Expressions of some equations and figures. from Vibroacoustic coupling and sound transmission of mechanical metastructure shell with active feedback control

Lightweight shell structures stiffened by different core layers are widely used and analysed among various industries including aerospace, marine and ocean engineering. In this work, the vibroacoustic coupling and sound transmission of a metastructure shell is studied. Both reinforced by orthogonal rib-stiffeners and local resonators with active control are considered. Cascaded proportional integral (PI) control is applied to reduce steady-state errors and illustrate superior stability. The space harmonic expansion method and principle of virtual work are employed to derive the dynamic effective parameter and sound transmission loss (STL). Results show that the dynamic effective density is affected by the resonator and negative density can be extended as the unit cell increases. STL can be significantly tuned by cascaded PI active control near the resonant frequency of the local resonator. Moreover, finite-element simulation and vibroacoustic experiments are performed to support theoretical predictions and the comparisons exhibit good agreement. This research provides useful vibroacoustic coupling structures for vibration and noise reduction of engineering applications.