黏弹性Pasternak地基上修正Timoshenko梁横向自振特性分析  

Analysis of transverse free vibration characteristics of modified Timoshenko beam on viscoelastic Pasternak foundction

作　　者：柳伟 汪过兵 赵志鹏 赵晓军 LIU Wei;WANG Guo-bin;ZHAO Zhi-peng;ZHAO Xiao-jun(School of Civil Engineering,Lanzhou University of Information 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》2024年第8期1330-1338,共9页Journal of Vibration Engineering

基　　金：甘肃省科技计划资助项目(23JRRA1374);2022年甘肃省高等教育教学成果培育项目(197)。

摘　　要：基于修正Timoshenko梁理论,建立黏弹性Pasternak地基上修正Timoshenko梁的横向振动控制方程,运用回传射线矩阵法推导出黏弹性Pasternak地基上两端简支修正Timoshenko梁自振频率和衰减系数的解析解,结合二分法和黄金分割法计算了经典边界条件下黏弹性Pasternak地基上修正Timoshenko梁的自振特性,对比分析了考虑剪切变形引起的转动惯量、梁长及不同的边界条件对结构自振特性的影响。研究表明:黏弹性Pasternak地基上修正Timoshenko梁的各阶自振频率和衰减系数小于经典Timoshenko梁的各阶自振频率和衰减系数;梁越短,剪切变形引起的转动惯量对结构自振频率和衰减系数的影响越大,且对高阶的影响明显大于低阶;边界约束条件越强,振动能量衰减越明显。Based on the modified Timoshenko beam theory,the transverse vibration governing equation of the modified Timoshenko beam on the viscoelastic Pasternak foundation is established.The analytical solutions of the natural frequency and attenuation coefficient of the modified Timoshenko beam simply supported at both ends in the viscoelastic Pasternak foundation are derived with the reverberation-ray matrix method.The natural vibration characteristics of the modified Timoshenko beam on the viscoelastic Pasternak foundation under classical boundary conditions are calculated by dichotomy and golden section method.The effects of moment of inertia caused by shear deformation,beam length and different boundary conditions on the natural vibration characteristics of the structure are compared and analyzed.The results show that the natural frequency and attenuation coefficient of the modified Timoshenko beam on the viscoelastic Pasternak foundation are smaller than those of the classical Timoshenko beam;the shorter the beam,the more significant the influence of the moment of inertia caused by shear deformation on the natural frequency and attenuation coefficient of the structure,and the influence on the higher order is obviously greater than that on the low order;the stronger the boundary constraint condition,the more obvious the vibration energy attenuation.

关 键 词：黏弹性Pasternak地基 修正Timoshenko梁 回传射线矩阵法 解析解 边界条件 

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