基于非局部理论的粘弹性地基上欧拉梁自由振动特性分析

张大鹏,雷勇军

振动与冲击 ›› 2017, Vol. 36 ›› Issue (1) : 88-95.

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PDF(1249 KB)
振动与冲击 ›› 2017, Vol. 36 ›› Issue (1) : 88-95.
论文

基于非局部理论的粘弹性地基上欧拉梁自由振动特性分析

  • 张大鹏,雷勇军
作者信息 +

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

  • ZHANG Da-peng, LEI Yong-jun
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文章历史 +

摘要

基于非局部粘弹性理论,针对非局部阻尼欧拉梁在非局部粘弹性地基上的振动特性问题进行研究。首先通过引入广义Maxwell粘弹性模型、速度相关型外阻尼模型以及非局部粘弹性地基模型,建立了欧拉梁的振动控制方程。然后利用传递函数方法得到了不同边界条件下欧拉梁固有频率及相应模态振型的封闭解。通过与文献中已有研究结果进行对比验证了所建模型的正确性,并在此基础上分析了欧拉梁非局部参数、粘弹性参数、地基非局部参数、刚度及长度等影响因素对固有频率的影响情况。结果表明,所建的动力学模型及计算分析方法对解决非局部阻尼欧拉梁在非局部粘弹性地基支撑下的动力学问题准确有效。

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.
 

关键词

自由振动 / 非局部地基 / 欧拉梁 / 非局部弹性理论 / 传递函数方法

Key words

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

引用本文

导出引用
张大鹏,雷勇军. 基于非局部理论的粘弹性地基上欧拉梁自由振动特性分析[J]. 振动与冲击, 2017, 36(1): 88-95
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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