Time-Domain Boundary Element Methods for the Neumann Problem: A Stable Formulation for Sound Emissions
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In mechanical engineering, structural vibrations are one of the primary causes of sound radiation. With increasing environmental regulations, Noise, Vibration, and Harshness (NVH) analysis has developed into its own engineering discipline. Flexible multibody simulations have proven to be a powerful method for accurately predicting structural vibrations in the time domain. However, in industrial applications, acoustic analyses are typically conducted in the frequency domain. Direct calculation of sound radiation in the time domain is potentially advantageous but fails to achieve stability and thus has not yet found widespread application in engineering practice. The Time-Domain Boundary Element Method (TD-BEM) is particularly attractive for acoustic problems in NVH analysis, as it only requires discretizing the boundary of the vibrating structure, reducing complexity and making the method appealing to small and medium-sized enterprises. This underscores the importance of our research, which focuses on further investigations of a stable boundary integral formulation using the hypersingular boundary integral operator. Our focus lies in applying the method to practically relevant simulation parameters such as geometric complexity, spatial and temporal discretization, and time interval length. The selected objects are examined in various test cases within an anechoic chamber, where they are excited by an electromagnetic shaker under both stationary and transient conditions. The resulting sound radiation is recorded over time using a measurement setup. The same scenarios are calculated using the hypersingular boundary integral operator. This enables direct comparison between experimental and numerical results. Another key focus of our investigations is the long-term stability of the hypersingular boundary integral operator which provides a well-posed and numerically stable framework in theory. In previous publications, this aspect has been marginally addressed, so we conduct simulations for various geometries with several hundred thousand time steps. Compared to other solution approaches, such as second-kind boundary integral formulations using Galerkin discretization or collocation methods, the hypersingular operator demonstrates stable and consistent results even over very long simulation times, highlighting its potential for robust industrial application.
