Analysis of thermoelastic damping and frequency shift of nano-scale piezoelectric fiber-reinforced thermoelastic composite beam under single, dual, and three phase-lag models: A comparative approach

Abstract

Thermoelastic damping (TED) & frequency shift (FS) have become key concerns in modeling and designing micro and nanoelectromechanical systems (MEMS/NEMS). As a result, significant research efforts are focused on reducing thermoelastic damping in MEMS/NEMS. This motivated us to analytically study TED and FS in nano-scale piezoelectric fiber-reinforced composite (PFRC) thermoelastic beams comprising PZT-5A and epoxy. The linearized Euler–Bernoulli theory is assumed and the adopted generic beam structure is treated by four sets of different conditions at its boundaries to model four distinct beams, viz., clamped-clamped (CC), simply supported-simply supported (SS), clamped-free (CF) & clamped simply supported (CS) types. We employed the Newton–Raphson method to calculate the eigenvalues of each type of beam for numerically accurate results. One of the highlights of this work is the simultaneous analysis of three-phase-lag (TPL), dual-phase-lag (DPL), and single-phase-lag (SPL) thermoelastic models under Green–Naghdi III (G-N III) thermoelasticity theory. The influences of thermal relaxation parameters, volume fraction of fibers, nano beam dimensions, and first two modes on the TED & FS are studied by means of graphs. The influences of all existing parameters on critical thickness and critical length of all four beams are also meticulously analyzed. By comparing the results with previous literature, their validity is confirmed. In comparison to a monolithic piezothermoelastic beam, the PFRC thermoelastic beams exhibit higher quality factor (Q-factor). This generates appropriate values of V${}_f$ to design & optimize frequency-sensitive PFRC thermoelastic nano beams.