CAJ | 학술논문

针对有限元法等数值方法较难处理的质量偏心梁问题，考虑质心、形心不重合情形下的弯－纵耦合效应，建立了有偏心 Timoshenko 梁弯－纵耦合振动的数学模型，推导了相应的特征方程。进而给出了若干偏心工况下 Timosh-enko 梁弯－纵耦合振动的解析表达式，并探讨了偏心率和典型边界条件对纵向和弯曲振动固有频率和模态振型的影响规律。分析结果表明，固有频率随着偏心率的增大而减小，且质量偏心对纵向振动的影响较弯曲振动更为明显。
침대유한원법등수치방법교난처리적질량편심량문제，고필질심、형심불중합정형하적만－종우합효응，건립료유편심 Timoshenko 량만－종우합진동적수학모형，추도료상응적특정방정。진이급출료약간편심공황하 Timosh-enko 량만－종우합진동적해석표체식，병탐토료편심솔화전형변계조건대종향화만곡진동고유빈솔화모태진형적영향규률。분석결과표명，고유빈솔수착편심솔적증대이감소，차질량편심대종향진동적영향교만곡진동경위명현。
Natural vibration of a beam with mass eccentricity is difficult to deal with using numerical methods,such as,the finite element method.Considering the coupling effect caused by the center of mass not coinciding with the center of geometry,the mathematical model of a Timoshenko beam's flexural-longitudinal coupled vibration was established,the corresponding characteristic equation was derived.Then the analytic solutions to Timoshenko beam's flexural-longitudinal coupled natural vibration under several mass eccentric conditions were deduced.The effect laws of eccentricities and boundary conditions on the natural frequencies and modal shapes of flexural-longitudinal coupled natural vibration were explored.The results showed that the natural frequencies decrease with increase in eccentricity,and the effects of eccentricity on the longitudinal vibration are more obvious than those on the flexural vibration.