Sound transmission control through a hybrid smart double sandwich plate structure

A three-dimensional analytical model is developed for control of sound transmission through an acoustically baffled simply supported hybrid smart double sandwich panel partition of rectangular planform. The hybrid structure includes spatially distributed piezoelectric (PZT) and electro-rheological fluid (ERF) actuator layers arranged in a non-collocated configuration in the incident or transmitted panels. The basic formulation utilizes the relevant classical thin plate theories, Kelvin-Voigt viscoelastic damping model, Maxwell’s equations of electrodynamics, and the linear acoustic wave equations coupled by the pertinent structure/fluid compatibility relations. The conventional multi-input multi-output sliding mode control (MIMOSMC) strategy is subsequently applied to improve the sound transmission loss (STL) through the composite partition by smart (semi-active) variation of the stiffness/damping characteristics of the ERF core layer in collaboration with the (active) uniform force PZT actuator layer according to the control commands. Extensive numerical simulations present both the uncontrolled and controlled STL performances of the composite sandwich structure for four different arrangements of the active and semi-active control elements (i.e. PZT/PZT, ERF/ERF, ERF/PZT, and PZT/ERF) as well as for the single partition (ERF, PZT) sandwich panels at selected incident angles and air cavity dimensions. Four different types of vibroacoustic resonances for the composite structure are identified and briefly discussed, namely, the mass-air-mass resonance, the sandwich panel resonances, the cavity standing-wave resonances, and the coincidence resonance. The remarkable overall advantages of all four MIMOSMC-based double panel control configurations in significant attenuation of sound transmission at very low frequencies, and in the vicinity of the coupled mass-air-mass resonances as well as at the panel resonance frequency dips, are demonstrated. In particular, the proposed hybrid smart double panel (ERF/PZT or PZT/ERF) configuration (which integrates the high performance, precision, and capability of the active PZT-based panel with simplicity, reliability, and stability robustness of the semi-active ERF-based panel) is observed to display a considerably smoother broadband sound proof ability in comparison with the conventional full active (PZT/PZT) system. More importantly, it is particularly capable of delivering up to 90% of the full active control performance, with inherently less energy and actuation demands. Limiting cases are considered and validity of the formulation is rigorously confirmed by comparison with the FEM results as well as with the available data.