  On-chip phononic circuits tailor the transmission of elastic waves, which can
couple to electronic and photonic systems, enabling new signal manipulation
capabilities. Phononic circuits rely on waveguides that transmit elastic waves
within desired frequency passbands, typically designed based on the Bloch modes
of the waveguide constitutive cell, assuming linearity and periodicity. MEMS
waveguides composed of coupled drumhead (membrane) resonators offer tunable MHz
operation frequencies for applications in nonlinear optomechanics, topological
insulators, phononic cavities, and acoustic switching. Here, we construct a
reduced-order model (ROM) to demonstrate the switching of signal transmission
in drumhead-resonator waveguides due to thermoelastic buckling. The ROM shows
that buckling amplifies existing structural disorders, breaking the periodicity
required for waveguide transmission through the first passband. This
periodicity breaking manifests in the localization of the first-passband modes,
like classical Anderson localization caused by disorders. The proposed ROM is
essential to study the investigated phenomena since Bloch mode analysis fails
for weakly-disordered (< 5%) finite waveguides due to the disorder
amplification caused by the thermoelastic buckling. The illustrated
transmission control should be useful for logical acoustic operations, like
switching, and can be extended to 2D circuits in the future.
