Effect of magnetic field on dynamic responses of nonuniform nanobeams resting on a viscoelastic foundation

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (4) : 116-122.

ZHANG Da-peng, LEI Yong-jun, SHEN Zhi-bin

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Abstract

The dynamic model was established and vibration responses were examined for a nonuniform nanobeam, which was resting on a viscoelastic foundation and subjected to a magnetic field. Based on nonlocal Euler-Bernoulli beam theory, Kelvin viscoelastic foundation model and Maxwell relation, the governing equations of the system were derived. The natural frequencies of the nonuniform nanobeams were then obtained by solving the governing equations via transfer function method incorporating with perturbation method. Subsequently, the influences of nonlocal parameter, the strength of the magnetic field, relaxation time and taper parameter on the damped frequencies and damping ratios were examined. The results show that the proposed model is available for dynamics analysis of a nonuniform nanobeam resting on a viscoelastic foundation in a magnetic field.

Key words

free vibration / viscoelastic foundations / nonuniform nanobeams / nonlocal elasticity theory / perturbation method

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ZHANG Da-peng, LEI Yong-jun, SHEN Zhi-bin. Effect of magnetic field on dynamic responses of nonuniform nanobeams resting on a viscoelastic foundation[J]. Journal of Vibration and Shock, 2018, 37(4): 116-122

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