Advances in nano research

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Free vibration analysis Silicon nanowires surrounded by elastic matrix by nonlocal finite element method

  • Uzun, Busra (Uludag University, Civil Engineering Department) ;
  • Civalek, Omer (Akdeniz University, Civil Engineering Department)
  • Received : 2018.12.03
  • Accepted : 2019.04.03
  • Published : 2019.03.25
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Abstract

Higher-order theories are very important to investigate the mechanical properties and behaviors of nanoscale structures. In this study, a free vibration behavior of SiNW resting on elastic foundation is investigated via Eringen's nonlocal elasticity theory. Silicon Nanowire (SiNW) is modeled as simply supported both ends and clamped-free Euler-Bernoulli beam. Pasternak two-parameter elastic foundation model is used as foundation. Finite element formulation is obtained nonlocal Euler-Bernoulli beam theory. First, shape function of the Euler-Bernoulli beam is gained and then Galerkin weighted residual method is applied to the governing equations to obtain the stiffness and mass matrices including the foundation parameters and small scale parameter. Frequency values of SiNW is examined according to foundation and small scale parameters and the results are given by tables and graphs. The effects of small scale parameter, boundary conditions, foundation parameters on frequencies are investigated.

Keywords

Acknowledgement

Supported by : The Scientific and Technological Research Council of Turkey (TUBITAK)

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