Sound transmission through a stiff double-panel structure periodically stabilized by negative stiffness module: Theoretical modeling

Analytic expressions are derived for models predicting the influence of periodically spaced structural links on sound transmission through a double-panel structure. The double panel has been configured to have two sets of structural links: a rib stiffener and negative stiffness component. The stiffener is identical and is spaced periodically at a distance. However, the negative element component is shifted by an amount q from the other set. The dynamic equation of the vibroacoustic of the system is formulated in terms of the space harmonics and by the principle of virtual work. The model is validated by comparing the model predictions with the existing result from the literature. Then, influences of the negative element, engineering safety, offset, and elevation angle are investigated. A new antiresonance with a huge sound transmission loss value can be engineered at the low-frequency region when these parameters are varied. In addition, the application of the stiff model is implemented for a periodic acoustic metamaterial structure. The negative stiffness inclusion can prevent wave propagation at low frequency. The periodic structure can be designed to obtain more and wider frequency bandgaps.