轴向载荷条件下弹性边界约束梁结构振动特性分析  

Vibration characteristics analysis for an axially loaded beam with elastic boundary restraints

作　　者：赵雨皓 杜敬涛[1] 许得水 ZHAO Yuhao;DU Jingtao;XU Deshui(College of Power and Energy Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨工程大学动力与能源工程学院,哈尔滨150001

出　　处：《振动与冲击》2020年第15期109-117,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11972125);霍英东青年教师基金(161049)。

摘　　要：采用改进傅里叶级数展开建立了轴向载荷条件下弹性边界约束梁结构振动分析模型。通过在梁结构两端引入平动和旋转位移约束弹簧,相应设置约束弹簧刚度系数可以实现对任意边界条件及其组合的模拟。梁结构振动系统位移场采用傅里叶级数附加边界光滑函数进行构建,利用能量原理建立轴向载荷作用下梁结构总动能、总势能和外力做功项,并结合瑞利-里兹步骤获得系统特征矩阵方程。通过数值算例,验证了该模型对不同边界条件、轴向载荷作用下梁结构振动特性分析的正确性与可靠性。在此基础上,研究了边界约束弹簧横向刚度、旋转刚度、轴向载荷等系统参数及激振力对梁结构振动特性的影响。该模型具有高效、高精度等特点,为研究轴向载荷作用下复杂边界条件梁结构振动行为提供了有效分析手段。Here, an improved Fourier series expansion was employed to establish the vibration analysis model for an axially loaded beam with elastic boundary restraints. Through introducing translational restrained springs and rotatingones at both ends of the beam, setting the corresponding restrained springs’ stiffness coefficients could simulate all boundary conditions and their combinations. The beam structure’svibrational displacement field was constructed witha Fourier series and additional boundary smooth functions. According to the energy principle, the total kinetic energy, total potential one and external work items of the whole beam system werebuilt, and the system characteristic matrixwas obtained with Rayleigh-Ritz method.Numerical examples were then given to verify the correctness and reliability of the proposed model for vibration characteristics analysis of the beam structure under different boundary conditions and axial loads. Furthermore, effects of system parameters including boundary restrainttransverse stiffness and rotating one, axial load and excitation forces on vibration characteristics of the beam structure were investigated. Results showed thatthe proposed model has advantages of higher efficiency and precision;it can provide an effective analysismeans for studying vibration behaviors of axially loaded beam structuresunder complex boundary conditions.

关 键 词：轴向载荷 梁结构振动 弹性边界约束 傅里叶级数 

分 类 号：O327[理学—一般力学与力学基础]