Coupled efficient layerwise finite element modeling for active vibration control of smart composite and sandwich shallow shells

The active vibration suppression of smart composite and sandwich shallow shells equipped with distributed monolithic piezoelectric and piezo-fiber reinforced composite (PFRC) sensors and actuators is studied using a four-node quadrilateral shallow shell element based on a fully coupled, accurate and efficient layerwise (zigzag) theory. The shell element uses the concept of electric nodes to satisfy the equipotential condition of electroded sensor surfaces without making any approximations or averaging. The effective electromechanical properties of the PFRC laminas are computed using a coupled three-dimensional iso-field micromechanical model. Both classical (constant gain velocity feedback (CGVF)) and optimal (linear quadratic Gaussian (LQG)) control strategies are studied. A truly collocated actuator-sensor arrangement is proposed and shown to remove the instability in CGVF control of shallow shells with conventionally collocated actuators and sensors. The effects of piezoelectric fiber orientation and volume fraction ratio of PFRC, and the radius of curvature and span to thickness ratio of the shell on the control performance, are studied. It is shown that the LQG control not only suppresses the transient vibration under step/impulse excitations, but also eliminates the beating phenomena under harmonic excitation when the forcing frequency is close to the natural frequency of the system.