarity of the two techniques is shown here both use a convolution of the measured pressure patch to obtain a better estimate of the wavenumber spectrum backward propagated on the structure by using the morozov discrepancy principle to compute the regularization parameter the two methods lead to very close results

data extrapolation method for boundary element method based near field acoustical holography a new data extrapolation method for boundary element method bem based near field acoustical holography nah is proposed to reduce an error of the reconstructed result obtained from the pressure measured on an aperture small compared with the structure the finiteness of the measurement aperture is a serious impediment to actual large scale implementation of nah because nah requires the measurement of the pressure field over a complete surface of structure to eliminate the requirement the wave number space data extrapolation method for fast fourier transform fft based nah has been proposed in this paper the extension of this data extrapolation method to bem based nah is presented the effectiveness of this method is demonstrated by experiments the experiment results confirm that the reconstruction error is sufficiently suppressed by the proposed method

existence of the universal attractor for the 3 d viscous primitive equations of large scale moist atmosphere abstract in this paper we consider the initial boundary value problem for the three dimensional viscous primitive equations of large scale moist atmosphere which are used to describe the turbulent behavior of long term weather prediction and climate changes by obtaining the existence and uniqueness of global strong solutions for the problem and studying the long time behavior of strong solutions we prove the existence of the universal attractor for the dynamical system generated by the primitive equations of large scale moist atmosphere

the relationship of singular value decomposition to wave vector filtering in sound radiation problems singular value decomposition svd has recently been suggested as a filtering tool to analyze acoustic radiation the relationship between this filtering technique and the more familiar wave vector filtering is examined for a geometry with a preferred axis the source modes are found to consist approximately of a single wave number and the accompanying radiation modes are thus beams some simple examples are worked out to illustrate the general behavior of the filtering and some of the properties of the beams are given

experimental force estimation in a constrained vibrating structure using modal based methods abstract in this paper three recently developed traction vector techniques will be experimentally validated common ground for the techniques are based on a modal expansion of the displacement field and utilization of sets of normal eigenmodes and displacement measurements in order to yield detailed descriptions of the traction vector field acting at the boundary comparison between the methods is made regarding the experimental estimation of traction vectors both point wise and in an l2 norm over the boundary in question the results are good especially regarding the normed results

effect of sensor proximity over the non conformal hologram plane in the near field acoustical holography based on the inverse boundary element method near field acoustical holography nah is a useful tool for the identification and visualization of vibro acoustic sources in particular nah can be applied to many practical sources having irregular shape if the inverse boundary element method bem is employed once the relation between the source and the radiated field is defined in the transfer matrix modeled by the bem the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface the usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface which can be a flat cylindrical or spherical shape for the measurement ease then the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill posed than the conformal case to investigate the effect of sensor proximity and distance variability on the reconstruction error simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate flat tilted and randomized hologram surfaces were adopted in the test it was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor to improve the reconstruction accuracy an investigation was conducted to find proper field points among a large number of overdetermined field points the number of field data was reduced gradually under various reduction schemes using condition number effective independence value and sensor distance it was demonstrated that the quality of reconstruction result given by the non conformal measurement can be improved by removing some field points that contribute to the ill conditioning of the inverse problem a small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation however further reduction of the field points becoming an underdetermined situation yielded a drastic improvement of the reconstruction accuracy

inverse aeroacoustic problem for a streamlined body i basic formulation the inverse aeroacoustic problem associated with a flat plate airfoil in unsteady compressible flow is formulated in terms of a fredholm integral equation of the first kind the feasibility of determining the unsteady pressure along the airfoil surface from the radiated acoustic signal is demonstrated it is shown that the hadamard conditions of existence and uniqueness of the inverse solution can be satisfied the third hadamard condition for the continuous dependence of the solution on the input acoustic data shows the problem to be ill posed the singular value decomposition method with regularization is used to treat the associated ill conditioned algebraic problem discretization and collocation techniques are used to represent the unsteady pressure on the airfoil both methods give very accurate reconstructions when perfect input data are used the collocation method requires only a small amount of input data either from the far field or the near field thus making it more suitable for applications

existence of weak solutions and trajectory attractors for the moist atmospheric equations in geophysics in this paper we consider the initial boundary value problem for the primitive equations of moist atmospheric dynamics that are used to describe the turbulent behavior of long term weather prediction and climate changes by the faedo galerkin method we obtain the existence of global weak solutions to the problem in a large scale atmosphere by studying the long time behavior of solutions we obtain trajectory and global attractors for the primitive equations of moist atmosphere

the round trip theory for reconstruction of green s functions at passive locations an expression for the green s function at an arbitrary set of passive locations no applied force is derived and validated by experiment three sets of points are involved the passive reconstruction points c which lie on a virtual boundary and two sets of auxiliary points denoted a and b located either side the reconstruction is achieved using green s functions forming a round trip from and to the reconstruction points via a and b a two stage measurement procedure is described involving excitation at b and a but with no excitation required at the reconstruction points a known round trip relationship is first introduced which is theoretically exact for points on a multi point interface between two linear time invariant subsystems experimental results for frequency response functions of a beam plate structure show that this relationship gives good results in practice it is then shown that the theory provides an nth order approximation for the green s function at arbitrary points where n is the number of points at b the expression is validated by reconstructing point and transfer frequency response functions at two passive points on an aluminum plate

numerical inverse method predicting acoustic spinning modes radiated by a ducted fan from free field test data spinning modes generated by a ducted turbofan at a given frequency determine the acoustic free field directivity an inverse method starting from measured directivity patterns is interesting in providing information on the noise sources without requiring tedious spinning mode experimental analyses according to a previous article equations are based on analytical modal splitting inside a cylindrical duct and on a rayleigh or a kirchhoff integral on the duct exit cross section to get far field directivity equations are equal in number to free field measurement locations and the unknowns are the propagating mode amplitudes there are generally more unknowns than equations a matlab procedure has been implemented by using either the pseudoinverse function or the backslash operator a constraint comes from the fact that squared modal amplitudes must be positive which involves an iterative least squares fitting numerical simulations are discussed along with several examples based on tests performed by rolls royce in the framework of a european project it is assessed that computation is very fast and it well fits the measured directivities but the solution depends on the method and is not unique this means that the initial set of modes should be chosen according to any known physical property of the acoustic sources

existence of a strong solution and trajectory attractor for a climate dynamics model with topography effects abstract the primitive three dimensional viscous equations for large scale atmosphere dynamics are commonly used in weather and climate predictions and multiple theoretical analyses have been performed on them however few studies have considered topographic effects which have a remarkable influence on climate factors e g atmospheric temperature and wind velocity in this study a climate dynamics model with topography and non stationary external force effects based on the navier stokes equations and a temperature equation is analyzed the existence and uniqueness of a global strong solution for this system is demonstrated based on the initial data assumptions in addition the existence of a universal attractor in the dynamic system is confirmed

the equations of the atmosphere with humidity and saturation uniqueness and physical bounds abstract in continuation of an earlier work coti zelati and temam 2012 8 devoted to the mathematical formulation and existence of solutions for the system of moist atmosphere with saturation we address here the question of the uniqueness of solutions which is essential for giving a physical justification for the analysis of the model in coti zelati and temam 2012 8 we also derive some physical bounds on the solution as well as additional results of regularity of the solutions

experimental study of the mapping relationship based near field acoustic holography with spherical fundamental solutions abstract this paper is a consequent work of the previously proposed mapping relationship based near field acoustic holography mrs based nah h j wu w k jiang and h b zhang jsv 373 66 88 2016 it is devoted to the performance study of its practical application with error analysis and experimental validation two types of errors the truncation errors due to the limited number of participant modes and the inevitable measurement errors caused by uncertainties in the experiment are considered in the analysis the influences of the errors on the performance of mrs based nah are systematically investigated first of all expression of the relative reconstruction error of the pressure energy is derived based on the two types of errors an approach is developed to estimate the lower and upper bounds of the relative error it gives a guide to predict the error for a reconstruction under the condition that the truncation error and the signal to noise ratio are given then the condition number of the inverse operator is investigated to measure the sensitivity of the reconstruction to the input errors asymptotic expressions of the condition number for a special case conformal spherical model and hologram are obtained which indicates the condition number has a geometric growth with the number of participant modes numerical examples with different kinds of errors are elaborately designed to validate the stability as well as the correctness of the error analysis at last the mrs based nah is further examined and verified by a physical experiment a vibrating cubic model reconstructed from measurement on a spherical hologram a satisfied agreement with the directly measured pressure on a validation surface is observed for both quantity and distribution of the reconstructed pressure

application of lp norm regularisation techniques in the synthesis of indoor tyre pass by noise with the inverse method abstract pass by noise measurements can nowadays be realised in a laboratory environment with a microphone array and a stationary vehicle on a rolling road according to iso 362 1 2016 within this indoor testing procedure the contributions from the various noise sources in a car can be estimated with a set of microphones close to the various sources and the pass by noise then synthesised the methods described in this paper use measured near field pressure data close to a rolling tyre at 50 km h to estimate virtual source strength using the inverse method and the synthesised far field tyre noise is then compared with the one measured directly at a far field microphone array a combination of l1 norm and l2 norm regularisation methods are investigated to optimise the equivalent source position and strength and subsequently the far field pass by noise pressure estimates through the frequency range of interest it is shown that by optimising the positions of 4 equivalent sources acceptable representations of the measured far field spectra can be synthesised

regularization method for the application of k space data extrapolation to near field acoustical holography a regularization method for applying the k space data extrapolation method to near field acoustical holography nah is proposed the influence of the finiteness of measurement aperture is a serious impediment to the nah reconstruction of structural vibration when the size of the measurement aperture is smaller than that of the structure the k space data extrapolation method has been proposed to reduce the influence of this finiteness an appropriate regularization method is necessary to apply the k space data extrapolation method if the measured pressure is contaminated by noise some regularization methods for nah have been proposed however it is difficult to determine an appropriate k space filter if the finiteness of the measurement aperture becomes an issue an estimation method of appropriate regularization filter for applying the k space data extrapolation method is proposed to solve this difficulty the effectiveness of this method is demonstrated by simulations the simulation results confirm

the problem of vibration field reconstruction statement and general properties abstract the paper addresses the problem of reconstructing the vibration field of a structure or the acoustic field of a bounded fluid from limited data the problem relates to practical situations when there is a need to know the dynamic stress and displacement distribution over the entire structure e g for estimating its remaining service life but the vibration may be measured only on accessible parts of the structure surface in the paper this problem is mathematically formulated and its general properties solvability uniqueness and continuity are studied most attention is paid to the analysis of the error of reconstruction one of the main results obtained is the proof of existence of the optimal vibration model of the structure which renders minimum to the reconstruction error the application of the results to discrete systems is discussed

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

the growth rate for the number of singular and periodic orbits for a polygonal billiard for any simply connected polygon in the plane the number of billiard orbits which begin and end at a vertex grows subexponentially with respect to the length or to the number of reflections this implies that the numbers of isolated periodic orbits and of families of parallel periodic orbits do grow subexponentially the main technical device is a calculation showing that the topological entropy of the poincare map for the billiard flow is equal to zero

acoustical inverse problems regularization direct definition of filter factors using signal to noise ratio abstract acoustic imaging aims at localization and characterization of sound sources using microphone arrays in this paper a new regularization method for acoustic imaging by inverse approach is proposed the method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors in place of regularization using classical methods such as truncated singular value decomposition and tikhonov regularization the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation defined from the estimated measurement noise the thresholding operation is achieved using modified filter functions the originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the tikhonov filter this has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems theoretical results show that this method is comparatively more accurate than tikhonov regularization and truncated singular value decomposition

construction of three dimensional orthogonal surface basis functions and well conditioned boundary traction vector estimation a well conditioned technique for the solution of the inverse problem of boundary traction estimation in the frequency domain from measured vibration responses on a solid structure is proposed the technique is based on recent results regarding lack of mode orthogonality on sub domains of the structure this is one of the reasons that modal based solutions to the inverse problems may be numerically ill conditioned herein construction of orthogonal three dimensional basis functions over a sub domain of the structure and a well posed model for inverse boundary traction estimation are proposed the technique is validated on a three dimensional example using direct fe calculated responses as simulation of measured responses with very good results

on the use of three dimensional h and p version finite elements in solving vibration response problems abstract the potential for reliably solving vibration response problems by using h and p versions of the finite element fe method is investigated each fe model is based on full three dimensional 3 d displacement based continuum theory special attention is given to the ability to handle thin and or nearly incompressible elastic and viscoelastic materials steady state time harmonic problems in the low and mid frequency ranges are treated convergence studies are performed on plate like model problems with simply supported boundary conditions using a series elasto dynamic navier solution extended to the viscoelasto dynamic case by means of the elasto viscoelastic correspondence principle the importance of eliminating the discretisation error when using numerical solutions to estimate the frequency dependent viscoelastic material parameters from experiments is stressed the superior efficiency of p enrichments compared to h refinements for resolving regular elastostatic solutions is observed in elasto viscoelasto dynamics as well requirements on p enrichments to avoid shear and volumetric locking are given the frequently used polynomial interpolation functions employed are shown to produce a mass contribution to the dynamic stiffness whose condition number deteriorates with increasing polynomial order the practical implications and limitations of this observation are outlined the recommended approach is corroborated using the measured frequency response on a laminate consisting of two aluminium plates and a constrained viscoelastic polymer damping treatment

global well posedness and finite dimensional global attractor for a 3 d planetary geostrophic viscous model in this paper we consider a three dimensional planetary geostrophic viscous model of the gyre scale mid latitude ocean we show the global existence and uniqueness of the weak and strong solutions to this model moreover we establish the existence of a nite dimensional global attractor to this dissipative evolution system c 2003 wiley periodicals inc

a method for the efficient construction of acoustic pressure cross spectral matrices abstract a method is presented for constructing with the minimum number of physical measurements the full cross spectral matrix of acoustic pressures associated with a number of measurement positions it is necessary to evaluate the elements of the matrix in question when using inverse methods for the reconstruction of acoustic source strength spectra the method presented uses the concept of reference microphones the relation between the rank of the cross spectral matrix of acoustic pressures and the number of uncorrelated acoustic sources is discussed and used to determine the required number of reference microphones a method is proposed for selecting this number in the inverse problem in which information regarding acoustic sources is unknown the results of computer simulations are presented which explore the main features of the technique under various conditions experimental results are also presented which validate the technique

estimation of acoustic source strength by inverse methods part ii experimental investigation of methods for choosing regularization parameters two regularization methods tikhonov regularization and singular value discarding are used to improve the accuracy of reconstruction of acoustic source strength by inverse techniques in this paper some methods are investigated for choosing the tikhonov regularization parameter and the singular values to be discarded of these we concentrate on the use of ordinary cross validation and generalized cross validation these methods can provide an appropriate regularization parameter without prior knowledge of either the acoustic source strength or the contaminating measurement noise some experimental results obtained using a randomly vibrating simply supported plate mounted in a baffle are presented to illustrate the performance of the methods for choosing the regularization parameters

beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array for sound field reproduction using multichannel spatial sound systems such as wave field synthesis and ambisonics sound field extrapolation is a useful tool for the measurement description and characterization of a sound environment to be reproduced in a listening area in this paper the inverse problem theory is adapted to sound field extrapolation around a microphone array for further spatial sound and sound environment reproduction a general review of inverse problem theory and analysis tools is given and used for the comparative evaluation of various microphone array configurations classical direct regularization methods such as truncated singular value decomposition and tikhonov regularization are recalled on the basis of the reviewed background a new regularization method adapted to the problem at hand is introduced this method involves the use of an a priori beamforming measurement to define a data dependent discrete smoothing norm for the regularization of the inverse problem this method which represents the main contribution of this paper shows promising results and opens new research avenues

implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography two integral equation methods are considered which can be inverted to provide the surface velocity and or pressure given a measurement of the pressure on an imaginary surface in the nearfield of a vibrating or scattering body this problem is central to nearfield acoustical holography nah the integral equations are discretized using boundary element methods bems the integral equation methods considered are 1 an indirect formulation method based on the single layer integral equation and 2 a direct formulation method based on a system of equations derived from the helmholtz kirchhoff integral equation the formation of integral equations from the mentioned methods will not involve the explicit inversion of matrices but instead will require this inversion to be done implicitly since these methods back track the sound field from the measurement surface to the surface of the source vibrator they are ill posed in nature and tikhonov regularization are used to stabilize the reconstruction problems a

simulation of damped vibrations based on augmented hooke s law and elastic modes of vibration abstract a linear unconditionally convergent modal vibration response modelling technique is presented material damping is simulated using the augmented hooke s law introduced by dovstam dovstam k 1995 augmented hooke s law in frequency domain a three dimensional material damping formulation international journal of solids and structures 32 2835 2852 the method is based on continuous elastic displacement modes and vibrational stress modes dual to the traditional displacement modes the stress modes are implicitly used to derive a generally convergent modal response model in generally damped cases with boundary traction excitation the real eigenvalue problem defining the stress modes is formulated and explicit frequency domain modal system equations of motion for computation of needed stress and displacement mode coefficient spectra are derived introduced parameters accounting for the interdependence of the different modal contributions modal coupling to the response are computable from known material properties elastic and damping and geometry by post processing results from three dimensional standard finite element fe eigenvalue calculations practical means for predicting whether modal coupling will occur or not are thus provided as well as means for predicting damped resonance frequencies when applied to an isotropic material the new response model for small damping approaches the modal receptance model recently introduced and discussed by dovstam dovstam k 1997 receptance model based on isotropic damping functions and elastic displacement modes international journal of solids and structures 34 2733 2754 a close agreement between direct fe calculations and response simulations using the proposed method is obtained for a highly damped three dimensional cantilever test plate

global well posedness of the three dimensional viscous primitive equations of large scale ocean and atmosphere dynamics in this paper we prove the global existence and uniqueness regularity of strong solutions to the three dimensional viscous primitive equations which model large scale ocean and atmosphere dynamics 1 introduction large scale dynamics of oceans and atmosphere is governed by the primitive equations which are derived from the navier stokes equations with rotation coupled to thermodynamics and salinity diffusion transport equations which account for the buoyancy forces and stratification effects under the boussinesq approximation moreover and due to the shallowness of the oceans and the atmosphere i e the depth of the fluid layer is very small in comparison to the radius of the earth the vertical large scale motion in the oceans and the atmosphere is much smaller than the horizontal one which in turn leads to modeling the vertical motion by the hydrostatic balance as a result

receptance model based on isotropic damping functions and elastic displacement modes abstract starting from a fundamental continuum mechanical constitutive material damping description the augmented hooke s law ahl introduced by dovstam dovstam k 1995 augmented hooke s law in frequency domain a three dimensional material damping formulation international journal of solids and structures32 2835 2852 a linear three dimensional damped vibration response model for isotropic material is proposed the derivations valid for a restricted but important class of cases are based on general continuous elastic vibration modes gurtin gurtin m e 1972 the linear theory of elasticity in encyclopedia of physics vol via 2 mechanics of solids ii eds flugge s and truesdell c springer berlin material damping is represented by two complex frequency dependent damping functions defined directly by constitutive parameters in the isotropic ahl alternatively for isotropic viscoelastic solids the damping functions are derived from two stress relaxation functions modal damping functions which define overall structural damping in terms of elastic modal parameters and the two material damping functions are introduced in the response model it is shown that the modal damping functions indirectly depend on the geometry and boundary conditions of the piece of material under investigation introduced are also new elastic modal parameters which determine the quantitative contribution to the modal damping functions from the two isotropic material damping functions the new modal parameters are easily computed using slightly modified standard finite element code and elastic modes resulting from standard finite element eigenvalue analyses a close agreement between direct finite element calculations and responses predicted using the proposed modal model is obtained for a studied three dimensional cantilever test plate

comparison of methods for parameter selection in tikhonov regularization with application to inverse force determination in performing transfer path analysis of structure borne sound transmission the operational forces at the excitation points and or at the connections within the structure borne paths are required these forces can be obtained by using inverse techniques but the measured data used will contain some unknown errors therefore the reconstructed forces may include large errors due to the inversion of an ill conditioned matrix of these measured data in this study tikhonov regularization is used in order to improve the conditioning of the matrix inversion several methods are available to select the optimal regularization parameter the purpose of this paper is to compare the performance of the ordinary and generalized cross validation methods and the l curve criterion simulations are carried out representing measurements on a rectangular plate for different noise levels in measured data also the robustness of the conclusions is investigated by varying the shape of the plates the force positions and the noise levels included in the measured data the l curve method is found to perform better than ocv or gcv particularly for high noise levels in the operational responses but less well when these noise levels are low it is therefore found to be less susceptible to producing large reconstruction errors but it tends to over regularize the solution in the presence of low noise leading to under estimates of the forces in practice measurements of operational responses may be susceptible to noise contamination which suggests that the l curve method is likely to be the most appropriate method in practical situations nevertheless it is important to obtain good estimates of the likely noise in the signals before determining the most appropriate regularization technique ordinary cross validation method is generally found to have a better performance than generalized cross validation method if the matrix condition numbers are high since the need for regularization is greater with high condition numbers it is consequently found that the ordinary cross validation method gives more reliable results overall than the generalized cross validation method

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

compensation for discarded singular values in vibro acoustic inverse methods the paper addresses the inverse problem where source strengths are back calculated from a sound pressure field sampled at several points regularization techniques such as singular value discarding or tikhonov regularization are commonly used to improve estimates of source strength in such situations however over regularization can result in even worse errors a simple procedure is proposed here to compensate for errors of over regularization the basis is to constrain the solution such that the spatial mean of the measured and reconstructed sound pressure are equal in other words to set the overall sound power of the equivalent calculated sources equal to that of the real source it is argued that the overall sound power is the most stable and reliable quantity on which to base source strength estimates examples of both singular value discarding and tikhonov regularization are given

formulation of the equations of the humid atmosphere in the context of variational inequalities abstract the equations of the humid atmosphere with saturation are considered in the case where the saturation concentration q s is not assumed to be constant and obeys the laws of thermodynamics 22 23 32 this article starts from the observation that these equations are not correct in the extreme cases where the atmosphere is totally dry or totally wet that is when the concentration q of water vapor is equal to 0 or 1 a new formulation of the equations is proposed to remedy this difficulty in the context of variational inequalities results of existence maximum principle and regularity of solutions are derived for these new variational inequalities

the quantification of structure borne transmission paths by inverse methods part 2 use of regularization techniques the inversion of an ill conditioned matrix of measured data lies at the heart of procedures for the quantification of structure borne sources and transmission paths in an earlier paper the use of over determination singular value decomposition and the rejection of small singular values was discussed in the present paper alternative techniques for regularizing the matrix inversion are considered such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography the application to structure borne sound transmission involves matrices which vary much more with frequency and from one element to another in this study tikhonov regularization is used with the ordinary cross validation method for selecting the regularization parameter an iterative inversion technique is also studied here a form of cross validation is developed allowing an optimum value of the iteration parameter to be selected simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques experiments are also performed to validate the results both techniques are found to give considerably improved results compared to singular value rejection