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黏弹性地基上欧拉梁横向自由振动
彭丽,王英
作者单位E-mail
彭丽 上海师范大学 建筑工程学院 pengl@shnu.edu.cn 
王英 上海师范大学 建筑工程学院  
摘要:
本文研究黏弹性三参数地基上有限长Euler-Bernoulli梁的横向自由振动。通过给出简支边界条件下的频率方程和模态方程,进而推导出模型地基梁的固有频率和模态函数的解析表达式,提供了精确计算任意一阶频率和模态的简便方法。在具体算例中,运用本文推导出的公式很方便地计算出低阶和高阶频率的精确值,避免了以往数值方法带来的计算误差。同时通过具体算例分析了不同物理参数对黏弹性地基上欧拉梁的振动特性的影响。
关键词:  欧拉梁  黏弹性地基  固有频率  模态
DOI:
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基金项目:
Transverse free vibration of Euler–Bernoulli beams resting on viscoelastic foundation
PENG Li,WANG Ying
Abstract:
This paper focuses on the free transverse vibration of an Euler–Bernoulli beam resting on three-parameter viscoelastic foundation. Under simply supported boundary conditions, the exact frequency equations and the modal functions are given, and the explicit formulae for natural frequencies and modal functions are derived. ThereforeStheSresearchSofStheSpaperSprovides a simple and convenient way to obtain analytical solution of any order natural frequencies and modal functions. In numerical examples, with the explicit formulae, the low and high order natural frequencies are calculated easily, avoiding calculation error from numerical methods. The effects of the different parameters of the Euler–Bernoulli beam and the viscoelastic foundation on the free vibration characteristics are also numerically demonstrated.
Key words:  Euler–Bernoulli beams, Viscoelastic foundation, Natural frequency, Mode