A resonator includes a piezoelectric plate and interdigitated electrode(s). The interdigitated electrode includes a plurality of conductive strips disposed over a top surface of the piezoelectric plate. A two-dimensional mode of mechanical vibration is excited in a cross sectional plane of the piezoelectric plate in response to an alternating voltage applied through the interdigitated electrode. The two-dimensional mode of mechanical vibration is a cross-sectional Lamé mode resonance (CLMR) or a degenerate cross-sectional Lamé mode resonance (dCLMR).