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Helmholtz resonator coupled with circular membrane
Author(s)
Date Issued
May 15, 2024
Type
Article
Abstract
The Helmholtz resonator is an old yet highly versatile model of various structures. The conventional form of this resonator with rigid surfaces has been extensively studied, and its characteristics are well understood. In many cases, however, the resonator consists of flexible surfaces that readily respond to the changes in the cavity volume, where recent examples include the base structures for acoustic metamaterials and energy harvesters. In the past, several models, including the two-degree-of-freedom lumped-element models, have been proposed to describe the acousto-mechanical coupling within the membrane-coupled Helmholtz resonator (MCH). However, the predictive scope of the previous models was limited only up to the first two modes of vibration, or they were relatively complicated to implement, offering little insight into the relationship between model parameters and output. In this study, a classic model of the circular membrane fitted to an air-tight cavity was modified and extended to predict the resonance characteristics of the MCH. By solving the equations that describe the transverse wave on the membrane and the motion of the equivalent air mass in the port, a conditioning formula was derived, with which the resonance frequencies could be estimated not only at the first two but also at higher modes of vibration. Moreover, the model was found to provide a unified framework for understanding the resonance characteristics and modal patterns of the three related systems: The circular membrane, the circular membrane with air-tight cavity, and the MCH. When validated in a measurement, the proposed model could reasonably predict the resonance frequencies up to the fifth mode of vibration, above 1.5 kHz, where the prediction accuracy was either comparable to or higher than some previous models.
Citation
Applied Acoustics, 221, 2024