Spectral Element Approach for Flexural Waves Control in Smart Material Beam With Single and Multiple Resonant Impedance Shunt Circuit

The accurate prediction of the dynamic characteristics of a structure is key to successful vibration control strategies. A typical vibration and wave propagation control is performed through periodic and shunted piezoelectric patches, also known as a smart material. Therefore, the smart metamaterial considers periodic arrangement of shunted piezoelectric patches providing a beam with attenuation properties which depend on the resonant behavior of the shunts. The vibration attenuation occurs due to an elastic-electrical system characterized by an internal resonance of the shunt circuit. The spectral element approach provides very accurate solutions for the structural dynamic response. In this paper, a beam-piezoelectric structure is introduced to focus on the control of flexural waves in beams with piezolayers connected to single and multiresonant shunt approaches. The smart structure is modeled using the spectral element method. It is shown that the effective wavenumber presents the locally resonant behavior at the same frequencies of the vibration attenuation for both single and multishunt approached, indicating that each shunt circuit is independently associated with a attenuation frequency. The spectral element approach presented in this paper shows to be an accurate and simple approach for the design smart metamaterial beams.