Traveling wave control in thin-walled structures through shunted piezoelectric patches

The wave propagation problem in thin-walled elastic structures with shunted piezoelectric patches is investigated in this work. Based on the finite element (FE) method and periodical structure theory, the wave finite element (WFE) approach is firstly developed as a prediction tool for wave propagation characteristics in thin-walled beam structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model (DMM). These numerical techniques enable the calculation of reflection and transmission coefficients of propagating waves in thin-walled structures with shunted piezoelectric patches. The performance of shunted piezoelectric patches on the control of wave propagation is analyzed numerically with the DMM. Forced response of thin-walled structures with shunted piezoelectric patches can also be obtained via the forced wave finite element (FWFE) formulation. With the frequency response issued from the FWFE calculation, the time response of these structures can be acquired via an inverse discrete Fourier transform (IDFT) approach. An extraction technique for reflection coefficient is proposed and can be applied in both numerical simulations and experiments. The formulations proposed in this work are general and can be applied to all types of slender structures. ► Multi-modal wave propagation in thin walled structures. ► Diffusion matrix at interface between assembled thin walled structures. ► Semi-active control through shunted piezoelectric materials. ► Wave propagation control through shunted piezoelectric materials. ► Optimization issues of the reflection and transmission of traveling waves in slender structures.