Effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in elastic medium

  • Zheng Lv
  • Hu LiuEmail author
  • Qi Li


The effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in an elastic medium is investigated by developing a nonlocal nanorod model with uncertainties. Considering limited experimental data, uncertain-but-bounded variables are employed to quantify the uncertain material properties in this paper. According to the nonlocal elasticity theory, the governing equations are derived by applying the Hamilton’s principle. An iterative algorithm based interval analysis method is presented to evaluate the lower and upper bounds of the wave dispersion curves. Simultaneously, the presented method is verified by comparing with Monte-Carlo simulation. Furthermore, combined effects of material uncertainties and various parameters such as nonlocal scale, elastic medium and lateral inertia on wave dispersion characteristics of nanorod are studied in detail. Numerical results not only make further understanding of wave propagation characteristics of nanostructures with uncertain material properties, but also provide significant guidance for the reliability and robust design of the next generation of nanodevices.


Wave propagation Nanorod Nonlocal elasticity theory Uncertain material properties Interval analysis method 



This work is financially supported by the National Nature Science Foundation of China under Grant No.11602283. The core idea of the proposed method is originally formulated by Zheng Lv; the data analysis is accomplished by all authors. In addition, the authors also would like to thank the editor and reviewers for their valuable suggestions.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Institute of Solid MechanicsBeihang University (BUAA)BeijingChina
  2. 2.State Key Laboratory of Robotics, Shenyang Institute of AutomationChinese Academy of SciencesShenyangChina

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