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Dynamic analysis of nano-beams embedded in a varying nonlinear elastic environment using Eringen's two-phase local/nonlocal model
Bakhshi Khaniki, H ; Sharif University of Technology | 2018
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- Type of Document: Article
- DOI: 10.1140/epjp/i2018-12128-5
- Publisher: Springer Verlag , 2018
- Abstract:
- Recently it was shown that the differential form of Eringen’s nonlocal elastic theory is unable to model, predict and track the mechanical behaviors of many nano-structures due to their boundary conditions. Therefore, having an accurate model for formulating such structures became an important issue. With respect to this concern, in this study, the influence of having an axially varying elastic environment on vibrational behavior of nanobeams is investigated for the first time. Size-dependent effects are modeled using Eringen’s two-phase local/nonlocal integral model which is well-posed with higher accuracy. The elastic environment is modeled using the Pasternak-Winkler method which could vary through the length of the nanobeam. Moreover, the environment’s stiffness variation is presented by using power-law function covering wide ranges of variations. The generalized differential quadrature method is used to solve the problem and verification is done by comparing the results with previous studies on simplified problems. First four natural frequency terms for different boundary conditions are computed considering the presence of the elastic medium. A comprehensive parametric study is done to show the influence of a varying elastic environment and nonlocal terms on first four natural frequencies of beams with different boundary conditions. It is concluded that increasing the nonlocal terms will reduce the natural frequency terms of nanobeam on the elastic environment especially for cantilever nanobeams in which previous studies were unable to track such behavior. This study could be a step forward in analyzing nanostructures resting on a medium as sensors, actuators, switches, resonators, etc. © 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature
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- Source: European Physical Journal Plus ; Volume 133, Issue 7 , July , 2018 ; 21905444 (ISSN)
- URL: https://link.springer.com/article/10.1140/epjp/i2018-12128-5