黏弹性四参数地基上两跨连续修正Timoshenko梁的横向自振特性分析  

Analysis of transverse free vibration characteristics of two-span continuously modified Timoshenko beams on viscoelastic four-parameter foundation

作　　者：柳伟 汪过兵 LIU Wei;WANG Guobing(School of Civil Engineering,Lanzhou University of Information Science and Technology,Lanzhou 730300,China;Geotechnical Engineering Research Institute,Xi’an University of Technology,Xi’an 710048,China)

机构地区：[1]兰州信息科技学院土木工程学院,甘肃兰州730300 [2]西安理工大学岩土工程研究所,陕西西安710048

出　　处：《振动工程学报》2025年第3期604-611,共8页Journal of Vibration Engineering

基　　金：甘肃省科技计划项目(23JRRA1374)。

摘　　要：为解决黏弹性四参数地基上两跨连续修正Timoshenko梁的横向振动问题,将两跨连续修正Timoshenko梁与黏弹性四参数地基进行组合,建立新的振动控制方程,运用回传射线矩阵法,结合二分法和黄金分割法,分析了黏弹性四参数地基上两跨(等跨、不等跨)连续修正Timoshenko梁与单跨修正Timoshenko梁自振特性之间的联系与区别。结果表明:对于黏弹性四参数地基上的修正Timoshenko梁,单跨梁的各阶自振频率小于两跨连续梁的各阶自振频率,单跨梁的偶数阶自振频率和衰减系数与两等跨连续梁的奇数阶自振频率和衰减系数相同,不等跨两跨连续梁奇数阶自振频率小于两等跨连续梁奇数阶自振频率;两等跨连续修正Timoshenko梁的偶数阶振型关于跨中支座对称,奇数阶振型关于跨中支座反对称。In order to solve the transverse vibration problem of two-span continuously modified Timoshenko beam on viscoelastic four-parameter foundation,a new vibration governing equation is established by combining two-span continuously modified Timoshenko beam with viscoelastic four-parameter foundation.By using the echo matrix method,bisection and golden section method,the relation and difference between the natural vibration characteristics of two-span(equal-span,unequal-span)continuously modified Timoshenko beam and single-span modified Timoshenko beam on viscoelastic four-parameter foundation are analyzed.The results show that for the modified Timoshenko beam on the viscoelastic four-parameter foundation,the natural frequency of each order of the single-span beam is less than that of the two-span continuous beam,the even-order natural frequency and attenuation coefficient of the single-span beam are the same as the odd-order natural frequency and attenuation coefficient of the two equal-span continuous beam,and the odd-order natural frequency of the unequal-span two-span continuous beam is less than that of the two-span continuous beam.The even-order mode shapes of two equal-span continuous modified Timoshenko beams are sym metrical with respect to the supports in the middle of the span,and the odd-order modes are antisymmetric with respect to the mid-span.

关 键 词：黏弹性四参数地基 两跨连续修正Timoshenko梁 回传射线矩阵法 横向振动 模态 

分 类 号：TU471.2[建筑科学—结构工程] TU348[建筑科学—土工工程]