Material-dependent thermoelastic damping limited quality factor and critical length analysis with size effects of micro/nanobeams

Micro/nanobeam-based resonators have found extensive applications in the micro/nanoelectromechanical system industry. Thermoelastic damping (TED) is a major energy loss issue in micro/nanobeam resonators that limits their important performance parameter, namely, the TED limited quality factor (Q TED ). The critical length (L c ) of a micro/nanobeam is another significant parameter that accounts for the maximum peak in the energy dissipation curve at which Q TED assumes a minimum value. To evaluate Q TED and Lc explicitly when the size of devices is scaled down, size effects play a decisive role and classical theories are inadequate. In this work, a higher-order theory, namely, modified couple stress theory (MCST), is used to overcome the size effects by including one internal material length scale parameter (l). The material-dependent thermoelastic coupled equations for a deflected Euler-Bernoulli microbeam are presented using variational and Hamilton principles. Moreover, the solutions for Q TED are developed on the basis of a complex frequency approach with the appropriate material indices. The effects of material length scale parameters, material performance indices, mechanical boundary conditions (clamped-clamped, simply supported, and cantilever types), mode switching, and plane stress/strain conditions on Q TED and Lc are analyzed. Numerical results are extracted from the analytical expressions by using MATLAB R2015a to quantify thermoelastic energy dissipation. The numerically computed Q TED and L c values are fully investigated to design high-performance resonators. The analyses verify that Q TED is enhanced by optimizing the structural material and augmenting the material length scale parameter. The material order in which Q TED is enhanced is the same for classical theories and MCST, i.e., it is inversely related to the TED index parameter. The influences of boundary types and mode switching on Q TED are relatively less in accordance with the analysis. The effect of plane stress condition compared with that of plane strain condition on Q TED is also remarkable. The L c of the beam is determined to be dependent on the thermal diffusion length of the material used. From an adequate material point of view, poly-silicon has been proven to provide the maximum quality factor while silicon carbide yields the maximum L c . These observations are significant and extremely helpful when designing low-loss micro/nanobeam resonators with superior performance by suitably selecting their geometry and structural materials.