Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries  

作　　者：Yanan LI Jieyu DING Hu DING Liqun CHEN 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,Shanghai Frontier Science Center of Mechanoinformatics,School of Mechanics and Engineering Science,Shanghai University,Shanghai 200072,China [2]School of Mathematics and Statistics,Qingdao University,Qingdao 266071,Shandong Province,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第9期1523-1538,共16页应用数学和力学（英文版）

基　　金：Project supported by the YEQISUN Joint Funds of the National Natural Science Foundation of China(No.U2341231);the National Natural Science Foundation of China(No.12172186)。

摘　　要：In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

关 键 词：translating beam Timoshenko beam non-homogeneous boundary natural frequency critical velocity 

分 类 号：O326[理学—一般力学与力学基础]