On the potential of tuned resonators to obtain low-frequency vibrational stop bands in periodic panels

Over the last decade, Computer Aided Engineering (CAE) tools have become essential in the assessment and optimization of the acoustic characteristics of products and processes. The possibility of evaluating these characteristics on virtual prototypes at almost any stage of the design process reduces the need for very expensive and time consuming physical prototype testing. However, despite their steady improvements and extensions, CAE techniques are still primarily used by analysis specialists. In order to turn them into easy-to-use, versatile tools that are also easily accessible for designers, several bottlenecks have to be resolved. The latter include, amongst others, the lack of efficient numerical techniques for solving system-level functional performance models in a wide frequency range. This paper reviews the CAE modelling techniques which can be used for the analysis of time-harmonic acoustic problems and focusses on techniques which have the Trefftz approach as baseline methodology. The basic properties of the different methods are highlighted and their strengths and limitations are discussed. Furthermore, an overview is given of the state-of-the-art of the extensions and the enhancements which have been recently investigated to enlarge the application range of the different techniques. Specific attention is paid to one very promising Trefftz-based technique, which is the so-called wave based method. This method has all the necessary attributes for putting a next step in the evolution towards truly virtual product design.

/pdf/trefftz-based-methods-for-time-harmonic-acoustics-5bn5orgn5t.pdf

Trefftz-Based Methods for Time-Harmonic Acoustics

The wave based method: An overview of 15 years of research

Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain oscillating basis functions and may achieve better approximation properties than classical piecewise-polynomial spaces. We review the construction and properties of several Trefftz variational formulations developed for the Helmholtz equation, including least squares, discontinuous Galerkin, ultra weak variational formulation, variational theory of complex rays and wave based methods. The most common discrete Trefftz spaces used for this equation employ generalised harmonic polynomials (circular and spherical waves), plane and evanescent waves, fundamental solutions and multipoles as basis functions; we describe theoretical and computational aspects of these spaces, focusing in particular on their approximation properties. One of the most promising, but not yet well developed, features of Trefftz methods is the use of adaptivity in the choice of the propagation directions for the basis functions. The main difficulties encountered in the implementation are the assembly and the ill-conditioning of linear systems, we briefly survey some strategies that have been proposed to cope with these problems.

/pdf/a-survey-of-trefftz-methods-for-the-helmholtz-equation-2zeakrzion.pdf

A Survey of Trefftz Methods for the Helmholtz Equation

Modeling and analysis of an impact-acoustic method for bolt looseness identification

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

A Trefftz-based numerical modelling framework for Helmholtz problems with complex multiple-scatterer configurations

On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach

This paper discusses the use of the Wave Based Method for the analysis of time-harmonic three-dimensional (3D) interior acoustic problems. Conventional element-based prediction methods, such as the Finite Element Method, are most commonly used for these types of problems, but they are restricted to low-frequency applications. The Wave Based Method is an alternative deterministic technique which is based on the indirect Trefftz approach. Up to now, this method's very high computational efficiency has been illustrated mainly for two-dimensional (2D) problem settings, allowing the analysis of problems at higher frequencies. The numerical validation examples presented in this work shows that the enhanced computational efficiency of the Wave Based Method in comparison with conventional element-based methods is kept when the method is extended to 3D case with and without the presence of material damping.

An efficient Wave Based Method for solving Helmholtz problems in three-dimensional bounded domains

https://msvlab.hre.ntou.edu.tw/PDF(cite).files/2010/cmame2010.pdf

Bert Van Genechten

Papers

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

A Trefftz-based numerical modelling framework for Helmholtz problems with complex multiple-scatterer configurations

On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach

An efficient Wave Based Method for solving Helmholtz problems in three-dimensional bounded domains

A multi-level wave based numerical modelling framework for the steady-state dynamic analysis of bounded Helmholtz problems with multiple inclusions