An approximation theory for the identification of linear thermoelastic systems

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures

Intrinsic dissipation in high-frequency micromechanical resonators

We report measurements of intrinsic dissipation in micron-sized suspended resonators machined from single crystals of galium arsenide and silicon. In these experiments on high-frequency micromechanical resonators, designed to understand intrinsic mechanisms of dissipation, we explore dependence of dissipation on temperature, magnetic field, frequency, and size. In contrast to most of the previous measurements of acoustic attenuation in crystalline and amorphous structures in this frequency range, ours is a resonant measurement; dissipation is measured at the natural frequencies of structural resonance, or modes of the structure associated with flexural and torsional motion. In all our samples we find a weakly temperature dependent dissipation at low temperatures. We compare and contrast our data to various probable mechanisms, including thermoelasticity, clamping, anharmonic mode-coupling, surface anisotropy and defect motion, both in bulk and on surface. The observed parametric dependencies indicate that the internal defect motion is the dominant mechanism of intrinsic dissipation in our samples

Fundamental thermal fluctuations in microspheres

We present a theoretical analysis and the results of measurements of thermorefractive noise in microcavities. These measurements may be considered direct observations of fundamental fluctuations of temperature in solid media. Our experimentally measured noise spectra are in agreement with our theoretical model

Flow-plate interactions: Well-posedness and long-time behavior

We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a novel treatment of the so called Kutta-Joukowsky flow conditions are given in the subsonic case. The goal of the paper is threefold: (i) to provide an accurate review of recent results on existence, uniqueness, and stability of weak solutions, (ii) to present a construction of finite dimensional, attracting sets corresponding to the structural dynamics and discuss convergence of trajectories, and (iii) to state several open questions associated with the topic. This second task is based on a decoupling technique which reduces the analysis of the full flow-structure system to a PDE system with delay.Comment: 1 figure. arXiv admin note: text overlap with arXiv:1208.5245, arXiv:1311.124

Modeling and simulation of brake judder considering the effects of thermo-mechanical coupling

Reproducing the real behavior of brake judder in time domain is useful for brake judder reduction, but it is hard to establish a time-domain model of brake judder due to the effects of thermo-mechanical coupling. To solve this problem, a modeling method is proposed taking into account the effects of thermo-mechanical coupling before hotspot occurs. In this method, an eight-degree-of-freedom dynamics model of brake caliper assembly with multi-contact points is established, and a semi-empirical model of friction coefficient is proposed by magic formula tyre model. The input of the dynamics model is the initial disc thickness variation (DTV) and the DTV caused by uneven heating, which is calculated by a transient FE model of thermo-mechanical coupling considering initial DTV. On this basis, a simulation of brake judder is conducted and an experiment is designed to validate the method. The simulated brake pressure and brake torque without and with thermo-mechanical coupling are compared with the experiment results respectively, and it indicates that the simulated results considering thermo-mechanical coupling have a good agreement with experiment results. Brake pressure variation (BPV) and brake torque variation (BTV) increase gradually in time domain because of the effects of thermo-mechanical coupling and the increments of BPV and BTV can reach 45 % and 50 % respectively in the simulation