Vibrational energy distribution in plate excited with random white noise
Time: 11:00 am
Author: victor tyrode
Abstract ID: 1712
In Statistical Energy Analysis (SEA) and more generally in all statistical theories of sound and vibration, the establishment of diffuse field in subsystems is one of the most important assumption. Diffuse field is a special state of vibration for which the vibrational energy is homogeneously and isotropically distributed. For subsystems excited with a random white noise, the vibration tends to become diffuse when the number of modes is large and the damping sufficiently light. However even under these conditions, the so-called coherent backscattering enhancement (CBE) observed for certain symmetric subsystems may impede diffusivity. In this study, CBE is observed numerically and experimentally for various geometries of subsystem. Also, it is shown that asymmetric boundary conditions leads to reduce or even vanish the CBE. Theoretical and numerical simulations with the ray tracing method are provided to support the discussion.
Solving linear systems from dynamical energy analysis – using and reusing preconditioners
Time: 12:00 pm
Author: Martin Richter
Abstract ID: 1740
Dynamical energy analysis (DEA) is a computational method to address high-frequency vibro-acoustics in terms of ray densities. It has been used to describe wave equations governing structure-borne sound in two-dimensional shell elements as well as three-dimensional electrodynamics. To describe either of those problems, the wave equation is reformulated as a propagation of boundary densities. These densities are expressed by finite dimensional approximations. All use-cases have in common that they describe the resulting linear problem using a very large matrix which is block-sparse, often real-valued, but non-symmetric. In order to efficiently use DEA, it is therefore important to also address the performance of solving the corresponding linear system. We will cover three aspects in order to reduce the computational time: The use of preconditioners, properly chosen initial conditions, and choice of iterative solvers. Especially the aspect of potentially reusing preconditioners for different input parameters is investigated.
Finite Element Method and Dynamical Energy Analysis in Vibroacoustics A Comparative Study
Time: 12:20 pm
Author: Sebastian Zettel
Abstract ID: 1906
Future aircraft concepts utilizing innovative lightweight structures and novel propulsion concepts are a necessity for long term sustainable air travel. These concepts pose new challenges for the vibro-acoustic assessment of cabin structures and the associated noise impact on passengers. Finite Element (FE) models derived from aircraft pre-design data are not optimized for use in acoustic analyses, i.e. the mesh is too coarse to provide meaningful results while setting up Statistical Energy Analysis models for this specific purpose is adding another time-consuming step. A possible alternative, Discrete Energy Analysis (DEA), is evaluated. This method allows to calculate the acoustic behavior of thin-walled structures in higher frequency ranges simply using existing FE meshes. In this paper an experimental lightweight aluminum structure and its respective FE model is investigated for a frequency range up to 5000 Hz. A comparison in terms of vibrational energy between DEA, FE and measurement results are presented. Finally, a lower-bound frequency range is identified in which DEA and FEM correlate and thus allow a substitution for further simulations at higher frequencies.
Subtractive modeling using the reverse condensed transfer function method: influence of the numerical errors
Time: 11:20 am
Author: Florent Dumortier
Abstract ID: 2186
Decoupling procedures based on substructuring methods allow to predict the vibroacoustic behaviour of a given system by removing a part of an original system that can be easily modelled. The reverse Condensed Transfer Function (rCTF) method has been developed to decouple acoustical or mechanical subsystems that are coupled along lines or surfaces. From the so-called condensed transfer functions (CTFs) of the original system and of the removing part, the behaviour of the system of interest can be predicted. The theoretical framework as well as a numerical validation have been recently published. In the present paper, we focus on the influence of numerical errors on the results of the rCTF method, when the CTFs are calculated using numerical models for the original system and/or the removed part. The rCTF method is applied to a test case consisting in the scattering problem of a rigid sphere in an infinite water domain and impacted by an acoustic plane wave. Discrete green formulation and finite element method are used to estimate the CTFs. Numerical results will be presented in order to evaluate the sensitivity of the method to model errors and the potential promises and limitations of the method will be highlighted.
Development of a hybrid SmEdA/SEA model for predicting the power exchanged between low and high modal density subsystems
Time: 11:40 am
Author: Guang ZHU
Abstract ID: 2535
Statistical modal Energy distribution Analysis (SmEdA) was developed from classical Statistical Energy Analysis (SEA). It allows computing power flow between coupled subsystems from the deterministic modes of uncoupled subsystems without assuming the SEA modal energy equipartition. SmEdA is well adapted in mid-frequency when the subsystems have not a very high modal density. However, for some systems e.g. the plate-cavity system, one subsystem can exhibit a low modal density while the other one a high one. The goal of the paper is then to propose an extension of SmEdA formulation that allows describing one subsystem by its deterministic modes, and the other one as a diffuse field statistically supposing modal energy equipartition. The uncertain subsystem is then characterized by sets of natural frequencies and mode shapes constructed based on Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. This formulation permits not only the computation of mean noise response but also the variance generated by the uncertainties and furthermore without bringing in much computation. It is demonstrated that the obtained analytical results from the proposed hybrid SmEdA/SEA are consistent with numerical results computed by FEM with an appropriate degree of uncertainty.