Olivier Bareille

A wave-based design of semi-active piezoelectric composites for broadband vibration control

This paper deals with the design of periodic piezoelectric structures for broadband vibration control. By shunting identical negative capacitances to the periodically distributed piezoelectric patches, a wide and continuous band gap is created so as to cover the frequency range of interest. This way the modal density of the structure is reduced and the modal shapes are localized at the boundaries. A large proportion of the energy can then be removed or dissipated by a small number of dampers or energy harvesters integrated within the negative capacitance circuits. A design process is proposed to achieve the wide band gap. The overall amount of piezoelectric materials is constrained in order to keep mass of structures low. The wave electromechanical coupling factor is proposed and used as a criterion. This allows to reach the largest width of the band gap by using a stable value of negative capacitance. The control of multiple high-order modes of a cantilever beam is considered as an example. The vibration reduction performance of the designed piezoelectric structures is presented and the influences of band gap resonance, resistor and the boundary condition are discussed. The proposed approach is fully based on wave characteristics and it does not rely on any modal information. It is therefore promising for applications at mid- and high frequencies where the access to the exact modal information is difficult.

Dynamic Mechanical Properties and Weight Optimization of Vibrated Ground Recycled Rubber

The aim in this paper is first and foremost to present an experimental method for measuring the dynamic characteristics of granular rubber. Dynamic measurements on recycled granular rubbers are performed here using dynamic mechanical thermal analysis. The Young’s modulus and loss factor of these materials are estimated by using the frequency—temperature equivalence introduced by Williams—Landel—Ferry. It allows us to describe the dynamic properties over a wide range of frequencies. An increase in the wave speed and a decrease in the loss factor were observed with an increase in the frequency for ground tire rubber (GTR) and compound particles obtained by extrusion of GTR—ethylene vinyl acetate blend. However, for recycled polyurethane particles, the loss factor increases with increasing frequency. Then, we investigate the damping efficiency of granular rubbers introduced into a metallic tube, which was subjected to vibrating bending loads. A numerical model is presented to predict the frequency response for the displacement—force function of the tube—particles system. Model prediction is hence validated through a comparison with experimental results. Second, this paper also aims at calculating the optimum weight of granular material with maximum allowable damping effects on tube subjected to bending vibrations. For this purpose, a technique is proposed from the model developed by optimizing the apparent mass of granular material and the dissipation energy of the tube—particles system. Optimization is achieved by a nondominated storing genetic algorithm (NSAG-II). From the results, this technique can be successfully used to optimize the frequency dependence of wave speed and the loss factor of granular rubber with optimized weight.

A low power wireless sensor node with vibration sensing and energy harvesting capability

This paper describes the design of the wireless sensor network node (WSN) for distributed active vibration control (AVC) system for the automotive application. The approach of the system is presented in details. A WSN node using one piezoelectric element provides several features (sensing, shunting and energy harvesting). Integration of the vibration sensing capability for active vibration control system with the energy harvesting capability is described here. Simulation results are compared with the prototype design.

Wave Diffusion Sensitivity to Angular Positions of Defects in Pipes

This paper provides a numerical investigation onto the effect of the angular position of a defect on the wave diffusion in a steel pipe. The wave finite element method (WFEM) is used to calculate reflection and transmission coefficients from defects with different angular positions as a function of frequency. The modeled defects are impinged successively by torsional T(0, 1), longitudinal L(0, 2) and flexural F(1, 2) modes. The wave diffusion in each case is examined leading to several important remarks. Results show that the choice of the incident mode as well as the studied reflected and transmitted modes play a crucial role in the circumferential localization of defects in pipes.

Multimodal wave propagation in smart composite structures with shunted piezoelectric patches

Wave propagation in composite structures with shunted piezoelectric patches is investigated in this study. The wave finite element approach is first developed as a prediction tool for wave propagation characteristics such as dispersion curves in composite structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model. A three-layered composite beam equipped with a pair of resistor–inductor shunted piezoelectric patches is modeled and analyzed carefully with these numerical techniques. Reflection and transmission coefficients of propagating waves in this smart composite structure are calculated, and the performance of shunted piezoelectric patches on the control of wave propagation is investigated numerically with the diffusion matrix model. Another finite element formulation, named modified wave finite element method, which is dedicated to the analysis of wave propagation in multilayered composite structures, is proposed and developed for considering piezoelectric elements in the structures. It is a dynamic substructuring technique that allows the dynamics of a typical layer cross section to be projected on a reduced local wave mode basis with appropriate dimensions. Results issued from this method are compared to those issued from the classical wave finite element and diffusion matrix model formulations to demonstrate the pertinence of the modelings.

Structural Sources Localization in 2D Plate Using an Energetic Approach

This paper is concerned with the localization of structural forces acting in 2D plate at medium and high frequency ranges, through an inverse method based on energy quantities. An energy-based method, called simplified energy method (MES), has already been proposed to predict the energy density field repartition for structural–acoustic problems in mid- and high-frequency ranges. In order to illustrate but also to present one of the applications of this method, this paper presents a formulation to solve inverse structural problems. The main novelty of this paper is to localize the vibration sources in plates, thanks to experimental data of energy densities. The injected forces localization was obtained in the mid–high-frequency range. Experimental investigation was performed to test the validity of the presented technique using different positions of the shaker and measurement points. The experimental results show that the IMES method has an excellent performance in localizing the input forces.

On the Variability of the Sound Transmission Loss of Composite Panels Through a Parametric Probabilistic Approach

A robust model for the prediction of the variability of the vibro-acoustic response is presented in this paper. The dynamic response of composite panels is treated using a Statistical Energy Analysis (SEA) approach. One of the basic input parameters is the propagating flexural wavenumber of the modeled panel. The Wave Finite Element Method (WFEM) is used to investigate the dispersion characteristics of the layered panel. It is based on the evaluation of the mass and the stiffness matrices of a periodic segment of the structure. A polynomial eigenvalue problem is then formed for calculating the wavenumbers and the wave mode shapes. The main novelty in this paper consists in evaluating the influence of the variability of the mechanical parameters of the composite panel on its vibro-acoustic response, that is on its sound transmission loss (STL). This influence is quantified using the generalized polynomial chaos expansion. The efficiency of the approach is exhibited for isotropic and orthotropic panels.

Wave Electromechanical Coupling Factor for the Guided Waves in Piezoelectric Composites

A novel metrics termed the ‘wave electromechanical coupling factor’ (WEMCF) is proposed in this paper, to quantify the coupling strength between the mechanical and electric fields during the passage of a wave in piezoelectric composites. Two definitions of WEMCF are proposed, leading to a frequency formula and two energy formulas for the calculation of such a factor. The frequency formula is naturally consistent with the conventional modal electromechanical coupling factor (MEMCF) but the implementation is difficult. The energy formulas do not need the complicated wave matching required in the frequency formula, therefore are suitable for computing. We demonstrated that the WEMCF based on the energy formula is consistent with the MEMCF, provided that an appropriate indicator is chosen for the electric energy. In this way, both the theoretical closure and the computational feasibility are achieved. A numerical tool based on the wave and finite element method (WFEM) is developed to implement the energy formulas, and it allows the calculation of WEMCF for complex one-dimensional piezoelectric composites. A reduced model is proposed to accelerate the computing of the wave modes and the energies. The analytical findings and the reduced model are numerically validated against two piezoelectric composites with different complexity. Eventually an application is given, concerning the use of the shunted piezoelectric composite for vibration isolation. A strong correlation among the WEMCF, the geometric parameters and the energy transmission loss are observed. These results confirm that the proposed WEMCF captures the physics of the electromechanical coupling phenomenon associated with the guided waves, and can be used to understand, evaluate and design the piezoelectric composites for a variety of applications.

Parameter Identification of a Sandwich Beam Using Numerical-Based Inhomogeneous Wave Correlation Method

To achieve low calculation-cost structural identification process, a numerical-based Inhomogeneous Wave Correlation (IWC) method is proposed in this paper as an extension to the experiment-based IWC. It consists, in a wave propagation framework also called wavenumber space (k-space), on identifying the propagation parameters such as the wavenumber and the spatial damping from the Frequency Response Functions (FRFs) computed using numerical simulations. The proposed method is applied to a sandwich beam with honeycomb cores in flexural vibration. Compared to its implementation based on experimentally-measured FRFs, the proposed numerical-based IWC proves to be an efficient tool for more inner structural parameter identification in wide frequency band with respect to the Mc Daniel method considered as reference.

Inhomogeneous Wave Correlation for Propagation Parameters Identification in Presence of Uncertainties

In order to achieve more realistic structural parameter identification, it is inevitable to account for uncertainties. The present paper proposes a stochastic identification process to identify propagation parameters such as the wavenumber, the damping loss factor, and the wave attenuation, in presence of uncertainties. The proposed stochastic identification process combines, in a wave propagation framework, the Inhomogeneous Wave Correlation method with the Latin Hypercube Sampling method. It is compared to the identification process combining the Mc Daniel method and the Latin Hypercube Sampling method which are considered as reference for structural identification and uncertainty propagation, respectively. An isotropic beam example is considered and identification is done from Frequency Response Functions computed at several measurement points which coordinates are supposed to be the uncertain parameters. The effects of uncertainties on parameter identification are evaluated through statistical quantifications of the variability of the identified parameters. Obtained results show that all identified parameters are affected by uncertainties, except damping.