Nonlocal dual-phase-lag thermoelastic damping analysis in functionally graded sandwich microbeam resonators utilizing the modified coupled stress theory

Abstract

Functionally graded (FG) sandwich structures stand as one of the most representative composite structures owing to the thermal resistance and the energy absorption property in non-unfiorm thermal environment. Additionally, accurately estimating thermoelastic damping (TED) is of great importance for the design of high-performance micro/nano-resonators. Nevertheless, the classical TED models fail on the micro/nano-scale structures due to without considering the influences of the spatial size-dependent effects related to heat transfer and elastic deformation. The nonlocal heat conduction model and modified coupled stress theory are responsible for the size-dependent effects. To address this issue, present study aims to conduct the size-dependent TED model of FG sandwich microbeam resonators for TED analysis by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are formulated, and then, the analytical solution is solved by complex frequency method. Exact and closed-form expressions for TED can be obtained through the complex frequency method. The results are validated, and the parameter effects of the nonlocal thermal parameter, the material length-scale parameter, the power-law index and the vibration modes on the TED are analyzed. The results show that the energy dissipation can be reduced by the size-dependent effects resulting in improving the quality factor of microstructures. It is expected that these results may provide a theoretical basis for predicating TED in the design of FG sandwich micro/nano-resonators with high quality factor in extreme heat transfer environment.