We study experimentally, numerically and theoretically the elastic response of mechanical resonators along which the temperature is not uniform, as a consequence of the onset of steady-state thermal gradients. Two experimental setups and designs are employed, both using low-loss materials. In both cases, we monitor the resonance frequencies of specific modes of vibration, as they vary along with variations of temperatures and of temperature differences. In one case, we consider the first longitudinal mode of vibration of an aluminum alloy resonator; in the other case, we consider the antisymmetric torsion modes of a silicon resonator. By defining the average temperature as the volume-weighted mean of the temperatures of the respective elastic sections, we find out that the elastic response of an object depends solely on it, regardless of whether a thermal gradients exists and, up to 10% imbalance, regardless of its magnitude. The numerical model employs a chain of anharmonic oscillators, with first- and second-neighbor interactions and temperature profiles satisfying Fourier’s Law to a good degree. Its analysis confirms, for the most part, the experimental findings and it is explained theoretically from a statistical mechanics perspective with a loose notion of local equilibrium.

Elasticity of mechanical oscillators in non-equilibrium steady states: experimental, numerical and theoretical results

Bonaldi, Michele;Crivellari, Michele;Serra, Enrico;
2012

Abstract

We study experimentally, numerically and theoretically the elastic response of mechanical resonators along which the temperature is not uniform, as a consequence of the onset of steady-state thermal gradients. Two experimental setups and designs are employed, both using low-loss materials. In both cases, we monitor the resonance frequencies of specific modes of vibration, as they vary along with variations of temperatures and of temperature differences. In one case, we consider the first longitudinal mode of vibration of an aluminum alloy resonator; in the other case, we consider the antisymmetric torsion modes of a silicon resonator. By defining the average temperature as the volume-weighted mean of the temperatures of the respective elastic sections, we find out that the elastic response of an object depends solely on it, regardless of whether a thermal gradients exists and, up to 10% imbalance, regardless of its magnitude. The numerical model employs a chain of anharmonic oscillators, with first- and second-neighbor interactions and temperature profiles satisfying Fourier’s Law to a good degree. Its analysis confirms, for the most part, the experimental findings and it is explained theoretically from a statistical mechanics perspective with a loose notion of local equilibrium.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11582/81602
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
social impact