This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

The classical Equivalent Radiated Power (ERP) approximation, while computationally efficient for early-stage acoustic performance assessment, has known limitations, particularly at low Helmholtz numbers where it tends to overpredict acoustic power radiation. This paper introduces an improved method called "Radiation Efficiency Varying Equivalent Radiated Power" (revERP), which significantly enhances the accuracy of classical ERP while maintaining its computational advantages. The revERP method introduces a geometry-, frequency-, and vibration pattern-dependent approximation of radiation efficiency as a corrective factor for classical ERP calculations. This approximation is developed through two key innovations: First, a characteristic size of the vibrating body is approximated using a simple optimizations scheme to fit a virtual spherical surface to the vibrating body. Second, the radiation efficiency is approximated using a weighted average of analytical solutions for spherical multipoles, based on spherical harmonic decomposition. The revERP method may be viewed as a simple post-processing step, requiring no other information than what is already required in the classical ERP approximation. Enabled by the highly efficient modern algorithms for evaluating special functions (notably for the current method Spherical Hankel functions, Legendre Polynomials and Bessel functions) as well as modern algorithms for performing fast spherical harmonic decomposition, the revERP method adds negligible computation time to the classical ERP approximation. Most notably, the revERP method requires no surface integrals to be evaluated. Numerical tests on components of industrial complexity demonstrate that revERP significantly outperforms classical ERP, particularly at low Helmholtz numbers. The method converges to classical ERP at high frequencies, preserving its known accuracy in this regime. While the method shows limitations for bodies with large aspect ratios or locally resonant subsystems, it provides a valuable compromise between accuracy and computational efficiency for early-stage acoustic performance prediction in product development. The accompanying paper contributes to the field of numerical acoustics by providing a physically-principled enhancement to a widely-used engineering approximation, enabling more reliable early-stage acoustic assessments without sacrificing the computational efficiency that makes ERP valuable in industrial applications.