Analysis of Thermoelastic Damping and Frequency Shift in Ultra-Small Rectangular Plates with Moore–Gibson–Thompson Heat Conduction via Nonlocal Strain Gradient Elasticity

Precise understanding and measurement of thermoelastic damping (TED) is essential for optimizing the functionality of ultra-small resonators. Scientists have found that the classical continuum theory (CCT) and the Fourier heat conduction model are inadequate for describing mechanical components at very small scales. By leveraging the frequency-based analysis, this work develops a novel approach for TED calculation in extremely small rectangular plates, drawing on the nonlocal strain gradient theory (NSGT) and Moore–Gibson–Thompson (MGT) heat transfer model to address classical formulation drawbacks at micro/nanoscales. In pursuit of this objective, the coupled equations of motion and heat are initially formulated within the NSGT and MGT model frameworks. Next, through the separation of the real and imaginary parts of the plate’s frequency and the application of frequency-based analysis, explicit expressions for TED and frequency shift are derived. The developed formulation’s credibility is assessed by comparing its outcomes to previously published data. In the numerical results section, the effects of essential factors, with a focus on the specific constants of the NSGT and MGT model, on TED and frequency shift are appraised.

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