Frequency shifts and thermoelastic damping in distinct Micro-/Nano-scale piezothermoelastic fiber-reinforced composite beams under three heat conduction models

Abstract

The present work aims to fulfill two primary objectives. Firstly, to present the micro-mechanics model of piezothermoelastic fiber-reinforced composite (PTFRC) medium using analytical techniques, viz., Strength of Materials (SM) & Rule of Mixtures (RM) and graphically establish some of its electro-mechanical-thermal advantages over monolithic PT materials. Secondly, to analytically study the thermoelastic damping (TED) and frequency shift (FS) in micro-/nano-scale PTFRC beams. TED and FS are analyzed considering the linear Euler-Bernoulli theory when the beam is under four distinct boundary conditions, viz., clamped-clamped (CC), simply supported-simply supported (SS), clamped-free (CF), and clamped-simply supported (CS). The eigenvalues of each beam are calculated numerically with 20 iterations each using the Newton-Raphson technique, followed by the analysis of TED and FS considering the assumed boundaries. The Classical dynamical coupled (CL), Lord-Shulman (LS), and Green-Lindsay (GL) thermoelasticity theories are exclusively analyzed. The effects of thermal relaxation parameters, fiber volume fraction, micro and nano beam dimensions, and the first two modes (M1 & M2) on the TED and FS are graphically illustrated. The critical thickness (CrTh) and critical length (CrLt) of all four beams influenced by the existing parameters are scrupulously investigated. The robustness of the obtained results is validated by matching them with previous literature. For high Ωf, the PTFRC beam has superior electro-mechanical-thermal properties and greater Q-factors compared to monolithic beam. However, the Q-factor increases as Ωf decreases. This facilitates the choice of a suitable value of Ωf for designing and optimizing frequency-sensitive microelectromechanical (MEM) and nanoelectromechanical (NEM) PTFRC beams.