黏弹性Pasternak地基上两跨连续Timoshenko梁横向自振特性分析

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (11) : 1-10.

论文

余云燕1，付艳艳1，张伟2

作者信息 +

Analysis of transverse natural frequency of two-span continuous Timoshenko beam on viscoelastic Pasternak foundation

YU Yunyan1, FU Yanyan1, ZHANG Wei2

Author information +

文章历史 +

摘要

以黏弹性Pasternak地基上的Timoshenko梁为研究对象，研究其在两端简支、两端固支、简支-固支边界条件下的单跨地基梁及两跨连续地基梁（等跨和不等跨两种工况）的自振频率、衰减系数和模态。基于回传射线矩阵法，根据各种约束条件下的节点耦合条件，推导横向振动频率方程，通过观察两跨连续地基梁与单跨地基梁的频率方程，并通过具体算例，研究两跨连续地基梁与单跨地基梁自振频率之间的联系与区别，进一步给出前三阶模态。结果表明：两等跨连续地基梁自振频率方程可分为两个部分，且这两部分分别与两端简支和简支-固支边界条件下单跨地基梁的频率方程形式类同；其奇数阶自振频率与两端简支边界条件下单跨地基梁的偶数阶自振频率相等，而其偶数阶自振频率则与两端固支边界条件下单跨地基梁的偶数阶自振频率相同；不等跨的两跨连续Timoshenko地基梁的模态函数曲线幅值随阶数的增加降低最快。

Abstract

Timoshenko beams on viscoelastic Pasternak foundations are studied for their self-vibration frequencies, attenuation coefficients and modalities for single-span foundation beams and two-span continuous foundation beams (both equal-span and unequal-span conditions) under classical boundary conditions including two-end simply supported, two-end fixed, simply supported-fixed. Based on the method of reverberation-ray matrix, the transverse vibration frequency equations are derived based on the nodal coupling conditions under various constraints. By observing the frequency equations of two-span continuous foundation beams and single-span foundation beams, and by using specific arithmetic examples, the connection and difference between the self-vibration frequencies of two-span continuous foundation beams and single-span foundation beams are investigated, and the first three orders of modes are further given. The results show that the frequency equation for a two-span continuous foundation beam can be divided into two parts, which are similar in form to the frequency equation for a single-span foundation beam under simply-supported and simply-supported-solidly-supported boundary conditions at both ends, respectively. The amplitude of the modal function curve for a two-span continuous Timoshenko foundation beam with unequal spans decreases fastest with increasing order.

导出引用

余云燕1，付艳艳1，张伟2. 黏弹性Pasternak地基上两跨连续Timoshenko梁横向自振特性分析[J]. 振动与冲击, 2023, 42(11): 1-10

YU Yunyan1, FU Yanyan1, ZHANG Wei2. Analysis of transverse natural frequency of two-span continuous Timoshenko beam on viscoelastic Pasternak foundation[J]. Journal of Vibration and Shock, 2023, 42(11): 1-10

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