Abstract. A multimodal damping strategy is implemented by coupling a beam to its analogue electrical network. This network comes from the direct electromechanical analogy applied to a transverse lattice of point masses that represents the discrete model of a beam. The mechanical and electrical structures are connected together through an array of piezoelectric patches. A discrete and a semi-continuous model are proposed to describe the piezoelectric coupling. Both are based on the transfer matrix formulation and consider a finite number of patches. It is shown that a simple coupling condition gives a network that approximates the modal properties of the beam. A multimodal tuned mass effect is then obtained and a wide-band damping is introduced by choosing a suitable positioning for resistors in the network. The strategy and the models are experimentally validated by coupling a free-free beam to a completely passive network. A multimodal vibration reduction is observed, which proves the efficiency of the control solution and its potential in term of practical implementation.

This paper addresses the problem of identifying mechanical exciting forces from vibration measurements. The proposed approach is based on a generalized Tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity. To solve such a regularization problem efficiently, a Generalized Iteratively Reweighted Least-Squares (GIRLS) algorithm is introduced. Proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the GIRLS algorithm.

Elastic lattice of point masses can be a suitable representation of a continuous rod for the study of longitudinal wave propagation. By extrapolating the classical tuned mass damping strategy, a multimodal tuned mass damper is introduced from the coupling of two lattices having the same modal properties. The aim of the study is then to implement this multimodal control on a rod coupled to an electrical network. The electromechanical analogy applied to a lattice gives the required network and the energy conversion is performed with piezoelectric patches. The coupled problem is modeled by a novel semicontinuous transfer matrix formulation, which is experimentally validated by a setup involving a rod equipped with 20 pairs of piezoelectric patches. The broadband efficiency of the multimodal control is also experimentally proved with vibration reductions up to 25 dB on the four first resonances of the rod. At last, the practical interest of the network is pointed out as it limits the required inductance. This is confirmed by the present purely passive setup that only involves standard low value inductors.

Additive regularizations, such as Tikhonov-like approaches, are certainly the most popular methods for reconstructing forces acting on a structure. These approaches require, however, the knowledge of a regularization parameter, that can be numerically computed using specific procedures. Unfortunately, these procedures are generally computationally intensive. For this particular reason, it could be of primary interest to propose a method able to proceed without defining any regularization parameter beforehand. In this paper, a multiplicative regularization is introduced for this purpose. By construction, the regularized solution has to be calculated in an iterative manner. In doing so, the amount of regularization is automatically adjusted throughout the resolution process. Validations using synthetic and experimental data highlight the ability of the proposed approach in providing consistent reconstructions.

Multimodal damping can be achieved by coupling a mechanical structure to an electrical network exhibiting similar modal properties. Focusing on a plate, a new topology for such an electrical analogue is found from a finite difference approximation of the Kirchhoff-Love theory and the use of the direct electromechanical analogy. Discrete models based on element dynamic stiffness matrices are proposed to simulate square plate unit cells coupled to their electrical analogues through two-dimensional piezoelectric transducers. A setup made of a clamped plate covered with an array of piezoelectric patches is built in order to validate the control strategy and the numerical models. The analogous electrical network is implemented with passive components as inductors, transformers and the inherent capacitance of the piezoelectric patches. The effect of the piezoelectric coupling on the dynamics of the clamped plate is significant as it creates the equivalent of a multimodal tuned mass damping. An adequate tuning of the network then yields a broadband vibration reduction. In the end, the use of an analogous electrical network appears as an efficient solution for the multimodal control of a plate.

a b s t r a c tThis paper is concerned with the development of a general methodology for identifying mechanical sources from prior local information on both their nature and location over the studied structure. For this purpose, the formulation of the identification problem is derived from the Bayesian statistics, that provides a flexible way to account for local a priori on the distribution of sources. Practically, the resulting optimization problem can be seen as a group generalized Tikhonov regularization, that is solved in an iterative manner. The main features of the proposed identification method are illustrated with both numerical and experimental examples. In particular, it is shown that properly exploiting the local spatial information drastically improves the quality of the source identification.

The resonant piezoelectric shunt requires specific inductance and resistance values in order to reach an optimum in terms of vibration reduction. Yet, practical limits appear in the low frequency range: the required inductance and the corresponding quality factor are often too high to be satisfied with standard passive components. In this paper, inductors are designed with closed magnetic cores made of high permeability materials. Those components are successively integrated into a piezoelectric shunt dedicated to vibration control of a cantilever beam. It is shown that custom designs can definitely extend the application of passive resonant shunt strategies to lower frequency.

Of particular interest is the experimental feasibility of replacing wind tunnel measurements with a substitute experiment to simulate Turbulent Boundary Layer (TBL) induced vibrations. This paper describes the development of an experimental procedure to address this issue. The proposed approach is based on the concept of uncorrelated wall pressure plane waves, which is introduced as a prelude to this study. Concretely, an array of acoustic monopoles can be used to generate these wall pressure plane waves. To this end, the design parameters of the array are studied numerically. However, when dealing with experimental applications, the number of monopoles required being prohibitive, the principle of synthetic array is applied instead. This technique allows simulating the effect of an array of acoustic monopoles from sequential measurements. To assess the validity of the proposed approach, the whole procedure is applied to simulate TBL induced vibrations of a thin elastic plate. The results obtained are in good agreement with those