Affiliation:
1. Department of Mechanical Engineering, Boston University, Boston, MA 02215
Abstract
Abstract
This paper presents a method to simultaneously predict the elastic modulus, axial load, and boundary conditions of a nanoelectromechanical system (NEMS) beam from a minimum of two measured natural frequencies. The proposed method addresses the challenges of the inverse problem at the nano scale, which include high natural frequencies, small geometric beam dimensions, and measurements limited to natural frequencies. The method utilizes a finite element model of an Euler–Bernoulli beam under axial loading to predict the response of the beam with axial loading and flexible boundary conditions. By expressing the finite element model in terms of dimensionless beam parameters, the proposed method may be applied to nano scale beams while maintaining numerical stability of the finite element equation of motion. With the stabilized finite element model, the NEMS beam properties are predicted by iterating through values of dimensionless beam parameters until the normalized error between predicted and measured natural frequencies is minimized. A key feature of the proposed method is the simultaneous prediction of the elastic modulus during the iterative search, resulting in a reduction of the search space and significant computational savings. Additionally, the proposed method readily accommodates an arbitrary number of measured natural frequencies without the reformulation of procedures and analyses. Numerical examples are presented to illustrate the proposed method’s ability to predict the elastic modulus, axial load, and boundary conditions. The proposed method is applied to experimental measurements of a NEMS beam, where the normalized error between predicted and measured natural frequencies is reduced below 10−3.
Funder
National Science Foundation
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献