Cédric Camier

Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells

The effect of geometric imperfections and viscous damping on the type of nonlinearity (i.e., the hardening or softening behaviour) of circular plates and shallow spherical shells with free edge is here investigated. The Von Karman large-deflection theory is used to derive the continuous models. Then, nonlinear normal modes (NNMs) are used for predicting with accuracy the coefficient, the sign of which determines the hardening or softening behaviour of the structure. The effect of geometric imperfections, unavoidable in real systems, is studied by adding a static initial component in the deflection of a circular plate. Axisymmetric as well as asymmetric imperfections are investigated, and their effect on the type of nonlinearity of the modes of an imperfect plate is documented. Transitions from hardening to softening behaviour are predicted quantitatively for imperfections having the shapes of eigenmodes of a perfect plate. The role of 2:1 internal resonance in this process is underlined. When damping is included in the calculation, it is found that the softening behaviour is generally favoured, but its effect remains limited.

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...

Perceptual evaluation of multichannel synthesis of moving sounds as a function of rendering strategies and velocity

Sound-field synthesis for static sound sources has been extensively studied. Recently, dynamic sound sources synthesis has garnered increased attention. Classical sound-field rendering strategies discretize dynamic sound-fields as a sequence of stationary snapshots. The use of discrete multichannel arrays can generate further artifacts with moving sounds. Depending on the technique used, this results in an amplitude modulation due to successive loudspeaker contributions (VBAP) or in multiple comb-filtering (WFS) which could affect localization cues, especially at off-centered listening positions. We first present a detailed description of these artifacts. We then introduce a hybrid rendering strategy combining propagation simulation and VBAP at audio rate. We used this rendering strategy and WFS to synthesize white noise revolving around listeners on a circular 48-loudspeaker array. On each trial, participants had to identify the trajectory (circle, triangle, or square) for velocities ranging from 0.5 to ...

Fly-over aircraft noise measurement campaign at Montreal-Trudeau airport using a microphone array

Engines being quieter due to high by-pass ratios, the airframe noise, produced for instance by landing gears or high-lift devices, has become a significant contributor to the total noise radiated by aircraft during approach and landing. As part of the investigations carried out to understand noise generation mechanisms, the beamforming techniques developed over the last decade and applied to microphone array measurements have shown to be effective tools for localization and quantification of these aerodynamic noise sources. In order to validate their in-house beamforming softwares, Bombardier Aerospace and the Groupe d’Acoustique de l’Universite de Sherbrooke have conducted a 5-day measurement campaign in June 2012. The 95-microphone array was located on the roof of a building next to the Montreal-Trudeau airport. Aircraft position was determined by two high-definition cameras, both synchronized with the microphone array by inter-range instrumentation group time codes generators. This paper summarizes the...

Nonlinear vibrations of impacted rectangular plates. Comparison between numerical simulation and experiments

Large amplitude vibrations of free‐edge rectangular plates, subjected to an impulse excitation is addressed. In particular, this work is devoted to the analysis and simulation of a nonlinear von Karman plate equations and by associate experimental investigations. Time domain simulations are achieved using implicit finite differences (FD) schemes recently developed by Bilbao. These energy‐conserving methods guarantee the stability of the algorithm. To compare with simulations results, an experimental setup which allows reproducible impulse excitation and measurements by laser vibrometry has been developed. The time history of the force applied to a rectangular steel plate is recorded and this signal is used as excitation term in the simulations. We perform a parametric study, with both experimental and numerical approaches, by increasing gradually the amplitude of forcing. Non‐linear phenomena, such as pitch glide and chaotic behaviour are observed and discussed.

Numerical study of the transition to chaos in nonlinear forced vibrations of plates

Geometrically nonlinear vibrations of free edge circular plates subjected to a harmonic excitation are discussed. Particularly, transition from periodic to chaotic motion is observed when increasing the amplitude of the forcing. The present work is devoted to reproduce numerically these highly nonlinear behaviours. The temporal integration of such dynamics, including instabilities and chaotic regimes, is not straight forward because a stiff problem with a very large number of dofs is at hand. Consequently, numerical instabilities are observed when typical Runge‐Kutta schemes are applied. To settle the matter, two methods have been tested and compared. They both rely on a modal approach applied to the von Karmans model for large amplitude vibrations of plate. For the first one, the energies of the plates are expressed at the continuous level. The Hamiltonian of the system is then derived and discretized using the eigenmodes. The Hamiltonian formulation ensures the conservation of energy. An implicit time ...