Gilles Tondreau

Piezoelectric vibration damping using resonant shunt circuits: an exact solution

The objective of this paper is to propose an exact closed-form solution to the optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits. Realizing that Den Hartogʼs method which imposes fixed points of equal height in the receptance transfer function is approximate, the parameters of the piezoelectric tuned vibration absorber are calculated through the direct minimization of the maxima of the receptance. The method is applied to a one-degree-of-freedom primary oscillator considering various values of the electromechanical coupling coefficients.

Experimental Localization of Small Damages Using Modal Filters

This work investigates the experimental application of a damage localization technique based on local modal filters on a small clamped-free steel plate equipped with eight piezoelectric (PVDFs) sensors, and excited with a PZT patch. A small damage responsible of a small shift of the eigenfrequencies (less than 4%) is introduced at different locations by fixing a stiffener. By following the guidelines established in previous numerical studies, the modal filters are applied on three local filters in order to locate damage, and a new feature extraction procedure is proposed. Univariate control charts are used to locate automatically all the damage positions correctly. The very nice results obtained with this first experimental application of modal filters based on strains show the real interest of this very simple method for output-only non-model based automated damage localization of real structures.

Equivalent loads for two-dimensional distributed anisotropic piezoelectric transducers with arbitrary shapes attached to thin plate structures

When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamiltons principle and two different mathematical approaches leading to the same results: Greens theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given.

Tuning of a piezoelectric vibration absorber attached to a damped structure

The objective of this paper is to derive an approximate closed-form solution to the H ∞ optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits in the presence of damping in the primary structure. To this end, the homotopy perturbation method (HPM) is utilized in which the zero-order solution is the recently-developed exact solution for an undamped primary system. Simplified, though accurate, expressions for the optimum frequency and damping ratios are also provided.

Towards a more realistic modelling of the uncertainty on identified mode shapes due to measurement noise

Many damage identification methods use the information from mode shapes. In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the mode shapes in the form of independent noise at each measured location. In doing so, the potential spatial correlation in the mode shapes uncertainty is not taken into account. A better approach consists in adding uncorrelated noise on the time domain responses at each sensor before doing the identification. The spatial correlation resulting from the identification can then be evaluated using the covariance matrices of the identified mode shapes. In this study, we apply this approach to the numerical example of a simply supported beam. Modal identification is performed using stochastic subspace based algorithms developed in the toolbox MACEC. The covariance matrices of the mode shapes shows that there is a strong spatial correlation in the mode shapes uncertainty. This result shows that adding independent noise directly on the mode shapes is not a very realistic approach to assess the impact of noise on damage identification methods. The approach used to characterize noise uncertainty on modeshapes identification is totally general and can be applied to any mode, structure or sensing technology.