【作者】 许得水； 杜敬涛； 张赟； 杨铁军； 李玩幽； 刘志刚；

【Author】 Deshui Xu;Jingtao Du;Tiejun Yang;Wanyou Li;Zhigang Liu;College of Power and Energy Engineering,Harbin Engineering University;

【机构】 哈尔滨工程大学动力与能源工程学院；

【摘要】 本文采用一种改进傅立叶级数方法建立了弹性边界约束均匀杆纵向振动分析模型。基于弹性杆连续理论,采用能量原理对其纵向振动进行描述,边界条件通过相应的势能与动能项引入。将杆结构纵振位移容许函数采用一种改进傅立叶级数进行构建,结合瑞利-里兹方法进而得到弹性杆纵振特征方程。对于更为复杂的质量-弹簧边界及外部载荷激励情况,可以通过修改系统拉格朗日函数势能、动能及增加外力做功项而方便得到系统矩阵方程。采用MATLAB编程仿真,通过调整约束弹簧刚度系数而统一获得各种边界条件,结果表明本文模型所得到模态信息和强迫振动响应均能同现有文献方法很好地吻合,充分验证了本文方法的正确性和有效性,为后续开展一维弹性结构振动特性分析及其控制提供模型基础。更多还原

【Abstract】 In this paper,an improved Fourier series method is employed to analyze the longitudinal vibration of elasticuniform straight rod with elastic boundary restraints.Based on thecontinuous theory of elastic rod,energy principle is used to describe its longitudinal vibration,with its boundary conditions described through the introduction ofstoredpotential and kineticenergies.The displacementadmissiblefunction forlongitudinal vibration is constructedviaan improved Fourier series,and the system characteristic equation is derived in conjunction with Rayleigh-Ritz method.For much more complicated cases,such as spring-mass end and/or external excitation,the system equation can be easily obtained via the modification of energy terms in system Lagrangian function.The simulation model is developed in MATLAB environment.All the boundary conditions can be uniformly realized by setting the boundary restraining spring coefficients.The results show that the modal information and forced vibration response from the current model can agree very well with those from other approaches in literature,then the correctness and effectiveness have been validated.It is believed that the current work can provide an efficient model for future investigation on the dynamic analysis of such one-dimensional elastic structure as well as its vibration control.更多还原