Active invisible metamaterial of elastic waves with double targets in a thick plate

Wave invisibility has received increasing attention due to its great theoretical value and application to aerospace, military and other fields. In this work, the invisible flexural cloak for double hole targets in an elastic thick plate is proposed and proportional integral derivative (PID) active control is applied. Based on Mindlin thick plate theory and wave function expansion method, the wave equation for the thick plate is derived and scattering mode coefficients are obtained. The influences of structural and material parameters on dynamic stress concentration, scattering amplitude and scattering cross section (SCS) for double targets are investigated. With the consideration of specific hole targets, the cloaking configuration includes cloaks 1 and 2 and consists of periodically arranged piezoelectric (PZT) patches. Every PZT patch is attached to the active circuit with PID control function. The theoretical and experimental results illustrate that the cloak can achieve an invisible function for double targets within multiple frequency regions. On the other hand, the cloak can reduce the dynamic stress concentration, scattering amplitude and SCS of the thick plate. Different from the original structure without control, the effective frequency range of the PID active cloak can be widely extended.