Thermoelastic damping and frequency shift in micro/nano-ring resonators considering the nonlocal single-phase-lag effect in the thermal field

•Two generalized models of thermoelastic damping (TED) in micro/nano-rings are derived.•Temperature varies with the nonlocal single-phase-lag (SPL) effect of heat conduction.•Frequency-shift ratio for micro/nano-rings under the nonlocal-SPL effect is investigated•TED at high frequencies is affected by the nonlocal-SPL effect.•Equivalent relaxation times for rings under the nonlocal-SPL effect are discussed.