Application of boundary elements in the optimization of noise barriers

Abstract

The Boundary Element Method (BEM) arises as the most suitable technique in the study of outdoor sound propagation prediction [1-3]. However, the exclusive implementation of the Method in its classical formulation makes the study of certain barrier configurations unaffordable in many cases. On one hand, fictitious frequencies (representing the natural frequencies of the barrier) may be revealed when dealing with non-thin configurations. On the other hand, the complexity normally associated with some barrier designs raises the need to consider some geometric simplification to ease their assessment. A proper solution to tackle these challenges demands a specific BE formulation. In this respect, the so-called Dual BEM approach (a BE formulation that combines the standard singular integral equality of the Method with a hyper-singular variant -obtained by derivation of the former-) arises as the most appropriate strategy involving BE to address the proposed problems numerically by allowing us 1) to assume a simplification of reality by idealizing very thin elements as null-thickness type, greatly facilitating the geometric definition of complex configurations with no substantial influence on the acoustic performance for the considered thickness of very thin sections [4] (widely present in diverse barrier designs) and 2) to mitigate the fictitious eigenfrequencies associated with the inner domain of the barrier that may adversely affect to the assessment of the screening efficiency. In dealing with these issues with BE often results, according to the individual case, in serious numerical drawbacks if not to a singular system of equations when dealing with the idealization of very thin elements. Depending on the geometric nature of the barrier, the Dual approach is applied differently to enable us to deal with: i) volumetric barrier designs. It is the case of real barriers featuring thick elements, such as M-shaped barriers; ii) very thin barriers. The assessment of these types of barriers is performed by idealizing the whole design as a single-wire body –see Image 1(a)–; iii) volumetric barriers featuring very thin elements. It is a mixed case. The general configuration remains its real geometry while the very thin elements are idealized and studied as null- thickness type –see Image 1(b).

This contribution intends to be an overview of the achievements made so far by the authors of this work in this research line, framed into a methodology involving the coupled use of Boundary Elements (BE) and Evolutionary Algorithms for the systematic geometric modifications of road barriers in pursuing ever- increasing performance.