Active control of geometrically non-linear transient response of sandwich beams with a flexible core using piezoelectric patches

Active control of geometrically non-linear dynamic response of sandwich beams impacted by blast pulses with integrated piezoelectric sensor/actuator patches is addressed. The analysis is based on a higher-order structural model using the first-order shear deformation theory for the face sheets and piezoelectric patches, and the extended high-order sandwich theory for the flexible core. Geometrical non-linearity is considered in the von Karman sense. Hamilton’s principle is employed to introduce a novel smart sandwich beam element which has eighteen physical nodes with mechanical and electric potential degrees of freedom plus two electric nodes for the electric potentials of the electroded surfaces. The presented smart sandwich beam element is used to develop finite element equations of motion. Constant negative velocity feedback algorithm is adapted in the active control. The solution of non-linear equations is sought by Newmark and the modified Newton–Raphson methods for dynamic analysis. Furthermore, the model behavior in free vibrations is assessed by using a direct iteration technique suitably modified for non-linear eigenvalue problems based on the QZ algorithm. A detailed analysis of the influence of geometrical non-linearity, core flexibility and piezoelectric patch arrangement on the dynamic response, frequency and loss factor of active sandwich beams is carried out.