Symmetry in Piezoelectric Disks and Rings: Modal and Harmonic Analysis with Experimental Comparison

Exploiting geometrical symmetry to reduce the computational domain is a well-established strategy in finite element analysis. However, its systematic application to coupled piezoelectric modal problems requires that symmetry conditions be satisfied simultaneously by the mechanical and electrical fields. In this work, a parity-based framework is developed for class 6 mm piezoelectric disks and rings. Starting from coupled piezoelastic constitutive equations, the displacement components and electric potential, together with the associated stresses and electric displacements, are classified into eight electromechanical symmetry classes. The corresponding mechanical and electrical boundary conditions are then derived, allowing each symmetry class to be computed independently using only one eighth of the original geometry. Comparison with full-domain finite element calculations shows that the complete set of modes can be recovered and classified with very small frequency differences, while the reduced models achieve a substantially lower computational cost. The framework is subsequently applied to piezoelectric rings with varying outer diameters to track the evolution and degeneracy of modal families and to identify symmetry-equivalent classes. Finally, selected resonances are experimentally tracked through impedance measurements as the ring diameter is varied and compared with harmonic finite element predictions. The proposed approach therefore provides not merely a domain reduction technique but a physically interpretable classification of coupled electromechanical modes that facilitates efficient modal identification and resonance tracking in piezoelectric disks and rings.