Analysis on Modal Distribution and Modal Density-Based Crossover Frequency in Cabin-Sized Enclosures

Abstract

Vehicle cabins, as typical small-scale enclosures, exhibit modal characteristics critical to sound field control. Existing modal property formulations—most notably the Schroeder frequency, which distinguishes sparse and dense modal distributions via simplified modal parameters—were developed for large enclosures. However, their potential inadequacy in capturing the modal properties necessitates validation for small-scale enclosures. To investigate the modal characteristics of cabin-sized enclosures, five models are constructed: three rectangular models with varied aspect ratios and two non-rectangular models mimicking vehicle geometry. Models have volumes of 8 m³ (cabin-sized enclosures) and 80 m³ (serving as reference enclosures). Modal distributions and decay characteristics are obtained using the finite element method to determine the modal density-based crossover frequency (MDCF). It is shown that, the MDCF is roughly 70 to 140 Hz lower than the Schroeder frequency for cabin-sized models with a boundary absorption coefficient of 0.1 (typical of vehicle interiors); this difference decreases in larger enclosures. Furthermore, the MDCF varies across different room geometries, whereas the Schroeder frequency retains consistent across models with same volume. These results indicate that the MDCF directly reflects the sensitivity of modal density to room shape, providing a more precise indicator for characterizing modal density, especially for small enclosures.