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• Investigation of thermoelastic damping (TED) in electrostatically shallow arches based on non-classical formulation. • The non-Fourier heat conduction model with a single relaxation time is considered. • A thermo-mechanical modal analysis is carried out for the first time. • The derived model is implemented and validated to be efficient in analysis of bistable micro-structures. • The results of the present work may be used to design MEMS devices. Thermoelastic damping is a major source of intrinsic damping in vacuum operated Micro Electro Mechanical Systems (MEMS). In this article, the non-linear vibration of electrically actuated curved micro-beams is investigated, considering the effect of thermoelastic damping. The coupled thermoelasticity equations are derived on the basis of non-classical formulation, which is the modified couple stress theory and generalized heat conduction thermoelasticity equation. Afterwards, the order of the governing equations is reduced using the Generalized Differential Quadrature Method (GQDM). The validation of the derived model is achieved through comparison with existing published results. Then the effects of design parameters on snap-through buckling and pull-in instability have been investigated. Furthermore, it is observed that the GDQM with small number of nonuniform grid spacing performs accurate results without dealing with complicated shape functions and integrations. Finally the coupled thermo-mechanical modal analysis is carried out by FE simulation. [ABSTRACT FROM AUTHOR]