Size-dependent analysis of thermoelastic damping in thermoflexoelectric nanobeam resonators

Abstract This paper develops new analytical models for thermoelastic damping (TED) in transversely isotropic flexoelectric beams by combining the Lord–Shulman heat-conduction theory with the advanced strain gradient theory of flexoelectricity. For the first time, two size-dependent TED models for flexoelectric nanobeams are proposed using complex-frequency and energy approaches. A free-vibration model of simply supported Euler–Bernoulli beams is formulated by accounting for thermoelastic coupling, micro-stiffness, pyroelectric, piezoelectric, and flexoelectric effects. The governing equations for piezoflexoelectric beams under open-circuit conditions are derived from Hamilton’s principle, including an additional micro-inertia term to capture microstructural effects in dynamics. Energy dissipation in thermoflexoelectric beams is analyzed for one- and two-dimensional heat-conduction problems. The proposed TED models are validated through comparison with available analytical results. A parametric study examines the combined influence of flexoelectricity, micro-stiffness, and micro-inertia on TED in piezoelectric nanoresonators for different vibration modes and beam dimensions. A comparison between the two approaches is carried out. The results demonstrate that flexoelectricity and microstructural effects strongly influence the thermoelastic behavior of nanobeams; therefore, their interaction must be considered in the design of piezoelectric resonators. The findings provide useful guidelines for developing high-quality electro-thermo-elastic devices.