Mechanically tunable bending-wave actuators via defective phononic crystals on elastic foundations

Abstract

Piezoelectric actuators that leverage defect modes in phononic crystals (PnCs) have the capacity to significantly amplify longitudinal or flexural waves, rendering them a compelling option for nondestructive testing applications. However, conventional PnCs exhibit a deficiency in their inability to adapt their wave-propagation characteristics to changing environments. To address this limitation, the present study incorporates defective PnC-based bending wave actuators within elastic foundations, thereby facilitating mechanical tuning. An analytical model, founded upon the Euler-Bernoulli beam theory and formulated with transfer matrix and S parameter techniques, has been developed to capture both electroelastic coupling and foundation effects. Two practical configurations are examined: (1) a uniform foundation supporting the entire defective PnC, including the piezoelectric defect, and (2) a selective foundation supporting only the intact beams, leaving the defect region free. In both cases, the proposed analytical model accurately predicts the results in band structure and wave-actuation analyses, showing excellent agreement with COMSOL Multiphysics simulations. The following are the most significant findings: (1) the closed-form analytical model validated against COMSOL for rapid parametric design, (2) near-linear tuning of the bandgap and defect-band frequencies via foundation stiffness while retaining strong defect-mode-enabled energy localization, (3) robust defect-mode shapes that sustain large, symmetric strain fields for efficient bending-wave actuation, and (4) enhanced voltage-to-velocity actuation sensitivity and discovery of an additional low-frequency defect mode when the defect region is left unsupported.