A tunable electromechanical Helmholtz resonator

Acoustic liners are used in turbofan engine nacelles for the suppression of engine noise. For a given engine, there are different optimum impedance distributions associated with take-off, cut-back, and approach flight conditions. The impedance of conventional acoustic liners is fixed for a given geometry, and conventional active liner approaches are impractical. This project addresses the need for a tunable impedance through the development of an electromechanical Helmholtz resonator (EMHR). The device consists of a Helmholtz resonator with the standard rigid backplate replaced by a compliant piezoelectric composite. Analytical models (i.e., a lumped element model (LEM) and a transfer matrix (TM) representation of the EMHR) are developed to predict the acoustic behavior of the EMHR. The EMHR is experimentally investigated using the standard two-microphone method (TMM). The measurement results validate both the LEM and the TM of the EMHR. Good agreement between predicted and measured impedance is obtained. Short- and open-circuit loads define the limits of the tuning range using resistive and capacitive loads. There is approximately a 9% tuning limit under these conditions for the non-optimized resonator configuration studied. Inductive shunt loads result in a 3 degree-of-freedom (DOF) system and an enhanced tuning range of over 47% that is not restricted by the short- and open-circuit limits. Damping coefficient measurements for a piezoelectric backplate in a vacuum chamber are performed and indicate that the damping is dominated by structural damping losses. A Pareto optimization design based on models of the EMHR is performed with non-inductive loads. The EMHR with non-inductive loads has 2DOF and two resonant frequencies. The tuning ranges of the two resonant frequencies of the EMHR with non-inductive loads cannot be optimized simultaneously, so a trade-off (Pareto solution) must be reached. The Pareto solution shows how design trade-offs can be used to satisfy specific design requirements. The goal of the optimization of the EMHR with inductive loads is to achieve optimal tuning of the three resonant frequencies. The results indicate that it is possible to keep the acoustic reactance of the resonator nearly constant within a given frequency range.