Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach

We apply adjoint-based sensitivity analysis to a time-delayed thermo-acoustic system: a Rijke tube containing a hot wire. We calculate how the growth rate and frequency of small oscillations about a base state are affected either by a generic passive control element in the system (the structural sensitivity analysis) or by a generic change to its base state (the base-state sensitivity analysis). We illustrate the structural sensitivity by calculating the effect of a second hot wire with a small heat-release parameter. In a single calculation, this shows how the second hot wire changes the growth rate and frequency of the small oscillations, as a function of its position in the tube. We then examine the components of the structural sensitivity in order to determine the passive control mechanism that has the strongest influence on the growth rate. We find that a force applied to the acoustic momentum equation in the opposite direction to the instantaneous velocity is the most stabilizing feedback mechanism. We also find that its effect is maximized when it is placed at the downstream end of the tube. This feedback mechanism could be supplied, for example, by an adiabatic mesh. We illustrate the base-state sensitivity by calculating the effects of small variations in the damping factor, the heat-release time-delay coefficient, the heat-release parameter, and the hot-wire location. The successful application of sensitivity analysis to thermo-acoustics opens up new possibilities for the passive control of thermo-acoustic oscillations by providing gradient information that can be combined with constrained optimization algorithms in order to reduce linear growth rates. © Cambridge University Press 2013.

Direct comparison of the gravimetric responsivities of ZnO-based FBARs and SMRs

Film bulk acoustic resonators (FBARs) and solidly mounted resonators (SMRs) have the potential to significantly improve upon the sensitivity and minimum detection limit of traditional gravimetric sensors based on quartz crystal microbalances (QCMs) and surface acoustic wave resonators (SAWs). To date, neither FBAR nor SMR devices have been demonstrated to be superior to the other; hence the choice between them depends primarily on the users' ability to design/fabricate membranes and/or Bragg reflectors. In this work, it is shown that identically designed FBAR and SMR devices resonating at the same frequency exhibit different responsivities to mass loadings, Rm, and that the SMRs are less responsive than the FBARs. For the specific device design and resonant frequency (~2 GHz) of the resonators presented here, the FBARs' mass responsivity is ~20% greater than that of the SMRs', and although this value is not universal for all possible device designs, it clearly shows that FBAR devices should be favoured over SMRs in gravimetric sensing applications where the FBARs' fragility is not an issue. Numerical calculations based on Mason's model offer an insight into the physical mechanisms behind the greater FBARs responsivity, and it was shown that the Bragg reflector has an effect on the acoustic load at one of the facets of the piezoelectric films which is in turn responsible for the SMRs' lower responsivity to mass loadings. © 2013 Elsevier B.V.

An analysis of competing toughening mechanisms in layered and particulate solids

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus 90 ° symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic-plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale. © 2013 Springer Science+Business Media Dordrecht.