Simultaneous determination of Young's modulus and residual stress via dynamic analysis of nanobridge exhibiting beam-to-string behaviors using a genetic algorithm

Abstract

The mechanical properties of nanostructures, particularly Young's modulus and residual stress, exert significant influence on the performance and reliability of nanomechanical devices. However, conventional methods prove inadequate for evaluating these properties due to the impact of fabrication processes on nanostructures. This study addresses this challenge by proposing a dynamic model that considers the transition between “beam-like” and “string-like” characteristics under residual stress, a factor overlooked in previous research. Through analysis of nanobridge vibration modes and utilization of genetic algorithms (GAs) to reverse-engineer Young's modulus and residual stress from resonant frequencies, we introduce a novel and precise methodology. In contrast to the conventional Euler-Bernoulli beam theory, our proposed model integrates the system's kinetic and potential energies for resonant frequency calculation. This energy-based approach, grounded in physical principles, excels at capturing dynamic changes in structural behavior. Particularly in the critical “transition region” where the resonator shifts from “beam-like” to “string-like” behavior, our method adeptly accounts for energy conversion processes, resulting in more accurate resonant frequency estimations. By comparing with existing published data, our proposed method achieves a maximum error of 5.87 % in the determination of Young's modulus and residual stress of nanostructures.