Dynamic characteristics and thermoelastic damping of surface-damaged hemispherical shell resonators

This paper investigates the dynamic characteristics and thermoelastic damping behavior of hemispherical shell resonators (HSRs) with surface-damaged layers. To characterize stiffness degradation caused by near-surface damage, the resonator is modeled as a three-layer hemispherical shell comprising two damaged surface layers and an undamaged substrate. A semi-analytical dynamic model is developed based on Hamilton's principle to determine the natural frequencies and mode shapes, and the thermoelastic quality factor Q_TED is evaluated using the thermal energy method. The numerical consistency of the model is assessed through convergence analysis and COMSOL comparison, while chemical etching experiments provide independent observations of processing-dependent resonant-frequency evolution. Numerical results show that increasing the damaged-layer thickness reduces the natural frequencies due to stiffness degradation, whereas Q_TED exhibits a non-monotonic variation, with an initial decrease followed by a gradual increase. Although the dominant normalized temperature-field topology remains broadly similar, the temperature amplitude, near-surface gradient, and thickness-direction heat flux vary appreciably with the damaged-layer thickness. Increasing the Young's modulus of the damaged layers raises both the natural frequencies and Q_TED. Symmetric stiffness variation in the two damaged layers has a stronger impact than asymmetric variation in only one layer. These findings provide theoretical guidance for damage assessment, performance prediction, and structural optimization of high-precision HSRs.