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Stability analysis of Timoshenko nanobeam with material uncertainties using a double-parametric form-based analytical approach and Monte Carlo simulation technique

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Abstract

This study is aimed at analyzing the effects of material uncertainties on the stability of Timoshenko nanobeam. Here, the uncertainties are considered to be associated with the diameter, length, and Young’s modulus of the nanobeam in terms of special fuzzy number, namely Symmetric Gaussian Fuzzy Number (SGFN). The governing equations for stability analysis of uncertain model are obtained by incorporating the Timoshenko beam theory along with Hamilton’s principle and double-parametric form of fuzzy numbers. The small-scale effect of the nanobeam is addressed by Eringen’s elasticity theory, and the double-parametric form-based Navier’s method is employed to calculate the results of the uncertain models for the lower bound (LB) and upper bound (UB) of the buckling loads. The results obtained by the uncertain model are validated with the deterministic model in particular case as well as with the results obtained by Monte Carlo simulation (MCS) technique in terms of the lower bound and upper bound of the buckling loads, exhibiting robust agreement. Further, a parametric study is conducted to investigate the fuzziness or spreads of the buckling loads with respect to different uncertain parameters.

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Acknowledgements

We are thankful to Defence Research & Development Organization (DRDO), New Delhi, India (Sanction Code: DG/TM/ERIPR/GIA/17-18/0129/020), for the funding to carry out the present research work.

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  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, India

    Subrat Kumar Jena, S. Chakraverty & Rajarama Mohan Jena

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  1. Subrat Kumar Jena
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  2. S. Chakraverty
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  3. Rajarama Mohan Jena
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Correspondence to S. Chakraverty.

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Jena, S.K., Chakraverty, S. & Jena, R.M. Stability analysis of Timoshenko nanobeam with material uncertainties using a double-parametric form-based analytical approach and Monte Carlo simulation technique. Eur. Phys. J. Plus 135, 536 (2020). https://doi.org/10.1140/epjp/s13360-020-00549-8

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