Internal resonance of an axially transporting beam with a two-frequency parametric excitation  

作　　者：Dengbo ZHANG Youqi TANG Ruquan LIANG Yuanmei SONG Liqun CHEN 

机构地区：[1]School of Mechanical and Vehicle Engineering,Linyi University,Linyi,Shandong Province,276000,China [2]School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai,201418,China [3]School of Mechanics and Engineering Sciences,Shanghai University,Shanghai,200072,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第12期1805-1820,共16页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos.12002142,11872159;51976087);the National Natural Science Foundation of Shanghai of China (No.21ZR1462500);the Natural Science Foundation of Shandong Province of China (No.ZR2021QB137)。

摘　　要：This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation.The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam.The governing equation and the associated boundary conditions are obtained by Newton’s second law.The method of multiple scales is utilized to obtain the steady-state responses.The RouthHurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses.The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations.Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation.The approximate analytical method is validated via a differential quadrature method.

关 键 词：axially transporting viscoelastic beam internal resonance two-frequency excitation nonlinear vibration perturbation technique 

分 类 号：O327[理学—一般力学与力学基础]