A general analogy mass-spring system analytical model for sound reduction of side-branch resonators.

This study introduces a general analytical model designed to predict the sound reduction frequency of side-branch resonators, regardless of their geometric shapes. Grounded in a continuous analogy mass-spring system, we conceptualize the air within the branch cavity of the resonator as a series of infinitesimal continuous air layers. Each air layer is represented as a mass-spring unit, influenced by the pressure distribution inside the branch cavity. These mass-spring units, following mass conservation principles, are systematically transformed into planar configurations and stacked in a singular direction. These stacked mass-spring units are then converted into an effective one-dimensional mass-spring. Standing wave and the conservation of energy are employed to determine the natural frequency of the effective one-dimensional mass-spring, which corresponds to the sound reduction frequency of the side-branch resonator. This analytical model offers precise predictions for the sound reduction frequencies of side-branch resonators, regardless of their geometric variations. The analytical model can help designers design side-branch resonators in various shapes that accurately target specific sound reduction frequencies in real-world applications. Our analytical model's predictions for sound reduction frequencies were benchmarked against simulations from COMSOL 5.4. The comparative analysis demonstrates the adaptability of the proposed analogy mass-spring system model to side-branch resonators of varied geometric designs. Furthermore, the model exhibits both high predictive accuracy and robustness. Further details and examples will be elaborated upon subsequently.