Flexural-mode solid-state thermoacoustics

Abstract

Recent studies have indicated that axial waves traveling in a one dimensional solid rod can give rise to a thermoacoustically unstable response when in presence of an externally applied spatial temperature gradient. Similar to fluid-based thermoacoustics, both standing and traveling axial thermoacoustic waves can exist in solids. Elastic waves in solids are polarized, hence it is reasonable to hypothesize that thermoacoustic instabilities can affect also shear-type waves, such as flexural waves. This study extends previous research on axial-mode solid-state thermoacoustics to flexural-mode solid-state thermoacoustics (F-SSTAs). More specifically, it is shown how flexural waves can grow unbounded when traveling in a bilayer beam subject to a spatial thermal gradient. A theoretical framework is developed to analyze the dynamics of the system and to establish the criterion controlling the onset of flexural thermoacoustic instability. Numerical calculations conducted in both the frequency and the time domains show the occurrence of two main effects due to the presence of thermal coupling: (1) the dynamic amplification of the flexural motion, and (2) the time-varying location of the neutral axis. An experimental investigation is also conducted in order to corroborate the existence of this thermal-to-mechanical energy conversion mechanism associated with flexural waves.