Active vibration control of composite shallow shells: An integrated approach

Active vibration control of smart composite shallow shells with distributed piezoelectric sensors and actuators is presented in this work. An integrated approach is used for recording the uncontrolled and controlled vibration response under pressure impulse load. The FE model developed in ABAQUS is utilized to generate the global mass, stiffness and load matrices of the system. The system matrices are arranged in state space format and the dynamic equations of the system are obtained. The controlled responses are achieved using the inputs from FE model in ABAQUS in conjunction with the developed MATLAB codes for Constant Gain Velocity Feedback (CGVF) and Linear Quadratic Regulator (LQR) control strategies. The method is first validated by comparing the natural frequencies obtained using the ABAQUS generated matrices with that obtained using an FE model with four noded quadrilateral shallow shell element based on efficient zigzag theory. The shell element uses the concept of electric nodes to satisfy the equipotential condition of electrode surface. An 8-noded linear piezoelectric brick element is used for piezoelectric layers and an 8-noded quadrilateral continuum shell element is used for the elastic layers of hybrid shells for making the finite element mesh in ABAQUS. The non-dimensional natural frequencies and active vibration control responses for hybrid composite cylindrical and spherical shells are presented for clamped-clamped and cantilever boundary conditions. Boundary conditions have significant effect on vibration amplitude, control voltage and settling time. In comparison to CGVF controller, a better control in lesser time is achieved with LQR controller for a shell with similar boundary conditions. Larger gain values (G) are required for vibration control of thick shells.