Olivier Thomas

FORCED VIBRATIONS OF CIRCULAR PLATES: FROM PERIODIC TO CHAOTIC MOTIONS

e ∗ Unit´ e de M´ ecanique (UME) ENSTA-ParisTech Chemin de la Huni` ere ABSTRACT A numerical study of the transition from periodic to chaotic motions in forced vibrations of circular plates, is propose d. A pointwise harmonic forcing of constant excitation frequen cy Ω and increasing values of the amplitude is considered. Perfe ct and imperfect circular plates with a free edge are studied wi thin the von K´ arm´ an assumptions for large displacements (geometric non-linearity). The transition scenario is observed for di fferent excitation frequencies in the range of the first eigenfreque ncies of the plate. For perfect plate with no specific internal resona nce re- lationships, a direct transition to chaos is at hand. For imp erfect plate tuned so as to fulfill specific internal resonance relations, a coupling between internally resonant modes is first observ ed. The chaotic regime shows an attractor of large dimension, an d thus is studied within the framework of wave turbulence.

Fabrication and characterization of mechanical resonators integrating microcontact printed PZT films

We report on the fabrication and characterization of lead zirconate titanate (PZT)-coated cantilever resonators for the realization of piezoelectric nanoelectromechanical systems (NEMS) with integrated actuation and detection capabilities. PZT is deposited by microcontact printing, resulting in a relatively thin PZT film without deterioration of its piezoelectric properties induced by etching damage. The cantilever fabrication process is based on stepper ultraviolet lithography and standard micromaching. Electrical characterization was carried out with a dedicated electrical set-up enabling the devices resonance frequency to be detected through the piezoelectric response. These characterizations validate the simultaneous actuation and detection capability of the PZT layer. Finally, modeling of the PZT cantilever results in the estimation of the piezoelectric coupling coefficient d*31. We have found excellent large signal d*31 of around 200 pm/V, even for PZT cantilevers with reduced dimensions.

Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.