Actuators are transducers that convert an electrical signal to a desired physical quantity. Active flow control actuators modify a flow by providing an electronically controllable disturbance. The field of active flow control has witnessed explosive growth in the variety of actuators, which is a testament to both the importance and challenges associated with actuator design. This review provides a framework for the discussion of actuator specifications, characteristics, selection, design, and classification for aeronautical applications. Actuator fundamentals are discussed, and various popular actuator types used in low-to-moderate speed flows are then described, including fluidic, moving object/surface, and plasma actuators. We attempt to highlight the strengths and inevitable drawbacks of each and highlight potential future research directions.

Actuators for Active Flow Control

This talk presents the development of an acoustic energy harvester using an electromechanical Helmholtz resonator (EMHR). The EMHR consists of an orifice, cavity, and a piezoelectric diaphragm. When the acoustic wave is incident on the EMHR, a portion of acoustic energy is converted to electrical energy via piezoelectric transduction in the diaphragm of the EMHR. Moreover, the diaphragm is coupled with energy reclamation circuitry to increase the efficiency of the energy conversion. Two power converter topologies are adopted to demonstrate the feasibility of acoustic energy reclamation using an EMHR. The first is comprised of only a rectifier, and the second uses a rectifier connected to a flyback converter to improve load matching. Experimental results indicate that approximately 30 mW of output power is harvested for an incident sound pressure level of 160 dB with a flyback converter. Such power level is sufficient to power a variety of low power electronic devices.

Acoustic energy harvesting using an electromechanical Helmholtz resonator.

This paper describes the development of a micro- machined microphone for aircraft fuselage arrays that are utilized by aeroacousticians to help identify aircraft noise sources and/or assess the effectiveness of noise-reduction technologies. The developed microphone utilizes piezoelectric transduction via an integrated aluminum nitride layer in a thin-film composite diaphragm. A theoretical lumped element model and an associated noise model of the complete microphone system are developed and utilized in a formal design-optimization process. Optimal designs were fabricated using a variant of the film bulk acoustic resonator process at Avago Technologies. The experimental characterization of one design is presented here, and measured performance was in line with sponsor specifications, including a sensitivity of -39 μV/Pa, a minimum detectable pressure of 40.4 dB, a confirmed bandwidth up to 20 kHz, a 129.5-kHz resonant frequency, and a 3% distortion limit approaching 172 dB. With this performance-in addition to its small size-this microphone is shown to be a viable enabling technology for low-cost, high-resolution fuselage array measurements.

An AlN MEMS Piezoelectric Microphone for Aeroacoustic Applications

This paper describes the design, fabrication, and characterization of a bulk-micromachined piezoelectric microphone for aeroacoustic applications. Microphone design was accomplished through a combination of piezoelectric composite plate theory and lumped element modeling. The device consists of a 1.80-mm-diam, 3-microm-thick, silicon diaphragm with a 267-nm-thick ring of piezoelectric material placed near the boundary of the diaphragm to maximize sensitivity. The microphone was fabricated by combining a sol-gel lead zirconate-titanate deposition process on a silicon-on-insulator wafer with deep-reactive ion etching for the diaphragm release. Experimental characterization indicates a sensitivity of 1.66 microVPa, dynamic range greater than six orders of magnitude (35.7-169 dB, re 20 microPa), a capacitance of 10.8 nF, and a resonant frequency of 59.0 kHz.

Development of a micromachined piezoelectric microphone for aeroacoustics applications.

A new class of one-dimensional active acoustic metamaterials (AAMMs) with programmable effective densities is presented. The proposed AAMM is capable of producing densities that are orders of magnitudes lower or higher than the ambient fluid. Such characteristics are achieved by using an array of fluid cavities separated by piezoelectric diaphragms that are controlled to generate constant densities over wide frequency bands. The piezodiaphragms are augmented with passive electrical components to broaden the operating frequency bandwidth and enable densities higher than the fluid medium to be generated. The use of these components is shown to be essential to maintain the closed-loop compliance of the piezodiaphragm away from the zone of elastic instabilities. The values of the passive components are selected on a rational basis in order to ensure a balance between the frequency bandwidth and control voltage. With this unique structure of the AAMM, physically realizable acoustic cloaks can be implemented and objects treated with these active metamaterials can become acoustically invisible.

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The structure of an active acoustic metamaterial with tunable effective density

This paper presents an analytical two-port, lumped-element model of a piezoelectric composite circular plate. In particular, the individual components of a piezoelectric unimorph transducer are modeled as lumped elements of an equivalent electrical circuit using conjugate power variables. The transverse static deflection field as a function of pressure and voltage loading is determined to synthesize the two-port dynamic model. Classical laminated plate theory is used to derive the equations of equilibrium for clamped circular laminated plates containing one or more piezoelectric layers. A closed-form solution is obtained for a unimorph device in which the diameter of the piezoelectric layer is less than that of the shim. Methods to estimate the model parameters are discussed, and model verification via finite-element analyses and experiments is presented. The results indicate that the resulting lumped-element model provides a reasonable prediction (within 3%) of the measured response to voltage loading and the natural frequency, thus enabling design optimization of unimorph piezoelectric transducers.

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Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate

High by-pass turbofan engines have fewer fan blades and lower rotation speeds than their predecessors. Consequently, the noise suppression at the low frequency end of the noise spectra has become an increasing concern. This has led to a renewed emphasis on improving noise suppression efficiency of passive, duct liner treatments at the lower frequencies. For a variety of reasons, passive liners are comprised of locally-reacting, resonant absorbers. One reason for this design choice is to satisfy operational and economic requirements. The simplest liner design consists of a single layer of honeycomb core sandwiched between a porous facesheet and an impervious backing plate. These resonant absorbing structures are integrated into the nacelle wall and are very ef- ficient over a limited bandwidth centered on their resonance frequency. Increased noise suppression bandwidth and greater suppression at lower frequencies is typically achieved for conventional liners by increasing the liner depth and incorporating thin porous septa into the honeycomb core. However, constraints on liner depth in modern high by-pass engine nacelles severely limit the suppression bandwidth extension to lower frequencies. Also, current honeycomb core liners may not be suitable for irregular geometric volumes heretofore not considered. It is of interest, therefore, to find ways to circumvent liner depth restrictions and resonator cavity shape constraints. One way to increase effective liner depth is to skew the honeycomb core axis relative to the porous facesheet surface. Other possibilities are to alter resonator cavity shape, e.g. high aspect ratio, narrow channels that possibly include right angle bends, 180. channel fold-backs, and splayed channel walls to conform to irregular geometric constraints. These possibilities constitute the practical motivation for expanding impedance modeling capability to include unconventional resonator orientations and shapes. The work reported in this paper is in the nature of a progress report and is limited to examining the implications of resonator axis skew on the composite normal incidence impedance of an array of resonator channels. Specifically, experimental results are compared with a modified impedance prediction model for highaspect- ratio, rectangular, resonator channels with varying amounts of skew relative to the incident particle velocity. It is shown that for resonator channel widths of 1 to 2 mm, aspect ratios of 25 to 50, and skew angles of zero to sixty degrees, the surface impedance of test models can be predicted with good accuracy. Predicted resistances and reactances are particularly well correlated through the first resonance and first anti-resonance for all six test models investigated. Beyond the first anti-resonance, the impedance prediction model loses the ability to predict details of resistance and reactance but still predicts the mean trends very well.

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Effect of Resonator Axis Skew on Normal Incidence Impedance

The axisymmetric post-buckling behavior of a circular plate with initial in-plane compression loading is investigated. The von Karman plate equations are solved numerically for a clamped plate and solutions are presented for a range of transverse and in-plane loadings. These solutions can be used to predict the post-buckled behavior of microscale diaphragms. A tradeoff between sensitivity and linearity of post-buckled plates is also discussed.

The Nonlinear Behavior of a Post-Buckled Circular Plate

The dynamic behavior of an axisymmetric post- buckled circular plate with initial in-plane compression loading is investigated. The static von K´ arm´ an plate equations are solved numerically for clamped boundary conditions. The static solution is presented for a range of transverse and in-plane loads. Lumped element modeling is used to calculate the mass and compliance of the plate from results of the static solution. The resonant frequency, sensitivity, and maximum linear transverse pressure are calculated for a variety of in-plane loads. These solutions can be used to predict the post-buckled behavior of micromachined plates.

Vibration of Post-Buckled Homogeneous Circular Plates

*† ‡ † A microelectromechanical systems (MEMS) based piezoresistive microphone optimum design is presented, with a focus on improving the minimum detectable pressure over current technologies without sacrificing bandwidth. This microphone design addresses many of the problems associated with previous piezoresistive microphones. Here, a novel nonlinear circular composite plate mechanical model was employed to determine the stresses in the diaphragm, which was designed to be in the compressive quasi-buckled state. With this model, the inherent in-plane stresses that occur in the microelectronic fabrication process can be used to increase the sensitivity of the device. P-type ion-implanted silicon was chosen for the piezoresistors, and a fabrication recipe was devised that minimizes the inherent noise characteristics of the material. The piezoresistors are arranged in a Wheatstone bridge configuration with two resistors oriented for tangential current flow and two for radial current flow. A lumped element model was created to describe the dynamic characteristics of the microphone diaphragm and the cavity/vent structure. The geometry of this device was optimized with constraints using a sequential quadratic programming scheme. Results indicate a dynamic range in excess of 120 dB for devices possessing resonant frequencies beyond 120 kHz.

Brian Homeijer

Papers

Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate

Effect of Resonator Axis Skew on Normal Incidence Impedance

The Nonlinear Behavior of a Post-Buckled Circular Plate

Vibration of Post-Buckled Homogeneous Circular Plates

Design of a MEMS Piezoresistive Microphone for use in Aeroacoustic Measurements