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Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects

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Abstract

The present study introduces an analytical–computational model to simulate the effects of different simultaneous aspects on the behavior of nanobeams. The first one deals with the space nonlocality interaction and taking into account the microstructure effects, which has been formulated by using the nonlocal couple-stress elasticity. The second factor deals with the memory-dependent effect and has been investigated in the framework of linear viscoelasticity theory. It is the first time to apply the coupled effects of the microstructure and long-range interactions between the particles, to reflect the size-dependency of viscoelastic structures. Bernoulli–Euler nanobeam is taken as a vehicle to present the details of the proposed model. Eringen nonlocal elasticity and the modified couple-stress theory are used to formulate the two phenomena of long-range cohesive interaction and the microstructure local rotation effects, respectively. Boltzmann superposition viscoelastic model, endowed by Wiechert series, is used to simulate the linear behavior of isotropic, homogeneous and non-aging viscoelastic materials. The extended Hamilton’s principle is applied to formulate the analytical model of mechanical behavior of the nonlocal couple-stress nanobeam. The model has been verified and some results are compared with those published in the literature and a good agreement has been obtained. It is shown that the material-length scale parameter, nonlocal parameter, viscoelastic relaxation time and length-to-thickness ratio have a significant effect on the bending response of viscoelastic nanobeams with various boundary conditions.

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Acknowledgments

The authors would like to thank Prof. Ahmed G. El-Shafei, Zagazig University-Egypt, for his help in this research and for the useful discussions and advises.

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Authors and Affiliations

  1. Mechanical Design and Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    M. A. Attia & F. F. Mahmoud

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  1. M. A. Attia
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  2. F. F. Mahmoud
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Correspondence to M. A. Attia.

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Attia, M.A., Mahmoud, F.F. Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects. Int J Mech Mater Des 13, 385–406 (2017). https://doi.org/10.1007/s10999-016-9343-4

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  • DOI: https://doi.org/10.1007/s10999-016-9343-4

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