Three-dimensional analysis of thermoelastic damping in couple stress-based rectangular plates with nonlocal dual-phase-lag heat conduction.

Since thermoelastic damping (TED) plays a decisive role in the functioning of micro/nanoresonators, accurate assessment of its magnitude in these tiny systems is imperative. Successfully simulating the thermomechanical behavior of various mechanical elements requires consideration of heat transfer in all three principal directions. Furthermore, there is no denying the impact of size on the mechanical and thermal domains. In light of these reasons, the current study strives to create a three-dimensional (3D) size-dependent TED model for rectangular micro/nanoplates via the use of the modified couple stress theory (MCST) and nonlocal dual-phase-lag (NDPL) heat transfer model concurrently for the first time. To accomplish this, by applying the Galerkin method to the 3D NDPL-based heat equation, the relation of temperature field is derived. Moreover, the coupled thermoelastic constitutive relations are extracted by including the couple stress effect. Lastly, by exploiting the obtained relations in the energy dissipation approach, an analytical TED formula in the form of infinite trigonometric series is attained. To appraise the rightness of derived formulation, the method of model reduction is applied. Moreover, an elaborate convergence analysis is implemented to realize the number of sufficient terms of the provided solution that result in well-grounded outcomes. A rigorous simulation study is also accomplished on the role of 3D heat conduction, scale parameters of MCST and NDPL model, boundary constraints, geometry and material in the variations of TED. Findings imply the definite impact of heat conduction dimension on TED value in rectangular plates with a large ratio of thickness to length and width. • A three-dimensional (3D) thermoelastic damping (TED) model for small-sized rectangular plate resonators is established. • Scale effects are captured by the modified couple stress theory and nonlocal dual-phase-lag heat conduction model. • A comparison study is carried out to appraise the veracity of developed formulation. • A convergence analysis is performed to determine the number of terms required to reach the convergent answer. • Detailed numerical results are presented to assess the impact of key factors on the pattern and amount of TED. [ABSTRACT FROM AUTHOR]