Dynamical Energy Analysis (DEA) is a mesh-based high frequency method for modelling structure borne sound in complex built-up structures. Vibro-acoustic simulations are performed directly on finite element meshes, circumventing the need for re-modelling strategies. DEA provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. We will present here progress in the development of the DEA method towards handling complex FE-meshes including Rigid Body Elements and sound radiation. We also provide, for the first time, a detailed comparison of the simulations with measurements on a complex engineering structure consisting of the chassis and cabin of a tractor. Both structure borne vibrations and sound pressure levels (SPL) inside the cabin were considered. For the latter, a combined DEA/SEA analysis has been developed. The simulation results compare favourably with measurement results, both for vibration levels measured across the structure and for SPLs inside the cabin.

ABSTRACT Dynamical Energy Analysis (DEA) is a mesh-based high frequency method modelling structure borne sound for complex built-up structures. This has proven to enhance vibro-acoustic simulations considerably by making it possible to work directly on existing finite element meshes circumventing time-consuming and costly remodeling strategies. In addition, DEA provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. DEA was successfully applied and validated to a structure borne sound calculation of an assembled agricultural tractor. Modelling solid structures is still a challenge for DEA, however, as it is based on 2D wave transmission calculations. We propose a novel method to generate DEA elements based on measurement data in order to model solid parts of a complex structure. Advanced Transfer Path Analysis (ATPA) is employed to extract energy transmission characteristics of a structure. First, Frequency Response Functions are measured between interface points on a structure. Then a direct transfer function between interface points is calculated by using ATPA. Finally, DEA elements connecting interface points and representing energy transmission characteristics of the structure are created based on the ATPA result. Applications of the method will be presented.

Dynamical Energy Analysis (DEA) has been introduced as a mesh-based high frequency method modelling structure borne sound for complex built-up structures. This has proven to enhance vibro-acoustic simulations by making it possible to work directly on existing finite element meshes circumventing time-consuming and costly remodeling strategies. In addition, DEA provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. DEA has been used to calculate the structure borne sound of an assembled agricultural tractor and good agreement between measurements and DEA calculations has been shown. In particular, it has been demonstrated that DEA can model shell structures accurately. However, it is still difficult to model a solid structure because currently DEA is based on wave transmission calculations through plate/plate junctions. Additionally, accurate FE meshes of assembled complex structures are often not available due to the uncertainties of modelling welds, bolts and rubber bushes between components. We propose here to integrate measurement data into DEA to improve the effectiveness of DEA modelling. Advanced Transfer Path Analysis (ATPA) is employed to extract energy transmission characteristics of a structure. The direct transfer functions between interface points are calculated using ATPA based on measured frequency response functions. DEA elements connecting interface points and representing energy transmission characteristics of the structure are created based on the ATPA result. The proposed method is verified with a finite element model of a simple structure.

We consider the approximation of the phase-space flow of a dynamical system on a triangulated surface using an approach known as Discrete Flow Mapping. Such flows are of interest throughout statistical mechanics, but the focus here is on flows arising from ray tracing approximations of linear wave equations. An orthogonal polynomial basis approximation of the phase-space density is applied in both the position and direction coordinates, in contrast with previous studies where piecewise constant functions have typically been applied for the spatial approximation. In order to improve the tractability of an orthogonal polynomial approximation in both phase-space coordinates, we propose a careful strategy for computing the propagation operator. For the favourable case of a Legendre polynomial basis we show that the integrals in the definition of the propagation operator may be evaluated analytically with respect to position and via a spectrally convergent quadrature rule for the direction coordinate. A generally applicable spectral quadrature scheme for integration with respect to both coordinates is also detailed for completeness. Finally, we provide numerical results that motivate the use of p-refinement in the orthogonal polynomial basis.

Emissions from modern electronic circuitry are inherently complex and necessarily statistically characterized. The goal in this work is to characterise such emissions as they operate in a realistic environment. When the surrounding environment is electromagnetically large, or complex, the problem of simulating such emissions is further compounded by the intractability of full EM wave modeling: at high enough frequencies, approximate methods based on ray tracing may be the only feasible approach. In this paper, we present a statistical description of fluctuations in the high-frequency response of complex or ray-chaotic cavities to such stochastic sources. It is based on a method proposed in [1], which exploits information available as a byproduct of ray-tracing simulations to predict in addition to the averaged intensity that is typically obtained directly from ray tracing, higher moments which characterize fluctuations about the mean response. This paper extends that approach to provide full statistical distributions of the intensity when damping is moderate and under assumptions that multiple reflections in the surrounding environment are sufficiently randomizing.

We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.

Emission from complex EM sources may be characterised by measurements of two-point correlations functions, which contain directional as well as positional information for radiated power. When such sources radiate within enclosures, the average power arising from multiple reflection can be modelled by ray tracing techniques. In this paper we describe how a bootstrapping method may be employed which exploits information gained as part of such ray-tracing simulations to provide additional information regarding fluctuation about the mean.

Dynamical Energy Analysis (DEA) combined with the Discrete Flow Mapping technique (DFM) has recently been introduced as a mesh-based high frequency method modelling structure borne sound for complex built-up structures. This has proven to enhance vibro-acoustic simulations considerably by making it possible to work directly on existing finite element meshes circumventing time-consuming and costly re-modelling strategies. In addition, DFM provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. We will present here progress in the development of the DEA method towards handling complex FEM-meshes including Rigid Body Elements. In addition, structure borne transmission paths due to spot welds are considered. We will present applications for a car floor structure.

Predicting mid- and high- frequency vibrational energy distributions in vehicle structures has received considerable attention in recent years. The most widely used method at high frequencies is Statistical Energy Analysis (SEA). However, SEA is only valid for high frequencies, low damping and requires a considerable re-modelling effort. Dynamical Energy Analysis (DEA) is an alternative high frequency method that extends the validity of SEA by including information from the underlying ray dynamics and therefore is not limited in terms of damping or re-modelling. In fact, the flexibility of DEA allows for its implementation on existing mesh grids and the geometric simplicity of typical mesh elements facilitates a highly efficient computational strategy known as Discrete Flow Mapping (DFM). In this work we discuss recent developments in DEA and DEM, including high order approximations and the extension to three-dimensional volume elements.

Dynamical Energy Analysis (DEA) in the form of Discrete Flow Mapping (DFM) is a fairly new mesh-based method for numerically modelling structure borne sound transmission in complex structures. A key feature is the possibility to work directly on existing finite element (FE) meshes avoiding time-consuming and costly remodelling. Furthermore, DFM provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. In this work we will illustrate the method using a car floor structure which consists of a big panel and several rails connected by spot welds modeled in FE through Rigid Body Elements (RBE).

We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.

We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they arise in the context of the transport of Bose-Einstein condensates. We specifically show that, extending standard methods for non-interacting systems, the body of the statistical distribution of intensities for scattering states solving the Gross-Pitaevskii equation is very well described by a local Gaussian ansatz with a position-dependent variance. We propose a semiclassical approach based on interfering classical paths to fix the single parameter describing the universal deviations from a global Gaussian distribution. Being tail effects, rare events like rogue waves characteristic of non-linear field equations do not affect our results.