Yann Pasco

A hybrid analytical/numerical model of piezoelectric stack actuators using a macroscopic nonlinear theory of ferroelectricity and a Preisach model of hysteresis

Hysteretic behavior of polarized piezoelectric materials is of importance in the context of high power electro-mechanical transduction. The main goal of this article is to combine the Tiersten theory of electroelasticity and a Preisach model of hysteresis to model a simple force loaded piezoelectric actuator. The proposed theory of piezo-ferro-elasticity extends the derivation of Tiersten and Huang to the case of an arbitrary polarization direction in the ferroelectric domain. The general model is subsequently reduced to a mono-dimensional stack actuator under low operating voltage; therefore, the modeling focuses on minor loop modeling around the initial state of polarization. The model of hysteresis between polarization and electric field proposed here takes into account the nonlocal (macroscopic) memory of a piezoelectric ceramic by the use of a Preisach model. The Preisach model of hysteresis and the set of new ferro-electro-elastic constants that account for the irreversible relation between electric field and polarization are identified through experiments. The nonlinear model successfully reproduces the nonlinear dependence of generated displacements and forces as a function of applied electric field. Possible applications of this work involve nonlinear actuator behavior in the active control of vibration.

Optimizing the Thickness of Piezoceramic Actuators for Bending Vibration of Planar Structures

An analytical approach is proposed to optimize the thickness of piezoceramic (PZT) actuators bonded on structures for active shape, noise, or vibration control. The optimal thickness corresponds to maximal mechanical coupling between the PZT actuator and the substrate. The analysis is carried out for a planar geometry, considering a square simply supported flexural plate with a square and a centered PZT actuator bonded either in symmetric or asymmetric configuration. Optimal thicknesses obtained from explicit analytical expressions are compared with finite element (FE) results for various substrate thicknesses and for various values of actuator coverage ratio. Static and dynamic strain profiles through the thickness of the plate—actuator system are plotted. Laboratory experiments are carried out on aluminum and steel plates with free and clamped boundary conditions to verify the analytical and FE predictions in terms of optimal PZT actuator thickness.

Active noise control simulation of tonal turbofan noise in aero engines

Active Noise Control (ANC) of the tonal noise of a turbofan engine is introduced using active stator vanes and rings of loudspeakers as control actuators. It involves a unique coupling of two original analytical and numerical models for the primary and secondary sources respectively, and two different control strategies that attempt to independently control the propagative acoustic modes upstream and downstream for the first time. The primary noise source is based on the analytical model recently developed by De Laborderie that deals with rectilinear cascade responses due to wake-interaction applied in a strip theory framework. Good agreement with both numerical and experimental data is found on the blade pressure jumps. The secondary noise sources induced by the piezo-actuators embedded in the stator blade are shown to behave as compact dipoles that are radiating in an annular duct. The corresponding radiation can be obtained either numerically or analytically. Here the propagation is computed numerically using COMSOL. The noise control strategy can either Singular Values Decomposition (SVD) or Generalized Singular Values Decomposition (GSVD) without any knowledge on the physical form of the acoustic field. Simulation results are shown to achieve some significant tonal noise reduction and it is demonstrated that the GSVD is a great avenue to separate inlet and outlet radiation. Introduction Tonal noise from rotor/stator interaction in aircraft engines is predominant during landing and take-off phases of civil aircraft. Active Noise Control (ANC) is one of the solutions developed since the early 1990s to reduce tonal turbofan noise. Currently, most of published results rely on experimental data1,2, 3, 4, 5 but some analytical and numerical models were also developed.6,7, 8, 9 Sound Pressure Level (SPL) reductions from 3 to 20 dB at the Blade Passing Frequency (BPF) were obtained, most of them by using modal decomposition with feedforward control for low radial mode orders. Yet these configurations were too constrained in terms of weight and energy consumption to complete industrial implementation. Also, the available processing power was unsufficient at that time to reach the requested sampling rate for active control implementation. The next decade brought new advances in digital signal processing, especially the Field Programmable Gate Array (FPGA) hardware10 and new control algorithms like the Principal value Orthogonal Decomposition (POD). In 2006, ANC with aeroacoustic control sources provided a SPL reduction of up to 20.5 dB at the BPF.11 The latest advances were pursued in 2009 by the German Aerospace Center (DLR).12 An Ultra High Bypass Ratio (UHBR) turbofan was tested with a rotating rake for the modal decomposition, microphone rings as error sensors and loudspeaker rings as secondary sources, all among the stator vane cascade. Active control was implemented with a feedforward algorithm and POD for up to 32 dB in Sound Power Level (PWL) reduction for the azimuthal mode m = 6. ∗Research associate, GAUS, Mechanical Engineering Department, yann.pasco@usherbrooke.ca †Post-doctorate fellow, Mechanical Engineering Department, thomas.guedeney@usherbrooke.ca ‡MSc student, GAUS, Mechanical Engineering Department, arnaud.leung-tack@usherbrooke.ca §Professor, GAUS, Mechanical Engineering Department ¶Professor, Mechanical Engineering Department, AIAA Lifetime Member

Interior sound field control using generalized singular value decomposition in the frequency domain

The problem of controlling a sound field inside a region surrounded by acoustic control sources is considered. Inspired by the Kirchhoff-Helmholtz integral, the use of double-layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers. However, the practical implementation of the Kirchhoff-Helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions. The present study investigates the potential of the Generalized Singular Value Decomposition (GSVD) to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields, respectively. A proper truncation of the singular basis provided by the GSVD factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial Nyquist frequency of the control sources array while leaving the exterior sound field almost unchanged. Proofs of concept are provided through simulations achieved for interior problems by simulations in a free field scenario with circular arrays and in a reflective environment with square arrays.

Aircraft sound environment reproduction: Sound field reproduction inside a cabin mock-up using microphone and actuator arrays

Sound environment reproduction of various flight conditions in aircraft cabin mock-ups is useful for the design, demonstration, and jury testing of interior aircraft sound quality. To provide a faithfully perceived sound environment, time, frequency, and spatial characteristics should be preserved. Physical sound field reproduction approaches for spatial sound reproduction are mandatory to immerse the listener in the proper sound field so that localization cues are recreated. A 80-channel microphone array was built and used to capture a 2-h recording of in-flight sound environments within an actual Bombardier CRJ aircraft. An instrumented cabin mock-up was used to reproduce, in the least-mean-square sense, the recorded sound field using a 41-channel trim-panel actuator array. In this paper, experiments with multichannel equalization are reported. One of the practical difficulties was related to the use of the trim panels as sound sources. Windows and trim panels introduce audible squeaks and rattles if drive...

Experimental and numerical study of the noise generation in an outflow butterfly valve

The present study focuses on the noise generation mechanisms in outflow valves, which are commonly used in airplanes in order to regulate the cabin pressure and maintain a safe environment for the passengers. In order to make a detailed flow and acoustic investigation, experimental and numerical data are collected on a simplified 2D butterfly valve installed in a rectangular transparent channel. Two operating points are investigated : (a) a transient operating point at a flight altitude of 17 000 feet, where a high level tonal noise has been reported and creates acoustic nuisances in the cabin ; (b) the cruise condition operating point, that corresponds to a flight altitude of 40 000 feet, and where broadband noise may be reduced. Measurements of the far field noise and the wall static pressure as well as high speed Schlieren flow visualization are performed. They hightlight the very complex structure of the flow. Expansion waves and shock cells are observed at the upstream and downstream edges of the seal step, which are possible sources of tonal noise. Vortex shedding have also been observed for the transonic case, and might also generate tonal noise. In order to get a better understanding of the noise generation mechanisms, three-dimensional simulations of the experimental set-up are performed. They rely on steady or unsteady Reynolds-Averaged Navier-Stokes (Scale-Adaptive Simulations) computations and Large Eddy Simulations. All numerical results compare well with experiments on the mean flow. The unsteady simulations reveal strong shock oscillations on the forward-facing corner of the valve step and consequent strong vortex shedding when the jet shear layer interacts with this shock. The observed tonal noise is related to these two mechanisms and the shear layer instability upstream of the step, and the expansion fan on the backward-facing corner of the step. The LES also shows strong higher frequency peaks not yet available in the measurements that are clearly seen as the dominant noise-radiation mechanisms upstream of the valve in the dilatation field.

Singular value decomposition of plant matrix in active noise and vibration—some examples

In active noise and vibration control problems that involve many secondary sources and error sensors, the active control performance is largely related to the conditioning of the plant matrix (formed by the transfer functions between individual secondary sources and error sensors). The principal component transformation (or singular value decomposition) of the plant matrix is an interesting tool to extract dominant secondary paths and limit control efforts. Furthermore, it can be used in a feedforward LMS controller to prevent slow convergence due to ill‐conditioning of the plant matrix, and adjust the convergence rate of individual system modes. This approach is discussed through two different applications: (1) the multi‐harmonic active structural acoustic control of a helicopter main transmission noise using piezoceramic actuators; (2) the broadband, adaptive sound field synthesis using multiple reproduction sources. It is shown that the approach allows decreasing the required signal processing and limi...

A new analytic model of piezoelectric stack actuators including ferroelectric nonlinearities

The proposed numerical modeling of piezoelectric phenomena combines a mathematical model of hysteresis and a macroscopic theory of ferroelectricity including the nonlinear effect of polarized ceramics. Most of the time, modeling is sought between applied electric field versus displacement. Such an analytic model does not take into account ferroelectric phenomena and as a consequence never gives information about ferroelectric characteristics of ceramics, but gives a simple model of the ceramics’ behavior. Another advantage of the new model is that it can still be accurate even if the ceramic is blocked in force. In order to simplify equations, the quasistationarity of electric field is assumed and three‐dimensional equations will be reduced to a one‐dimensional stack actuator. Such a model could be used in active control of vibrations.