Many centuries ago glass blowers observed that sound could be generated when blowing through a hot bulb from the cold end of a narrow tube. This phenomenon is a result of thermoacoustic oscillations: a pressure wave propagating in a compressible fluid (e.g. air) can sustain or amplify itself when being provided heat. To date, thermoacoustic engines and refrigerators have had remarkable impacts on many industrial applications.
After many centuries of thermoacoustic science in fluids, it seems natural to wonder if such a mechanism could also exist in solids. Is it reasonable to conceive thermoacoustics of solids? Can a metal bar start vibrating when provided heat?
The study of the effects of heat on the dynamics of solids has a long and distinguished history. The theory of thermoelasticity, which explains the mutual interaction between elastic and thermal waves, has been an active field of research since the 1950s. However, the classical theory of thermoelasticity does not address instability phenomena that can arise when considering the motion of a solid in the presence of a thermal gradient. In an analogous way to fluids, a solid element contracts when it cools down and expands when it is heated up. If the solid contracts less when cooled and expands more when heated, the resulting motion will grow with time. In other terms, self-sustained vibratory response of a solid could be achieved due to the application of heat. Such a phenomenon would represent the exact counterpart in solids of the well-known thermoacoustic effect in fluids.
By using theoretical models and numerical simulations, our study indicates that a small mechanical perturbation in a thin metal rod can give rise to sustained vibrations if a small segment of the rod is subject to a controlled temperature gradient. The existence of this physical phenomenon in solids is quite remarkable, so one might ask why it was not observed before despite the science of thermoacoustics have been known for centuries.
“Figure 1. The sketch of the solid-state thermoacoustic device and the plot of the self-amplifying vibratory response.”
It appears that, under the same conditions of mechanical excitation and temperature, a solid tends to be more “stable” than a fluid. The combination of smaller pressure oscillations and higher dissipative effects (due to structural damping) in solids tends to suppress the dynamic instability that is at the origin of the thermoacoustic response. Our study shows that, with a proper design of the thermoacoustic device, these adverse conditions can be overcome and a self-sustained response can be obtained. The interface conditions are also more complicated to achieve in a solid device and dictates a more elaborate design.
Nonetheless, this study shows clear theoretical evidence of the existence of the thermoacoustic oscillations in solids and suggests that applications of solid-state engines and refrigerators could be in reach within the next few years.