Defect modes in phononic crystals (PnCs) provide strongly localized resonances that are essential for frequency-dependent wave filtering and highly sensitive sensing. Their functionality increases greatly when their spectral characteristics can be externally tuned without altering the structural configuration. However, existing feedback control strategies rely on laminated piezoelectric defects, which have uniform electromechanical loading that causes voltage cancellation for even-symmetric defect modes. Consequently, only odd-symmetric defect bands can be manipulated effectively, which limits multi-band tunability. To overcome this constraint, we propose a segmented piezoelectric sensor–actuator design that enables symmetry-dependent feedback at the defect site. We develop a transfer-matrix analytical framework to incorporate complex-valued feedback gains directly into dispersion and transmission calculations. Analytical predictions demonstrate that real-valued feedback yields opposite stiffness modifications for odd- and even-symmetric modes. This enables the simultaneous tuning of both defect bands and induces an exceptional-point-like coalescence. In contrast, imaginary feedback preserves stiffness but modulates effective damping, generating a parity-dependent amplification-suppression response. The analytical results closely match those of fully coupled finite-element simulations, reducing computation time by more than two orders of magnitude. These findings demonstrate that segmentation-enabled feedback provides an efficient and scalable approach to tunable, multi-band, non-Hermitian wave control in piezoelectric PnCs.
Soo-Ho Jo (2026) studied this question.