Mathieu Aucejo

Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network

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.

Multimodal coupling of periodic lattices and application to rod vibration damping with a piezoelectric network

An 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 semi-continuous 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. Finally, 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.

Multimodal vibration damping of a plate by piezoelectric coupling to its analogous electrical network

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.

Improving the Patch Transfer Function Approach for Fluid-Structure Modelling in Heavy Fluid

The vibro-acoustic behaviour of elastic structures coupled with cavities filled with a heavy fluid can be modelled by using the Finite Element Method. In order to reduce computing time, the Patch Transfer Function (PTF) approach is used to partition the global problem into different sub-problems. Different types of problem partitioning are studied in this paper. Partitioning outside the near field of structures to reduce the number of patches of the coupling surface for frequencies below the critical frequency is of particular interest. This implies introducing a non standard modal expansion to compute the PTF accurately enough to guarantee the convergence of the PTF method and reduce computation time in comparison to a direct Finite Element resolution. An application on a submarine structure illustrates the interest of this approach.

BAYESIAN FORMULATIONS FOR FORCE RECONSTRUCTION PROBLEMS

To identify mechanical sources acting on a structure, Tikhonov-like regularizations are generally used. These approaches, however, only provide point estimates, meaning that the uncertainty about the regularized solution is not quantified. In practice, such information is essential to guarantee the quality of reconstructed sources. In this contribution, three possible Bayesian formulations of the source identification problem are presented and their limitations discussed. To assess the posterior uncertainty on the parameters appearing in each formulation given a simulated vibration field and a mechanical model, a Gibbs sampler is implemented. The proposed numerical validations highlight the practical interest of these formulations in terms of parameters estimations and posterior uncertainty quantification.

Multimodal vibration damping through a periodic array of piezoelectric patches connected to a passive network

In damping devices involving piezoelectric elements, a single piezoelectric patch cannot consistently achieve multimodal control because of charge cancellation or vibration node location. In order to sense and control structural vibration on a prescribed frequency range, a solution consists in using an array of several piezoelectric patches being small compared to the smallest wavelength to control. Then, as an extension of the tuned mass damper strategy, a passive multimodal control requires to implement a damping system whose modes are as close as possible to those of the controlled structure. In this way, the electrical equivalent of the discretized mechanical structure represents the passive network that optimizes the energy transfer between the two media. For one-dimensional structures, a periodic distribution in several unit cells enables the use of the transfer matrix method applied on electromechanical state-vectors. The optimal passive networks are obtained for the propagation of longitudinal and transverse waves and a numerical implementation of the coupled behavior is performed. Compared to the more classical resonant shunts, the network topology induces promising multimodal damping and a reduction of the needed inductance. It is thus possible to create a completely passive electrical structure as it is demonstrated experimentally by using only purely passive components.

Robustness of a multimodal piezoelectric damping involving the electrical analogue of a plate

Multimodal passive damping of a mechanical structure can be implemented by a coupling to a secondary structure exhibiting similar modal properties. When considering a piezoelectric coupling, the secondary structure is an electrical network. A suitable topology for such a network can be obtained by a finite difference formulation of the mechanical equations, followed by a direct electromechanical analogy. This procedure is applied to the Kirchhoff-Love theory in order to find the electrical analogue of a clamped plate. The passive electrical network is implemented with inductors, transformers and the inherent capacitance of the piezoelectric patches. The electrical resonances are tuned to approach those of several mechanical modes simultaneously. This yields a broadband reduction of the plate vibrations through the array of interconnected piezoelectric patches. The robustness of the control strategy is evaluated by introducing perturbations in the mechanical or electrical designs. A non-optimal tuning is considered by way of a uniform variation of the network inductance. Then, the effect of local or boundary modifications of the electromechanical system is observed experimentally. In the end, the use of an analogous electrical network appears as an efficient and robust solution for the multimodal control of a plate.

Comparison of passive inductor designs for piezoelectric shunt damping

Considering piezoelectric damping, a resonant shunt can lead to a significant vibration reduction when tuned to the mechanical mode to control. However, limits appear when looking at practical applications in a low frequency range: the required inductance is often too high to be satisfied with standard passive components. Moreover, even if the inductor is eventually available, the internal resistance of the component generally exceeds the value which is required for a shunt optimization. Suitable inductors can be designed for applications requiring high inductance and low resistance values. Indeed, the permeance of a magnetic circuit can be significantly increased by the use of closed cores made of high permeability materials. In this paper, three designs are described and compared: an inductor from standard series and two handmade inductors involving a ferrite core and a nanocrystalline toroid. The components are successively integrated into a piezoelectric shunt dedicated to the vibration control of a cantilever beam. Depending on the frequency of the target mechanical mode to control, the benefits and the limits of the different inductors are observed. It is shown that custom designs can definitely extend to lower frequency the application of the passive resonant shunt strategy.

Multimodal Damping of a Plate with a Passive Piezoelectric Network

Multimodal vibration reduction can be obtained by coupling a mechanical structure to an electrical network approximating its modal properties. This strategy is applied to the control of a clamped plate with a 2D network of passive electrical components. The plate and the network are coupled through a periodic array of piezoelectric patches that enables the energy conversion. The network is experimentally implemented with inductors and transformers in order to create electrical resonances that present a spatial distribution approaching the first mode shapes of the plate. By tuning electrical resonances to mechanical ones, it becomes possible to introduce the equivalent of a tuned mass effect. This effect only occurs if the electrical and mechanical mode shapes are sufficiently close, which requires specific network topology and boundary conditions. Once the network is tuned, adding resistors introduces damping that can lead to a broadband vibration reduction of the plate. It is thus shown that a 2D control can be implemented with a purely passive solution, which could be of great interest for many embedded applications.

On a space-frequency regularization for source reconstruction

To identify mechanical sources acting on a structure, Tikhonov-like regularizations are generally used. These approaches, referred to as additive regularizations, require the calculation of a regularization parameter from adapted selection procedures such as the L- curve method. However, such selection procedures can be computationally intensive. In this contribution, a space-frequency multiplicative regularization is introduced. The proposed strategy has the merit of avoiding the need for the determination of a regularization parameter beforehand, while taking advantage of ones prior knowledge of the type of the sources as well as the nature of the excitation signal. By construction, the regularized solution is computed in an iterative manner, which allows adapting the importance of the regularization term all along the resolution process. The validity of the proposed approach is illustrated numerically on a simply supported beam.