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.

As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method (WFEM) is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers; the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials (PZT). Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative

Synchronized Switch Damping (SSD) is a semi-active damping technology based on piezoelectric materials. It has advantages such as broadband and no need to tune. Despite the nonlinear governing equations, structures with SSD exhibit quasi-linear behaviour such as the resonant frequencies hardly vary with respect to energy level of excitation. Inspired by these phenomena, in this paper we propose a linearisation method for SSD, where the nonlinear force is equivalent to frequency-dependent viscous damping and linear stiffness coefficients. Closed-form expressions of these linearised parameters are given, making the method applicable both for lumped parameter models and finite element (FE) models. In the derivation a general force equation is used, so the linearised method is applicable for several typical variants of SSD, such as SSDS (S for ‘on short-circuited’), SSDI (I for ‘on inductance’), SSDV (V for ‘on voltage’) and SSDNC (NC for ‘on negative capacitance’). The method is first validated against nonlinear simulations with harmonic and random vibration respectively, then further compared with experimental data in a published paper. Good agreements are found. We show that the proposed method can dramatically accelerate the computational efficiency, which is especially suitable for predicting the dynamic performance of complex structures with SSD. Eventually, a dummy integrally bladed disk with SSD is analysed to illustrate a potential application direction. There are more than 120k DOFs in the FE model, making full nonlinear simulation very time-consuming. However the simulation is finished within seconds by the proposed method and the typical damping characteristics of SSD are well captured.

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.