Multi-modal wave propagation in smart structures with shunted piezoelectric patches

The propagation of wave modes in elastic structures with shunted piezoelectric patches is dealt with in this work. The wave finite element approach, which is based on the finite element method and periodical structure theory, is firstly developed as a prediction tool for wave propagation characteristics in beam like structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model (DMM). With these numerical techniques, reflection and transmission coefficients of propagating waves in structures with shunted piezoelectric patches can be calculated. The performance of shunted piezoelectric patches on the control of wave propagation is investigated numerically with the DMM. Forced response of the smart structure can also be calculated, and based on which the time response of the structure can be obtained via an inverse discrete fourier transform approach. These general formulations can be applied to all types of slender structures. All these numerical tools can facilitate design modifications and systematic investigations of geometric and electric parameters of smart structures with shunted piezoelectric elements.