Quality factor analysis of cylindrical shell resonators considering surface residual stress and thermoelastic damping

Abstract

An effective method for evaluating the quality factor of cylindrical shells, incorporating the effects of surface residual stress and thermoelastic damping, is developed. The Stoney formula is extended to characterize the surface residual stress of the cylindrical shell, which is determined based on the thickness of the damaged layer. The equations of motion are derived using Hamilton’s principle and simplified via the Donnell–Mushtari–Vlasov (DMV) approximation. The thermoelastic governing equation is solved using the Galerkin method, yielding the natural frequency and thermoelastic quality factor of the shell. Additionally, an analytical model for the surface loss quality factor is established through the energy approach. The validity of the theoretical model is confirmed through comparisons with the existing literature and the finite element method (FEM). The influences of key parameters including damaged layer thickness, structural dimensions, and equilibrium temperature on the quality factors are investigated. It is observed that an increase in the damaged layer thickness significantly reduces the surface loss quality factor. Moreover, the thermoelastic quality factor and surface loss quality factor exhibit opposite trends in response to changes in structural sizes and equilibrium temperature. Therefore, a comprehensive consideration of these factors is essential for the design of high-performance cylindrical shell resonators.