QMU Analysis of Flexoelectric Timoshenko Beam by Evidence Theory

Abstract

In recent years, with the rapid development of nanotechnology, a new type of electromechanical coupling effect similar to the piezoelectric effect, the flexoelectric effect, has gradually come into the public’s view. The flexoelectric beam that is the main structural unit of the flexoelectric signal output has broad application prospects in the next generation of micro- and nanoelectromechanical systems. Therefore, the investigation of flexoelectric materials and structures has important scientific and engineering application significances for the design of flexoelectric devices. In this paper, a model of flexoelectric Timoshenko beam is established, the deflection, rotation angle, and dynamic electrical signal output of the forced vibration are taken as the system response, and the density $\rho$ , shear correction factor $\kappa$ , and frequency ratio $\lambda$ are selected as the key performance parameters of the system. The combination of available data and engineers’ experience suggests that there are random and cognitive uncertainties in the parameters. Therefore, the probability distribution of the system performance response is expressed by the likelihood function and belief function through the quantification of margins and uncertainties (QMUs) analysis methodology under the framework of evidence theory, and the system reliability or performance evaluation is measured by the calculated confidence factors. These results provide a theoretical basis for accurate analysis of flexoelectric components and provide guidance for the design of flexoelectric components with excellent performance.