Active control of elastic wave propagation in nonlinear phononic crystals consisting of diatomic lattice chain

This work studies the active control effects on nonlinear phononic crystals by the piezoelectric spring model. Both negative and positive proportional control actions are considered. Based on the Lindstedt-Poincaré method, the approximate solution is derived and the stop band properties are presented. Numerical calculations show that the structural stiffness and negative proportional control of the piezoelectric spring can create a new stop band which is under the acoustic branch. But the positive proportional case has a different influence because of a critical wave number appearing. Moreover, the optic branch can be uplifted by the elastic wave amplitude. Different from the soft nonlinear characteristic, the hard nonlinear property can increase the stop band width.