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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 106
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Paper 37

Dynamic Stiffness and Eigenvalues of Nonlocal Nano-Beams

S. Adhikari1 and T. Murmu2

1College of Engineering, Swansea University, Wales, United Kingdom
2School of Engineering, University of the West of Scotland, Glasgow, Scotland, United Kingdom

Full Bibliographic Reference for this paper
S. Adhikari, T. Murmu, "Dynamic Stiffness and Eigenvalues of Nonlocal Nano-Beams", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 37, 2014. doi:10.4203/ccp.106.37
Keywords: bending vibration, nonlocal mechanics, dynamic stiffness, asymptotic analysis, frequency response..

Free and forced bending vibration of damped nonlocal beams are investigated in this paper. Two types of nonlocal damping models, namely, strain-rate-dependent viscous damping and velocity-dependent viscous damping are considered. A frequency dependent dynamic finite element method is developed to obtain the forced vibration response. Frequency-adaptive complex-valued shape functions are used for the derivation of the dynamic stiffness matrix. The stiffness and mass matrices of the nonlocal beam are also obtained using the conventional finite element method. Results from the dynamic finite element method and conventional finite element method are compared. The frequency response function obtained using the proposed dynamic finite element method shows high modal density in the higher frequency ranges.

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