Elke Deckers

Spline-based boundaries: A first step towards generic geometric domain descriptions for efficient mid-frequency acoustic analysis using the Wave Based Method

The application of numerical simulation techniques for the analysis and optimization of the acoustic behavior of all kinds of products has become very important in almost every phase of a design process. The large computational burden associated with the Finite Element Method (FEM) limits its applicability to low-frequency problems. Recently, the Wave Based Method (WBM) was proposed as an efficient alternative to the element based methods. This method is based on an indirect Trefftz approach, using an expansion of exact solutions of the governing differential equation to describe the dynamic field variables. An important disadvantage of the WBM is the limited geometrical flexibility as compared to the element based techniques. This paper aims to alleviate the geometrical restrictions by using B-splines for the efficient description of curved edges. The introduction of B-splines within the WBM requires an adaptation of the numerical integration procedure used to evaluate the weighted residual formulation. To this end, different types of numerical integration techniques are studied: the Gauss-Legendre and the Romberg integration procedure. A comparative study with the finite element method and the original WBM indicates that the application of B-splines and the adapted numerical integration procedure leads to accurate and computationally affordable WB models.

Acoustic behavior of a rigidly backed poroelastic layer with periodic resonant inclusions by a multiple scattering approach

The acoustic response of a rigidly backed poroelastic layer with a periodic set of elastic cylindrical inclusions embedded is studied. A semi-analytical approach is presented, based on Biots 1956 theory to account for the deformation of the skeleton, coupling mode matching technique, Bloch wave representation, and multiple scattering theory. This model is validated by comparing the derived absorption coefficients to finite element simulations. Numerical results are further exposed to investigate the influence of the properties of the inclusions (type, material properties, size) of this structure, while a modal analysis is performed to characterize the dynamic behaviors leading to high acoustic absorption. Particularly, in the case of thin viscoelastic membranes, an absorption coefficient larger than 0.8 is observed on a wide frequency band. This property is found to be due to the coupling between the first volume mode of the inclusion and the trapped mode induced by the periodic array and the rigid backing, for a wavelength in the air smaller than 11 times the material thickness.

A wave based method to predict the absorption, reflection and transmission coefficient of two-dimensional rigid frame porous structures with periodic inclusions

This paper presents an extension to the Wave Based Method to predict the absorption, reflection and transmission coefficients of a porous material with an embedded periodic set of inclusions. The porous unit cell is described using the Multi-Level methodology and by embedding Bloch-Floquet periodicity conditions in the weighted residual scheme. The dynamic pressure field in the semi-infinite acoustic domains is approximated using a novel wave function set that fulfils the Helmholtz equation, the Bloch-Floquet periodicity conditions and the Sommerfeld radiation condition. The method is meshless and computationally efficient, which makes it well suited for optimisation studies.

Experimental validation of numerical structural dynamic models for metal plate joining techniques

Joined structures are of great industrial relevance. The dynamic effects of joints are, however, often practically difficult to accurately account for in numerical models, as they often lead to local changes in stiffness and damping. This paper discusses the comparison between measurements and simulations of joined panels considering four different joining techniques: adhesive bonding, metal inert gas welding, resistance spot welding and flow drill screwing. An experimental modal analysis is performed on the different systems and the power injection method is applied to determine the loss factors of single plate systems and their joined counterparts. The joined panels are modeled in a holistic simulation environment with particular focus on the joining region, by the application of predefined and generic joint models. A very good agreement is obtained between the simulated dynamic behavior and the experimental results, showing that an accurate representation of the joints has been obtained.

Prediction of transmission, reflection and absorption coefficients of periodic structures using a hybrid Wave Based – Finite Element unit cell method

Abstract This paper presents a hybrid Wave Based Method – Finite Element unit cell method to predict the absorption, reflection and transmission properties of arbitrary, two-dimensional periodic structures. The planar periodic structure, represented by its unit cell combined with Bloch–Floquet periodicity boundary conditions, is modelled within the Finite Element Method, allowing to represent complex geometries and to include any type of physics. The planar periodic structure is coupled to semi-infinite acoustic domains above and/or below, in which the dynamic pressure field is modelled with the Wave Based Method, applying a wave function set that fulfills the Helmholtz equation and satisfies the Sommerfeld radiation condition and the Bloch–Floquet periodicity conditions inherently. The dynamic fields described within both frameworks are coupled using a direct coupling strategy, accounting for the mutual dynamic interactions via a weighted residual formulation. The method explicitly accounts for the interaction between the unit cell and the surrounding acoustic domain, also accounting for higher order periodic waves. The convergence of the method is analysed and its applicability is shown for a variety of problems, proving it to be a useful tool combining the strengths of two methods.