Executive Summary : | The analysis of dynamics and stability of vibration in nano-electro-mechanical systems (NEMS) is a significant area of interdisciplinary research in applied mathematics, mechanics, and related areas. Piezoelectric nano materials, known as smart materials, have gained attention due to their excellent electro-mechanical coupling effect and low energy consumption. The performance of NEMS is measured by a dimensionless quantity called 'quality factor', which is defined as the ratio of stored energy in the system and dissipated energy by the system per cycle of vibration. NEMS with a lower rate of energy dissipation have a higher value of quality factor, which is beneficial for technical applications. Several energy loss factors in NEMS, such as air damping, anchor loss, and thermoelastic damping, have been identified. Thermoelastic damping (TED) is the most significant energy loss factor in NEMS, and TED analysis in NEMS is a topic of active research. Theoretical formulation and derivation of governing equations and constitutive relations for micro/nano structures is a challenging task, and classical continuum mechanics often ignores small-scale effects, leading to inaccurate results in analyzing the vibration of nano-sized structures. Non-classical continuum theories, such as non-local elasticity theory, couple stress theory, and strain gradient theory, have been developed to consider size effects for micro/nano structures. However, most work on vibration and TED analysis is carried out on the basis of uncoupled theory. This project aims to mathematically model thermoelastic vibration of nano piezo-electro-mechanical systems, considering the coupling effects of electric, thermal, and mechanical fields. |