Publications

2009

• High-resolution modal analysis
  
  • Ege Kerem
  • Boutillon Xavier
  • David Bertrand
  Journal of Sound and Vibration, Elsevier, 2009, 325 (4-5), pp.852-869. Usual modal analysis techniques are based on the Fourier transform. Due to the Delta T .Delta f limitation, they perform poorly when the modal overlap mu exceeds 30%. A technique based on a high-resolution analysis algorithm and an order-detection method is presented here, with the aim of filling the gap between the low- and the high-frequency domains (30% < mu < 100%). A pseudo-impulse force is applied at points of interests of a structure and the response is measured at a given point. For each pair of measurements, the impulse response of the structure is retrieved by deconvolving the pseudo-impulse force and filtering the response with the result. Following conditioning treatments, the reconstructed impulse response is analysed in different frequency-bands. In each frequency-band, the number of modes is evaluated, the frequencies and damping factors are estimated, and the complex amplitudes are finally extracted. As examples of application, the separation of the twin modes of a square plate and the partial modal analyses of aluminium plates up to a modal overlap of 70% are presented. Results measured with this new method and those calculated with an improved Rayleigh method match closely. (10.1016/j.jsv.2009.04.019)
  DOI : 10.1016/j.jsv.2009.04.019
• Robust filtering for joint state parameter estimation for distributed mechanical systems
  
  • Chapelle Dominique
  • Moireau Philippe
  • Le Tallec Patrick
  Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2009, 23 (1-2), pp.65-84. We present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an $H^\infty$ setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinite-dimensional mechanical system, the $H^\infty$ setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment - using a test problem inspired from cardiac biomechanics - demonstrates the effectiveness of our approach. (10.3934/dcds.2009.23.65)
  DOI : 10.3934/dcds.2009.23.65
• Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions
  
  • Bonnet Marc
  International Journal of Solids and Structures, Elsevier, 2009, 46, pp.2275-2292. This article concerns an extension of the topological derivative concept for 2D potential problems involving penetrable inclusions, whereby a cost function $J$ is expanded in powers of the characteristic size $\varepsilon$ of a small inclusion. The $O(\varepsilon^{4})$ approximation of $J$ is established for a small inclusion of given location, shape and conductivity embedded in a 2-D region of arbitrary shape and conductivity, and then generalized to several such inclusions. Simpler and more explicit versions of this result are obtained for a centrally-symmetric inclusion and a circular inclusion. Numerical tests are performed on a sample configuration, for (i) the O(\varepsilon^{4})$ expansion of potential energy, and (ii) the identification of a hidden inclusion. For the latter problem, a simple approximate global search procedure based on minimizing the $O(\varepsilon^{4})$ approximation of $J$ over a dense search grid is proposed and demonstrated. (10.1016/j.ijsolstr.2009.01.021)
  DOI : 10.1016/j.ijsolstr.2009.01.021
• Le sous-sol peut-il être étanche ?
  
  • Berest Pierre
  • Bérest P.
  , 2009.