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

Abstract

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.

Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia

“…A Bloch analysis has been performed (see e.g. [10,15,16]) on such metamaterial for waves traveling in the ΓX, ΓM and XM of the usual Brillouin zone, as well as for waves traveling in arbitrary directions within the Brillouin zone (see Fig. 3).…”

“…The goal that we want to reach finally is that of characterizing the material behavior of the metamaterial shown in Fig.2 by estimating the value of the elastic parameters appearing in the constitutive expression (1) of the strain energy density. To this aim, we present here the fitting procedure that has been used to superimpose the dispersion curves obtained via the relaxed micromorphic model as solutions of equations (15) to the dispersion curves obtained via the Bloch analysis performed by means of the software COMSOL .…”

Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

“…Periodic structures feature frequency band gaps (also termed the stop bands ) in which certain wave mode (Bloch wave modal shape) cannot propagate and the associated energy flow is forbidden [ 1 , 2 , 3 ]. Such unique wave filtering characteristics can find applications in vibration reduction [ 4 , 5 , 6 ], energy focus [ 7 ] and even acoustic cloaking [ 8 ]. There are three main mechanisms to create a band gap, namely the Bragg scattering, local resonance (LR) and locking phenomena respectively.…”

“…Alternatively, if we introduce piezoelectric materials to the unit cell, and deploy local electric impedance (via the shunting circuits) to the electrodes as shown in Figure 1 ; the electric impedance will be transmitted to the mechanical field and equivalent to for example local stiffness or mass [ 24 , 25 ] thanks to the piezoelectric effects. This provides light-weight and adaptive implementations for the Bragg [ 6 , 26 ] and LR band gaps [ 27 , 28 , 29 , 30 ].…”

Electromechanical wave finite element method for interconnected piezoelectric waveguides

“…Considering one-dimensional media, longitudinal wave propagation was first considered [3,4] and the strategy involving linear resonant shunts was then applied to the control of transverse waves [5][6][7][8][9][10]. The resonant shunts were also replaced by more broadband but not passive solutions as amplified resonant shunts [11,12], switch techniques [13,14] and negative capacitance shunts [15,16]. In all the aforementioned references, a periodicity of the one-dimensional structures enables the use of transfer matrix (TM) formulations to compute propagation constants as well as the global dynamics of the coupled structure [17].…”