A solidly mounted resonator structure includes an multi-layer acoustic reflector structure and a piezoelectric material layer arranged between the first and second electrode structures to form an active region, with the acoustic reflector structure providing enhanced reflection of shear and longitudinal modes of acoustic vibrations. The solidly mounted resonator structure is configured for transduction of an acoustic wave including a longitudinal component and a shear component. The acoustic reflector structure includes multiple sequentially arranged differential acoustic impedance layer units each including a low acoustic impedance material layer in contact with a high acoustic impedance material layer. A frequency corresponding to a minimum transmissivity of a second harmonic resonance of a longitudinal response is substantially matched to a frequency corresponding to a minimum transmissivity of a third harmonic resonance of a shear response.