Robust active sound radiation control of a piezo-laminated composite circular plate of arbitrary thickness based on the exact 3D elasticity model

Abstract

A multi-objective mixed [Formula: see text]2/[Formula: see text]∞ robust output feedback control synthesis with regional pole placement constraints in a linear matrix inequalities framework is adopted for active low-frequency sound radiation control of an arbitrarily thick, rigidly baffled, simply supported, multi-layered piezo-composite circular panel. The adopted control system concurrently captures the benefits of both [Formula: see text]2 transient control performance and [Formula: see text]∞ robust stability in the face of external disturbances and system uncertainties. Also, the implemented volumetric sensing/actuation configuration avoids the typical problems associated with conventional (spatially discrete) piezoelectric sensor/actuator patches, where the total volume velocity can be effectively cancelled with the main contribution being to the long wavelength acoustic power emission. The elasto-acoustic analysis is based on the spatial state-space method in the context of exact 3D elasticity theory along with the Rayleigh integral formula where Neumann’s addition theorem is incorporated in the associated Hankel transform representation to arrive at a computationally efficient expression for the nonaxisymmetric pressure field within the acoustic half-space, valid in both near and far fields. Subspace system identification of the fully coupled structure–fluid interaction problem is performed, and the truncated modes are considered as multiplicative uncertainties in synthesis of the mixed-norm controller. Numerical simulations establish the ability of the implemented volumetric sensing/actuation methodology in cooperation with the multi-objective robust active control scheme for restraining low-frequency sound radiation from a [Formula: see text]/steel/PZT4 circular piezo-laminated plate, without provoking instability of the closed-loop system. Also, superior bandwidth frequency and tracking performance in comparison to the [Formula: see text] and [Formula: see text] controllers are observed. This work is believed to be the first such attempt to exactly model (and actively control) the 3D nonaxisymmetric acousto-elastodynamic frequency response of an arbitrarily thick, smart piezo-laminated circular plate in heavy fluid loading condition (i.e. without using any kind of far-field, low-frequency, and/or light fluid coupling approximations), with straightforward extensibility for any arbitrary through-thickness variation of distributed material properties.