calculation of acoustic radiation using equivalent sphere methods among the methods generally used to solve a problem in the domain of acoustic radiation the equivalent sources method offers an interesting alternative it consists in replacing the vibrating surface with a distribution of acoustic sources placed inside the structure the contribution of each source is determined in such a way that the acoustic field radiated by these sources verifies the same boundary conditions on the structure the number of unknowns in the problem is no longer directly linked to the number of mesh points on the structure as with boundary elements methods but to the number of equivalent sources employed in the model the equivalent source method is therefore of major interest if the acoustic radiation of the structure can be approximated with a sufficiently low number of sources this paper proposes its application when the equivalent source is a sphere in this case the number of unknowns is equal to the number of modes in contrast to the one point multipole the sphere has a surface surrounding a closed volume to express the boundary conditions although sphere multipole equivalence has been demonstrated the surface of the sphere allows normalization of the functions used leading to stabilization of the system to be resolved first the main acoustic radiation characteristics of a sphere and of the linear system verified by the modal coefficients of an equivalent sphere are presented the different parameters of the model are then studied position and radius of the equivalent sphere truncation of the series and influence of the spatial sampling mesh in the same vein a second approach is presented it consists of making each point of the structure correspond to a point of the sphere and the vibrating field at the surface of the sphere is deduced from that of the structure by simple geometric projection results can be obtained very quickly as no matrix inversion is required the accuracy of the results depends on the distance between the sphere and the structure finally an experimental validation that uses both methods is presented and shows interesting results when the structure is closed and when its shape is not too far removed from a sphere

design sensitivity analysis for sequential structural acoustic problems abstract a design sensitivity analysis of a sequential structural acoustic problem is presented in which structural and acoustic behaviors are de coupled a frequency response analysis is used to obtain the dynamic behavior of an automotive structure while the boundary element method is used to solve the pressure response of an interior acoustic domain for the purposes of design sensitivity analysis a direct differentiation method and an adjoint variable method are presented in the adjoint variable method an adjoint load is obtained from the acoustic boundary element re analysis while the adjoint solution is calculated from the structural dynamic re analysis the evaluation of pressure sensitivity only involves a numerical integration process for the structural part the proposed sensitivity results are compared to finite difference sensitivity results with excellent agreement

a boundary element formulation for acoustic shape sensitivity analysis the helmholtz integral equation forms a conventional basis for acoustic boundary element analysis bea implicit differentiation of the discretized helmholtz integral equation is shown to yield an effective approach for the computation of rates of change sensitivities of acoustic response quantities with respect to changes in the shape of an acoustic model a theoretical formulation is presented that allows for the reuse of the factorization of the overall bea system left hand side matrix formed in a previous analysis thus obviating the need to factor perturbed matrices in the sensitivity analysis process the singularity strengths of the new kernel functions utilized to compute sensitivities of matrix coefficients required by this approach are shown to be the same as those present in ordinary bea an indirect approach for the computation of the diagonal contributions to sensitivity matrices associated with these new kernels is also discussed the sensitivity analysis formulation includes surface pressures and normal gradients velocities surface tangential pressure gradients and pressure and pressure gradients at arbitrary domain sample points it is concluded that the overall efficiency of implementations of these formulations is significant numerical results for a series of example problems are presented to quantify the accuracy and efficiency of this approach

the generalized riemann problem for reactive flows abstract a generalized riemann problem is introduced for the equations of reactive non viscous compressible flow in one space dimension initial data are assumed to be linearly distributed on both sides of a jump discontinuity the resolution of the singularity is studied and the first order variation in time of flow variables is given in exact form

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

the use of chief to obtain unique solutions for acoustic radiation using boundary integral equations this report is concerned with the problem of obtaining a unique solution for radiation problems at characteristic wavenumbers when a boundary integral equation formulation is used it is shown that the combined helmholtz integral equation formulation chief method works even when numerous interior points lie exactly on nodal surfaces of a mode corresponding to an eigenfrequency of the related interior problem when at least one interior point does not lie on a nodal surface the use of chief is illustrated with numerical radiation experiments for the sphere and the finite cylinder chief is compared to the helmholtz gradient formulation hgf for circumventing nonuniqueness and is found to yield a more accurate solution in at least one published example a procedure is used to indicate the solution error when using integral equation methods with or without a technique to circumvent nonuniqueness this procedure uses the velocity potential of an interior point as an indicator of solution error in all cases considered the interior potential correctly indicated a good or bad solution whereas the matrix condition number falsely indicated a bad solution in several instances work supported in part by onr

energy fields of partially coherent sources random acoustic fields and their energetic quantities acoustic active and reactive intensities potential and kinetic energy densities are described in terms of the mutual coherences between sources conditions to correctly construct the coherence matrix of sources in a multivariate random process are given it is shown that the description of a sound field using the coherence matrix of source is equivalent to the superposition of a number of independent coherent fields which do not correspond to the original localized sources a method based on processing the principal components of the coherence matrix of sources is given to reduce the number of necessary fields the coherence function between acoustic pressure and particle velocity and the curl of active intensity are proposed as two indicators for estimating the degree of coherence and the polarization of acoustic fields these indicators are analyzed theoretically and experimentally the description of the structure of partially coherent fields is generalized by the definition of the field matrix whose rank is an indicator of the local complexity of an acoustic field

spectral simulation of supersonic reactive flows we present in this paper numerical simulations of reactive flows interacting with shock waves we argue that spectral methods are suitable for these problems and review the recent developments in spectral methods that have made them a powerful numerical tool appropriate for long term integrations of complicated flows even in the presence of shock waves a spectral code is described in detail and the theory that leads to each of its components is explained results of interactions of hydrogen jets with shock waves are presented and analyzed and comparisons with eno finite difference schemes are carried out

stationary distributions of perturbed markov chains abstract techniques for updating the stationary distribution of a finite irreducible markov chain following a rank one perturbation of its transition matrix are discussed a variety of situations where such perturbations may arise are presented together with suitable procedures for the derivation of the related stationary distributions

a scaling approach for the prediction of high frequency mean responses of vibrating systems this analysis presents a scaling approach to predict high frequency mean responses of vibrating systems the basis of the approach lies in the dynamic similitude between the original systems and the scaled models a general scaling law is formulated using skudrzyk s mean value theorem and its specific form is derived for the case of a flexural plate modal density is scaled down to reduce the computational cost in the high frequency mean response prediction different scaling procedures are numerically experimented and some insights are given about the accuracy of the scaling approach as compared with a dense finite element analysis

space average and wave interference in vibration conductivity plane wave interference and space averages play a significant role in the derivation of some vibration conductivity equations that are becoming more and more popular in modelling vibroacoustic problems particularly the thermal approach and the modified vibration conductivity equations are here considered with the aim of establishing similarities and or differences between them and stating relevant consequences it is shown by formal developments that the thermal equation is obtained under the assumption of performing appropriate space averages while the modified vibration conductivity equation does not need in some cases this condition it is discussed however that in practical applications the conditions of validity of both approaches are quite similar

development of an energy boundary element formulation for computing high frequency sound radiation from incoherent intensity boundary conditions an energy boundary element analysis ebea formulation is presented for calculating sound radiation at high frequency from a radiator with arbitrary shape the ebea development presented in this paper compliments previous energy finite element analysis efea developments for computing high frequency vibration of structures immersed in an acoustic medium from the efea solution the structural vibrational energy throughout the structure and the acoustic power radiated from each surface element in contact with the surrounding fluid are computed the ebea utilizes the information for the acoustic power radiated from each element of the outer surface of the structure as a boundary condition in order to compute the acoustic field in an unbound medium with no damping that surrounds the radiating structure since the structural vibration between different elements is considered as incoherent in the efea the acoustic intensity associated with each surface element that radiates in the surrounding medium is also considered as incoherent between different elements in the ebea formulation the governing integral equation of ebea is established and a numerical solution is presented the present method is validated by comparing ebea results to analytical solutions and to numerical results from an axi symmetric hp finite element code with infinite acoustic elements suitable for structural acoustic computations good correlation is demonstrated for all the analyses

multiresolution schemes for the reactive euler equations we present multiresolution mr schemes for the efficient numerical solution of the one dimensional system of the reactive euler equations which has possibly stiff source terms the original version of the method was developed by a harten 1995 comm pure appl math 48 12 1305 for homogeneous hyperbolic conservation laws by computing the cell average mr representation of the solution we obtain much information about the solution s regularity this description of smoothness is then used to reduce the number of direct flux computations as well as the expensive high order eno essentially nonoscillatory reconstruction both of which are now performed only near discontinuities thereby the numerical solution procedure becomes considerably more efficient in the present case of the reactive euler equations the average efficiency factor measured by counting the number of actual flux computations ranges from about 5 to 12 this is on the same order of and in some cases comes reasonably close to actual speed up factors obtained by code timings which were between 3 to 5 the mr overhead rate was about 10 for the eno and 36 for tvd schemes respectively the quality of the solution is shown to be the same as that of the finest grid detailed numerical and performance results are shown for up to fourth order accuracy for source terms ranging from moderate to extremely stiff

a bridging domain method for coupling continua with molecular dynamics abstract a bridging domain method for coupling continuum models with molecular models is described in this method the continuum and molecular domains are overlapped in a bridging subdomain where the hamiltonian is taken to be a linear combination of the continuum and molecular hamiltonians we enforce the compatibility in the bridging domain by lagrange multipliers or by the augmented lagrangian method an explicit algorithm for dynamic solutions is developed results show that this multiscale method can avoid spurious wave reflections at the molecular continuum interface without any additional filtering procedures even for problems with significant nonlinearities the method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain a multiple time step algorithm is also developed within this framework

a unified coordinate system for solving the three dimensional euler equations it is well known that the use of eulerian coordinates for shock capturing methods results in badly smeared slip lines and that lagrangian coordinates while capable of producing sharp slip line resolution may result in severe grid deformation causing inaccuracy and even breakdown of computation a unified coordinate system is introduced in which the flow variables are considered to be functions of time and of some permanent identification of pseudo particles which move with velocity hq q being the velocity of fluid particles it includes the eulerian coordinates as a special case when h 0 and the lagrangian when h 1 for two dimensional inviscid flow the free function h is chosen so as to preserve the grid angles this results in a coordinate system which avoids excessive numerical diffusion across slip lines in the eulerian coordinates and avoids severe grid deformation in the lagrangian coordinates yet it retains sharp resolution of slip lines especially for steady flow furthermore the two dimensional unsteady euler equations of gasdynamics in the unified coordinates are found to be hyperbolic for all values of h except when h 1 i e lagrangian in the latter case the euler equations are only weakly hyperbolic lacking one eigenvector although all eigenvalues are real the consequences of this deficiency of the lagrangian coordinates are pointed out in connection with numerical computation

discrete lagrange equations for reacting thermofluid dynamics in arbitrary lagrangian eulerian frames abstract interest in the development of multiscale methods has focused attention on the marked differences in the numerical modeling techniques typically applied at different scales most continuum dynamics models construct approximate solutions to partial differential equations while most nanoscale models employ a discrete hamiltonian approach previous research has demonstrated that the introduction of entropies or internal energies as generalized coordinates along with separation of the discretization and model formulation steps allows general thermomechanical models to be developed at the continuum scale using a nonholonomic hamiltonian or lagrange equation formulation with the introduction of additional state variables and nonholonomic constraints the latter work may be further extended in order to model reacting systems employing a finite element interpolation and a lagrangian an eulerian or an ale mesh the new formulation has been validated by solving several one dimensional reacting shock physics problems the result is a continuum dynamics modeling approach highly compatible with the discrete energy methods normally used at the nanoscale

a judging principle of crucial vibrational transmission paths in plates abstract this paper developed a judging principle of crucial vibrational transmission path vtp in plates novel generalized definitions of vtps are given referred to the meaning of streamlines and by comparing governing equations the similarity between energy flow and fluid motion is firstly found so that an analytic method of vtps in plates is proposed by analogy with fluid motion hereafter the crucial vtp is defined for energy flows at objective points and relative judging criteria is given finally based on two numerical experiments of passive control the judging principle is indirectly verified by comparing the reduction effects of energy flows at focused points and relative judgment results of crucial vtps this paper is meaningful for analyzing and applying the vtps in plates to guide the control design in future

derivatives and perturbations of eigenvectors for a matrix bf a z whose entries are complex valued functions of a complex variable z results are presented concerning derivatives of an eigenvector bf x z of bf a z associated with a simple eigenvalue lambda z when bf x z is restricted to satisfy a constraint of the form sigma bf x z 1 where sigma is a rather arbitrary scaling function the differentiation formulas lead to a new approach for analyzing the sensitivity of an eigenvector under small perturbations in the underlying matrix finally an application is given which concerns the analysis of a finite markov chain subject to perturbations in the transition probabilities

explicit time scale splitting algorithm for stiff problems auto ignition of gaseous mixtures behind a steady shock a new explicit algorithm based on the computational singular perturbation csp method is presented this algorithm is specifically designed to solve stiff problems and its performance increases with stiffness the key concept in its structure is the splitting of the fast from the slow time scales in the problem realized by embedding csp concepts into an explicit scheme in simple terms the algorithm marches in time with only the terms producing the slow time scales while the contribution of the terms producing the fast time scales is taken into account at the end of each integration step as a correction the new algorithm is designed for the integration of stiff systems of pdes by means of explicit schemes for simplicity in the presentation and discussion of the different features of the new algorithm a simple test case is considered involving the auto ignition of a methane air mixture behind a normal shock wave which is described by a system of odes the performance of the new algorithm accuracy and computational efficiency is then compared with the well known lsode package its merits when used for the solution of systems of pdes are discussed although when dealing with a stiff system of odes the new algorithm is shown to provide equal accuracy with that delivered by lsode at the cost of higher execution time the results indicate that its performance could be superior when facing a stiff system of pdes

topology optimization of acoustic structure interaction problems using a mixed finite element formulation the paper presents a gradient based topology optimization formulation that allows to solve acoustic structure vibro acoustic interaction problems without explicit boundary interface representation in acoustic structure interaction problems the pressure and displacement fields are governed by helmholtz equation and the elasticity equation respectively normally the two separate fields are coupled by surface coupling integrals however such a formulation does not allow for free material re distribution in connection with topology optimization schemes since the boundaries are not explicitly given during the optimization process in this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables a u p formulation the helmholtz equation is obtained as a special case of the mixed formulation for the elastic shear modulus equating to zero hence by spatial variation of the mass density shear and bulk moduli we are able to solve the coupled problem by the mixed formulation using this modelling approach the topology optimization procedure is simply implemented as a standard density approach several two dimensional acoustic structure problems are optimized in order to verify the proposed method copyright 2006 john wiley sons ltd

energy flow models from finite element analysis computationally efficient methods are described by which the results of a finite element analysis of a system may be post processed to form energy flow models yielding time and perhaps frequency average subsystem energies as well as input and dissipated powers the methods are particularly efficient for excitation which is spatially distributed or broadband e g rain on the roof or if the frequency average response is required first a method based on a global finite element analysis is presented this involves a global modal decomposition and a reordering of the subsequent numerical calculations the properties of the distribution of the excitation and the system s mass and stiffness lead to subsystem force distribution mass distribution and stiffness distribution matrices the response is given by a sum of terms involving the interaction of a pair of global modes the contribution of each pair depending on the appropriate elements of the distribution matrices frequency averaging is performed by separating the resulting frequency dependent terms and integrating in most practical cases this integration can be done analytically next an alternative method involving component mode synthesis is described in this individual finite element analyses are performed for each subsystem using here the fixed interface method these are then assembled to perform a global modal analysis with the order of the model being much reduced the consequent results are then post processed in the same way finally a system comprising three coupled plates is presented as a numerical example

discrete hamilton s equations for viscous compressible fluid dynamics abstract lagrange s and hamilton s equations are used extensively in numerical modeling of rigid body dynamics and continuum solid dynamics problems the use of energy methods in viscous compressible flow problems has been by contrast rather limited largely confined to the development of basic balance laws in partial differential equation form however finite element interpolation of the modeled flow field allows for the direct application of the discrete form of hamilton s equations to viscous compressible fluid dynamics in eulerian frames the resulting model is a true energy formulation developed without reference to the partial differential balance equations which underlie conventional finite difference weighted residual finite element and finite volume methods

power flow paths in stiffened plates the structural intensity of a rectangular plate with stiffeners attached is calculated using the finite element method the power flow behaviors for the plate with stiffeners attached at various positions are investigated the effects of geometrical properties of stiffeners on the changes of power flow are quantitatively analyzed by numerical integration for the structural intensities a series of calculation results showed that the total amount of injected or transmitted power flow is dependent on the natural vibration frequency of the whole structure and the relative percentage of power flowing through the cross section of the plate or the stiffener depends on the ratio of their relative flexural rigidity

an advanced computational method for radiation and scattering of acoustic waves in three dimensions the method proposed in this paper provides a computational method for implementing the helmholtz integral formula for acoustic radiation and scattering problems associated with arbitrary shaped three dimensional bodies in particular an isoparametric element formulation is used in which both the surface geometry and the acoustic variables on the surface of the body are represented by second order shape functions within the local coordinate system a general formula for the surface velocity potential and the exterior field is derived this result is applicable to nonsmooth bodies i e it includes the case where the surface may have a nonunique normal e g at the edge of a cube test cases are shown involving spherical cylindrical and cubical geometry

models of space averaged energetics of plates the analysis of high frequency vibrations of plates is of particular interest for many cases of structure borne noise in aircraft the current methods of analysis are either too expensive finite element method or may have a confidence band wider than desirable statistical energy analysis an alternative technique to model the spaceand time averaged response of structural acoustics problems with enough detail to include all significant mechanisms of energy generation transmission and absorption is highly desirable the focus of this paper is the development of a set of equations that govern the space and time averaged energy density in plates to solve this equation a boundary value problem must be considered in terms of energy density variables using energy and intensity boundary conditions a verification study of the energy governing equation is performed a finite element formulation of the new equations is also implemented and several tests cases are analyzed and compared to analytical solutions cg d e e 6j f f h k p q q x w 17 v p

parametric design sensitivity analysis of high frequency structural acoustic problems using energy finite element method a design sensitivity analysis of high frequency structural acoustic problems is formulated and presented the energy finite element method efem is used to predict structural acoustic responses in the high frequency range where the coupling between structural junctions and the structural acoustic interface are modelled using power transfer coefficients the continuum design sensitivity formulation is derived from the governing equation of efem and the discrete method is applied in the variation of the structural structural and structural acoustic coupling matrices the direct differentiation and adjoint variable method are both developed for the sensitivity analysis where the difficulty of the adjoint variable method is overcome by solving a transposed system equation parametric design variables such as panel thickness and material damping are considered for sensitivity analysis and numerical sensitivity results show excellent agreement as compared to analytical finite difference results

aggregation disaggregation methods for computing the stationary distribution of a markov chain we implement and analyse aggregation disaggregation procedures constructed to accelerate the convergence of successive approximation methods suitable for computing the stationary distribution of a finite markov chain we define six of these methods and analyse them in detail in particular we show that some existing procedures lie in the aggregation disaggregation framework we set and hence can be considered as special cases also for all described methods we identify cases where they are promising numerical examples for the applications of some of the methods for nearly completely decomposable stochastic matrices are given as well

an acoustic boundary element method based on energy and intensity variables for prediction of high frequency broadband sound fields a boundary element method is formulated in terms of time averaged energy and intensity variables the approach is applicable to high modal density fields but is not restricted to the usual low absorption diffuse and quasiuniform assumptions a broadband acoustic energy intensity source is the basic building block for the method a directivity pattern for the source is derived to account for local spatial correlation effects and to model specular reflections approximately a distribution of infinitesimal uncorrelated directional sources is used to model the boundaries of an enclosure these sources are discretized in terms of boundary elements a system of equations results from applying boundary conditions in terms of incident reflected and absorbed intensity the unknown source power for each element is determined from this system of equations a two dimensional model problem is used to demonstrate and verify the method exact numerical solutions were also obtained for this model problem the results show that spatially varying mean square pressure levels are accurately predicted at very low computational cost

a finite element method for computation of structural intensity by the normal mode approach abstract a method for numerical computation of structural intensity in thin walled structures is presented the method is based on structural finite elements beam plate and shell type enabling computation of real eigenvalues and eigenvectors of the undamped structure which then serve in evaluation of complex response the distributed structural damping is taken into account by using the modal damping concept while any localized damping is treated as an external loading determined by use of impedance matching conditions and eigenproperties of the structure emphasis is given to aspects of accuracy of the results and efficiency of the numerical procedures used high requirements on accuracy of the structural response displacements and stresses needed in intensity applications are satisfied by employing the swept static solution which effectively takes into account the influence of higher modes otherwise inaccessible to numerical computation a comparison is made between the results obtained by using analytical methods and the proposed numerical procedure to demonstrate the validity of the method presented

sensitivity analysis methods for coupled acoustic structural systems part i modal sensitivities an analytical method is proposed for calculating the sensitivities of the eigenvalues and eigenvectors of coupled acoustic structural systems for the purpose of reducing vehicle interior noise the concept of the left and right eigenvectors with regard to the eigenvalue problems of coupled systems is presented first and four propositions concerning this concept are then proved based on these propositions the formulations for the eigenvalue and eigenvector sensitivity analysis of coupled systems are obtained it is shown that the new method provides better convergence than the modal method and modified modal method extensions of these methods to coupled systems and it achieves better calculation efficiency than the extended nelson s method when more than one eigenvector is being considered the theoretical results and computation equations are verified through application of the method to a coupled acoustic box structure and an actual vehicle interior noise problem

a wavelet optimized very high order adaptive grid and order numerical method wavelets detect information at different scales and at different locations throughout a computational domain furthermore wavelets can detect the local polynomial content of computational data numerical methods are most efficient when the basis functions of the method are similar to the data present by designing a numerical scheme in a completely adaptive manner around the data present in a computational domain one can obtain optimal computational efficiency this paper extends the numerical wavelet optimized finite difference wofd method to arbitrarily high order so that one obtains in effect an adaptive grid and adaptive order numerical method which can achieve errors equivalent to errors obtained with a spectrally accurate numerical method

analytical perturbations in markov chains abstract the problem of recomputing the steady state probabilities in a markov chain is considered after a small deviation is introduced to the original infinitesimal generator approximate expressions are developed to calculate the corresponding perturbed vector of probabilities computational stability and accuracy issues associated with the approximation are discussed as an application the perturbation approach is incorporated into an optimization scheme to identify workloads that maximize the output rate in a production line where qualitative and quantitative measures are introduced to control the accuracy of the perturbation

a multidomain spectral method for supersonic reactive flows this paper has a dual purpose it presents a multidomain chebyshev method for the solution of the two dimensional reactive compressible navier stokes equations and it reports the results of the application of this code to the numerical simulations of high mach number reactive flows in recessed cavity the computational method utilizes a newly derived interface boundary conditions as well as an adaptive filtering technique to stabilize the computations the results of the simulations are relevant to recessed cavity flame holders

on the vibrational conductivity approach to high frequency dynamics for two dimensional structural components abstract the vibrational conductivity approach to high frequency dynamics is applied here to the case of two dimensional structural components with this approach an equation which is analogous to the steady state heat conduction equation is used to model the spatial variation of the energy density of the structure it is shown that the standard derivation of the method is incomplete in the sense that the steady state heat conduction equation admits a class of solution which is not encompassed by the assumed form of response and a revised derivation is presented it is further shown that the associated boundary conditions for coupled structural components may be expressed in terms of the coupling loss factors which are used in statistical energy analysis a variational principle for the differential equation and the associated boundary conditions is then derived which permits the application of the rayleigh ritz technique to coupled problems and it is shown that a one term rayleigh ritz solution leads to standard statistical energy analysis the method is applied to a single plate and to two coupled plates and it is found that the technique is unable to provide an accurate estimate of the direct field due to point loading this difficulty is traced to the fact that the assumptions employed in the derivation become self contradictory for this case finally the usefulness or otherwise of the approach as an engineering tool is discussed

topology design optimization of structures at high frequencies using power flow analysis abstract a density based topology optimization method is developed for power flow problems in steady state using an adjoint design sensitivity analysis dsa method design variables such as young s modulus density and damping factor are parameterized using a bulk material density function a generalized compliance of structures defined as the inner product of prescribed loading and response function is selected as an objective function the objective is to minimize the generalized compliance within allowable material volume since already factorized system matrix obtained from the power flow analysis is utilized to evaluate the adjoint response and sensitivity computational cost for the dsa is trivial through several numerical examples the developed dsa method is verified to yield very accurate sensitivity requiring only 0 15 of cpu cost for finite difference sensitivity also it turns out that the developed method can yield an optimal structural layout to transmit the vibrational power effectively

efficient characteristic projection in upwind difference schemes for hyperbolic systems the standard construction of upwind difference schemes for hyperbolic systems of conservation laws requires the full eigensystem of the jacobian matrix this system is used to define the transformation into and out of the characteristic scalar fields where upwind differencing is meaningful when the jacobian has a repeated eigenvalue the associated normalized eigenvectors are not uniquely determined and an arbitrary choice of eigenvectors must be made to span the characteristic subspace in this report we point out that it is possible to avoid this arbitrary choice entirely instead a complementary projection technique can be used to formulate upwind differencing without specifying a basis for systems with eigenvalues of high multiplicity this approach simplifies the analytical and programming effort and reduces the computational cost numerical experiments show no significant difference in computed results between this formulation and the traditional one and thus we recommend its use for these types of problems this complementary projection method has other applications for example it can be used to extend upwind schemes to some weakly hyperbolic systems these lack complete eigensystems so the traditional form of characteristic upwinding is not possible

topological shape optimization of power flow problems at high frequencies using level set approach abstract using a level set method we develop a topological shape optimization method applied to power flow problems in steady state necessary design gradients are computed using an efficient adjoint sensitivity analysis method the boundaries are implicitly represented by the level set function obtainable from the hamilton jacobi type equation with the up wind scheme the implicit function is embedded into a fixed initial domain to obtain the finite element response and sensitivity the developed method defines a lagrangian function for the constrained optimization it minimizes a generalized compliance satisfying the constraint of allowable volume through the variations of implicit boundary during the optimization the boundary velocity to integrate the hamilton jacobi equation is obtained from the optimality condition for the lagrangian function compared with the established topology optimization method the developed one has no numerical instability such as checkerboard problems and easy representation of topological shape variations

a space averaged quadratic method for predicting one dimensional power transfers a method which is based on space averaged quadratic variables and does not assume the restrictive assumptions of the statistical energy analysis sea such as high overlap or damping conditions is described the results are spatially more detailed than an sea response and of a lower computational cost than the one of the usual displacement formulation some of the quadratic variables used like energy densities or structural intensity retain a strong energy meaning even when time and space averaged their governing equation is derived for a homogeneous and isotropic medium with hysteretic damping the main originality of this work lies in considering complex structural intensity and establishing appropriate energetic boundary conditions for both active and reactive space averaged structural intensities by using the usual boundary conditions for the displacement field and the stress tensor the numerical examples prove that this space averaged quadratic method is well suited to describe global energy transfers along one dimensional dissipative structures in a frequency range for which the overlap is too low to obtain a quadratic response from the sea and solving the wave equation by using the finite element method fem would require more elements besides describing junctions with impedances makes the resonant behaviour of the system still accessible on frequency responses

specular and diffuse reflections of rays in coupled thin plates at high frequencies the flexural energy distribution in two right angled point excited thin plates at high frequencies is investigated by means of an integral energy flow approach the fields of energy averaged over time and frequency are described by the superposition of uncorrelated cylindrical waves stemming from both boundaries and direct sources specular and diffuse laws are considered for the reflection and transmission of rays giving rise to two kinds of energy equations the diffuse law leads to a fredholm integral equation over the boundary sources while the specular law is shown to allow an image source solution when the plates have identical propagation properties the algorithm for computing the image position magnitude and directivities is described then some comparisons between the results from the both energy formulations and also from the statistical energy analysis and the numerical solution of the equations of motion are performed with two damped plates at high frequency the non diffuse pattern of the averaged flexural energy fields is well described by the energy flow approaches

complex envelope displacement analysis a quasi static approach to vibrations abstract a new model to analyze high frequency vibrations is presented instead of using the physical oscillating displacement the problem is described in terms of a complex envelope generated by an appropriate use of the hilbert transform the model can be put in the category of those methods that try to describe some representative characteristic of the oscillating solution average energy level thermal trend etc rather than the solution itself avoiding the computational problems connected with high frequency problems although the envelope solution by itself is sufficient and convenient to deal with structural acoustic coupling the proposed model presents the twofold advantage of avoiding computational problem connected with high frequency vibrations while keeping the capability of recovering the oscillating response when required

energy flow analysis and design sensitivity of structural problems at high frequencies the design sensitivity formulation of an energy finite element method is presented using the direct differentiation and adjoint variable methods the continuum method is used to derive the design sensitivity equation of the energy flow equation whereas the discrete method is used to calculate the variation of the coupling relation for design variables material property panel thickness and structural shape are taken into account in addition to the structural damping factor the design variable s effect on the power transfer coefficient is discussed in detail even if the system matrix equation is not symmetric the adjoint problem is solved using the same factorized matrix from response analysis design sensitivity results calculated from the proposed method are compared to the finite difference sensitivity results with a good agreement

a broadband maximum likelihood imager for a class of extended space time separable sources an algorithm is presented that reconstructs the shape of an extended incoherent source using only the broadband signals radiated from the source to a sparse array the source is modeled with a small set of parameters for the specific class of space time separable sources which have similar spatial structure at multiple frequencies the information radiated at each frequency is recombined into a broadband likelihood function in order to improve the estimation of the source parameters expressions for the cramer rao bounds crbs are provided and the performance of the algorithm is demonstrated for a gaussian lump shaped source

a hybrid method for vibroacoustics based on the radiative energy transfer method a hybrid method is proposed to predict the noise radiated in the high frequency range by a structure whose vibratory behavior is rather in the low frequency range this problem meets for instance when the structure radiates inside some closed acoustical spaces the proposed approach is called hybrid as it couples two methods valid on different frequency bands respectively used for the structural and acoustical systems low frequency structural approaches generally provide the velocity field on the vibrating surface while methods adapted to high frequency acoustical studies are based on energy data so the main difficulty for the coupling is a problem of data compatibility in the proposed hybrid method the radiated noise is predicted by using the radiative energy transfer method which is an energy boundary integral method basically equivalent to the known ray tracing method for acoustic applications adequate equivalent energy sources are estimated on the surface of the vibrating structure from the surface pressure and velocity fields these sources are then introduced in the integral equation of the radiative energy transfer method the approach is applied to predict the radiation of a ribbed plate sandwiched between two absorbant panels good agreement is observed with the results given by the boundary element method generally speaking the hybrid method can be considered to apply the radiative energy transfer method for high frequency acoustical predictions from the knowledge of the vibratory behavior of a structure

power flow boundary element analysis for multi domain problems in vibrational built up structures abstract a power flow boundary element methodology for the treatment of multi domain problems is developed to predict the vibrational responses of coupled structures in medium to high frequency ranges in the proposed methodology a matrix equation is formulated by utilizing the power flow coupling relationships at the interface of the domains this analysis method is successfully applied to the treatment of simply supported coupled beams and coupled plates the vibration analysis of these structures is then considered for all wave components the vibrational energy density and intensity of two coupled structures obtained through numerical simulations are compared with those of the original power flow analysis and these results show good agreement

theoretical and numerical structure for unstable one dimensional detonations the spatio temporal structure of unstable detonations in a single space dimension is studied through a combination of numerical and asymptotic methods a new high resolution numerical method for computing unstable detonations is developed this method combines the piecewise parabolic method ppm with conservative shock tracking and adaptive mesh refinement a new nonlinear asymptotic theory for the spatio temporal growth of instabilities is also developed this asymptotic theory involves a nonclassical hopf bifurcation because resonant acoustic scattering states with exponential growth in space cross the imaginary axis and become nonlinear eigenmodes in a complex free boundary problem for a nonlinear hyperbolic equation an interplay between the asymptotic theory and numerical simulation is used to elucidate the spatio temporal mechanisms of nonlinear stability near the transition boundary in particular a quantitative qualitative explanation is developed for the experimentally observed instabilities

high accuracy numerical methods for thermally perfect gas flows with chemistry the compressible navier stokes equations can be extended to model multi species chemically reacting gas flows the result is a large system of convection diffusion equations with stiff source terms in this paper we develop the framework needed to apply modern high accuracy numerical methods from computational gas dynamics to this extended system we also present representative computational results using one such method the framework developed here is useful for many modern numerical schemes we first present an enthalpy based form of the equations that is well suited both for physical modeling and for numerical implementation we show how to treat the stiff reactions via time splitting and in particular how to increase accuracy by avoidng the common practice of approximating the temperature we derive simple exact formulas for the characteristics of the convective part of the equations which are essential for application of all characteristic based schemes we also show that the common practice of using approximate analytical expressions for the characteristics can potentially produce spurious oscillations in computations we implement these developments with a particular high accuracy characteristic based method the finite difference eno space discretization with the 3rd order tvd runge kutta time discretization combined with the second order accurate strang time splitting of the reaction terms we illustrate the capabilities of this approach with calculations of a 1 d reacting shock tube and a 2 d combustor

numerical simulation of shock cylinder interactions i resolution abstract we apply two different high order shock capturing schemes to the study of a two dimensional unsteady inviscid flow in particular we study the interaction of a planar shock with o cylindrical volume of a light gas helium or hydrogen contained in air the two schemes used are the chebyshev collocation method and the eno finite difference scheme of osher and shu and they are applied to a physical model consisting of the euler equations with a real gas equation of state and multiple chemical species the parallel implementation and low level coding of the eno scheme on the thinking machines cm 5 results in much higher performance than is possible on a standard serial or vector machine the eno code is compared with an existing experimental result and agrees well with it the results of spectral and eno calculations are then compared with each other at different resolutions for a mach 2 interaction the spectral scheme though highly oscillatory in nature for discontinuous problems gibbs accurately predicts both large and fine scale structures of the interaction between the shock and the light gas cylinder good results can be recovered from the spectral results by post processing the raw numerical data to remove the gibbs phenomena these results are compared with the eno schemes the comparison is progressively better as the grid refinement and numerical order of the eno scheme is increased this demonstrates definitively the applicability and value of high order schemes to flows with shocks and complicated non linear physics

discrete hamilton s equations for arbitrary lagrangian eulerian dynamics of viscous compressible flow abstract a number of different arbitrary lagrangian eulerian ale formulations of continuum fluid and solid dynamics problems have been developed to address applications where more conventional lagrangian or eulerian modeling techniques are difficult to apply in general these ale formulations are based on finite difference or weighted residual finite element solutions of the partial differential equations for the system an alternative energy based ale model for fluid dynamics simulations may be obtained by direct application of hamilton s canonical equations to a finite element discretization of an open deforming control volume formulated in terms of convected coordinates and incorporating an adaptive mesh scheme this modeling approach yields a simple but general description of viscous compressible flows numerical application of the method demonstrates accurate results in the solution of several shock problems whether the calculations are performed using a lagrangian an eulerian or an ale mesh

spectral methods for hyperbolic problems we review the current state of fourier and chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations throughout the discussion we emphasize recent developments in the area such as spectral penalty methods the use of filters the resolution of the gibbs phenomenon and issues related to the solution of nonlinear conservations laws such as conservation and convergence we also include a brief discussion on the formulation of multi domain methods for hyperbolic problems and conclude with a few examples of the application of pseudospectral collocation methods for solving nontrivial systems of conservation laws

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation