Free vibration characteristics of an euler-bernoulli beam on a viscoelastic foundation based on nonlocal continuum theory

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (1) : 88-95.

ZHANG Da-peng, LEI Yong-jun

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Abstract

The vibration characteristics of a nonlocal damped Euler-Bernoulli beam on a nonlocal viscoelastic foundation were studied based on the nonlocal viscoelasticity theory here. The generalized Maxwell viscoelastic model, the velocity-dependent external damping model and the nonlocal viscoelastic foundation model were employed to establish the governing vibration equations of the beam system. A transfer function method was used to obtain natural frequencies and the corresponding modal shapes in a closed form for the Euler-Bernoulli beam with arbitrary boundary conditions. The proposed models were validated by comparing the obtained results with the available ones in literature. Subsequently, a detailed parametric study was conducted to examine the effects of nonlocal and viscoelastic parameters of the Euler-Bernoulli beam, and nonlocal parameters, stiffness and length of the foundation on natural frequencies of the beam system. The results demonstrated that the proposed dynamic modeling and analysis methods for dynamic characteristics of a nonlocal damped Euler-Bernoulli beam on a nonlocal viscoelastic foundation are effective and correct.

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free vibration / nonlocal foundations / Euler-Bernoulli beams / nonlocal elasticity theory / transfer function method

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ZHANG Da-peng, LEI Yong-jun. Free vibration characteristics of an euler-bernoulli beam on a viscoelastic foundation based on nonlocal continuum theory[J]. Journal of Vibration and Shock, 2017, 36(1): 88-95

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