title: Elasticity of mechanical oscillators in nonequilibrium steady states: experimental, numerical, and theoretical results.
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 gradient 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.
authors.affiliation: INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy.
authors.forename: Livia
authors.initials: L
authors.lastname: Conti
authors.forename: Paolo
authors.initials: P
authors.lastname: De Gregorio
authors.forename: Michele
authors.initials: M
authors.lastname: Bonaldi
authors.forename: Antonio
authors.initials: A
authors.lastname: Borrielli
authors.forename: Michele
authors.initials: M
authors.lastname: Crivellari
authors.forename: Gagik
authors.initials: G
authors.lastname: Karapetyan
authors.forename: Charles
authors.initials: C
authors.lastname: Poli
authors.forename: Enrico
authors.initials: E
authors.lastname: Serra
authors.forename: Ram-Krishna
authors.initials: RK
authors.lastname: Thakur
authors.forename: Lamberto
authors.initials: L
authors.lastname: Rondoni
mesh_terms: D003198:Computer Simulation; D055119:Elastic Modulus; D055617:Micro-Electrical-Mechanical Systems / Q000379:methods*; D008962:Models, Theoretical; D009991:Oscillometry / Q000379:methods*; D013814:Thermal Conductivity