经典边界条件粘弹性Pasternak地基上Bernoulli-Euler梁横向自振特性分析

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (1) : 173-182.

论文

付艳艳，余云燕

作者信息 +

Transverse free vibration characteristics of Bernoulli-Euler beam on viscoelastic Pasternak foundation under classical boundary conditions

FU Yanyan, YU Yunyan

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文章历史 +

摘要

自振特性在结构的动力分析中具有重要的意义。将回传射线矩阵法（MRRM）推广到地基梁自振特性的研究中，通过节点力平衡和位移协调方程及对偶局部坐标系下单元相位关系，建立两端简支、两端自由、两端固支、简支-自由、简支-固支及固支-自由这六种边界条件下粘弹性Pasternak地基上的Bernoulli-Euler梁的回传射线矩阵，进而得到其频率方程。根据单一局部坐标系下的边界条件，推导出模态函数解析表达式，进一步根据正交归一化条件求解模态函数表达式中的未知参数。通过具体算例验证了回传射线矩阵法求解的正确性，并对不同边界条件下的自振频率、衰减系数及模态函数进行了分析。为粘弹性地基梁的振动特性研究提供理论基础。

Abstract

Free vibration characteristics play an important role in structural dynamic analysis. Here, the method of reverberation ray matrix (MRRM) was proposed to study free vibration characteristics of foundation beams. Through node force balance equation, displacement compatibility equation and element phase relation in dual local coordinate system, reverberation-ray matrices of a Bernoulli-Euler beam on viscoelastic Pasternak foundation were established under classical boundary conditions including two-end simply supported, two-end free, two-end fixed, simply supported-free, simply supported-fixed and fixed-free, and then the beam’s frequency equations under the 6 types boundary conditions were deduced. According to boundary conditions in a single local coordinate system, analytical expressions for the beam’s modal functions were derived. Furthermore, unknown parameters in modal function expressions were solved according to the orthogonal normalization condition. Some examples were used to verify the correctness of the MRRM. Finally, natural frequencies, attenuation coefficients and modal functions of the beam under different boundary conditions were analyzed. The study results provided a theoretical basis for studying free vibration characteristics of beams on viscoelastic foundation.

导出引用

付艳艳，余云燕. 经典边界条件粘弹性Pasternak地基上Bernoulli-Euler梁横向自振特性分析[J]. 振动与冲击, 2021, 40(1): 173-182

FU Yanyan, YU Yunyan. Transverse free vibration characteristics of Bernoulli-Euler beam on viscoelastic Pasternak foundation under classical boundary conditions[J]. Journal of Vibration and Shock, 2021, 40(1): 173-182

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