基于非局部理论的黏弹性地基上欧拉梁自由振动特性分析

发布时间：2018-04-02 17:05

本文选题：自由振动　切入点：非局部地基　出处：《振动与冲击》2017年01期

【摘要】：基于非局部黏弹性理论,针对非局部阻尼欧拉梁在非局部黏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黏弹性模型、速度相关型外阻尼模型以及非局部黏弹性地基模型,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、黏弹性参数、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黏弹性地基支撑下的动力学问题准确有效。
[Abstract]:Based on the theory of nonlocal viscoelasticity, the vibration characteristics of non-local damped Euler beams on nonlocal viscoelastic foundations are studied.Firstly, the vibration governing equations of Euler beam are established by introducing the generalized Maxwell viscoelastic model, the velocity dependent external damping model and the nonlocal viscoelastic foundation model.Then the closed solutions of Euler beam natural frequencies and corresponding modal modes under different boundary conditions are obtained by using the transfer function method.The correctness of the model is verified by comparing the results with the previous research results, and the non-local parameters of the Euler beam, the viscoelastic parameters and the non-local parameters of the foundation are analyzed.The influence of stiffness and length on the natural frequency.The results show that the established dynamic model and the analytical method are accurate and effective for solving the dynamic problems of non-local damped Euler beams under the support of non-local viscoelastic foundation.
【作者单位】：国防科学技术大学航天科学与工程学院;
【基金】：国家自然科学基金资助项目(11272348);国家自然科学基金资助项目(11302254)
【分类号】：O327

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