复杂边界条件推进轴系结构纵向振动特性分析
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- 英文论文题名：Longitudinal vibration characteristics analysis of propulsion shaftingstructure with complicated boundary conditions
- 论文作者：许得水 ; 杜敬涛 ; 刘杨 ; 刘志刚
- 英文论文作者：Xu De-shui ; Du Jing-tao ; Liu Yang ; Liu Zhi-gang ; College of Power and Energy Engineering ; Harbin Engineering University
- 年：2016
- 作者机构：哈尔滨工程大学动力与能源工程学院;
- 论文关键词：弹性杆结构 ; 纵向振动 ; 复杂边界条件 ; 改进傅里叶级数
- 英文论文关键词：elastic rod structure ; longitudinal vibration ; complex boundary conditions ; improved Fourier series
- 会议召开时间：2016-07-28
- 会议录名称：第二十七届全国振动与噪声应用学术会议论文集
- 语种：中文
- 分类号：TB535
- 学会代码：ZDZD
- 会议名称：第二十七届全国振动与噪声应用学术会议
- 会议地点：中国黑龙江哈尔滨
- 主办单位：中国振动工程学会振动与噪声控制专业委员会
- 学会名称：中国振动工程学会振动与噪声控制专业委员会
- 页数：6
- 文件大小：1274k
- 原文格式：D
- 会议级别：全国
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。
In this paper, an improved Fourier series method is employed to analyze the longitudinal vibration of elastic uniform straight rod with elastic boundary restraints. Based on the continuous theory of elastic rod, energy principle is used to describe its longitudinal vibration, with its boundary conditions described through the introduction of stored potential and kinetic energies. The displacement admissible function for longitudinal vibration is constructed via an 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.
In this paper, an improved Fourier series method is employed to analyze the longitudinal vibration of elastic uniform straight rod with elastic boundary restraints. Based on the continuous theory of elastic rod, energy principle is used to describe its longitudinal vibration, with its boundary conditions described through the introduction of stored potential and kinetic energies. The displacement admissible function for longitudinal vibration is constructed via an 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.
引文
[1]王光荣.潜艇纵向振动计算及振动特性[J].海军工程大学学报,2005,17(2):59-63.
[2]赵耀,张赣波,李良伟.船舶推进轴系纵向振动及其控制技术研究进展[J].中国造船,2011,52(2):259-269.
[3]H.T Ma.Exact solutions of axial vibration problems of elastic bars[J].International Journal for Numerical Methods in Engineering,2008,75:241-252.
[4]周瑞,江祎,管文生.船舶推进轴系纵振计算方法及影响因素分析[J].中国舰船研究,2011,6(6):17-22.
[5]K.Yang.A unified solution for longitudinal wave propagation in an elastic rod[J].Journal of Sound and Vibration,2008,314:307-329.
[6]程利青,胡嗣柱.用Laplace变换法求解弹性杆的两类纵振动问题[J].福州大学学报,2007,35(4):532-536.
[7]L.Murawski.Axial vibrations of a propulsion system taking into account the couplings and the boundary conditions[J].Journal of Marine Science and Technology,2004,9(4):171-181.
[8]唐驾时,李骊,霍拳忠.具有复杂边界条件的杆的振动分析[J].应用数学与力学,1988,9(9):781-791.
[9]V.Jovanovic.A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditionsat each end[J].Journal of Engineering Mathematics,2013,79:125-142.
[10]F.Cortes,M.J.Elejabarrieta.Forced response of a viscoelastically damped rod using the superposition of modal contribution functions[J].Journal of Sound and Vibration,2008,315:58-64.
[11]吴崇健,陈志刚,徐志云.均匀有限杆纵向振动谐响应的WPA解法[A].2005年船舶结构力学学术会议论文集
[2]赵耀,张赣波,李良伟.船舶推进轴系纵向振动及其控制技术研究进展[J].中国造船,2011,52(2):259-269.
[3]H.T Ma.Exact solutions of axial vibration problems of elastic bars[J].International Journal for Numerical Methods in Engineering,2008,75:241-252.
[4]周瑞,江祎,管文生.船舶推进轴系纵振计算方法及影响因素分析[J].中国舰船研究,2011,6(6):17-22.
[5]K.Yang.A unified solution for longitudinal wave propagation in an elastic rod[J].Journal of Sound and Vibration,2008,314:307-329.
[6]程利青,胡嗣柱.用Laplace变换法求解弹性杆的两类纵振动问题[J].福州大学学报,2007,35(4):532-536.
[7]L.Murawski.Axial vibrations of a propulsion system taking into account the couplings and the boundary conditions[J].Journal of Marine Science and Technology,2004,9(4):171-181.
[8]唐驾时,李骊,霍拳忠.具有复杂边界条件的杆的振动分析[J].应用数学与力学,1988,9(9):781-791.
[9]V.Jovanovic.A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditionsat each end[J].Journal of Engineering Mathematics,2013,79:125-142.
[10]F.Cortes,M.J.Elejabarrieta.Forced response of a viscoelastically damped rod using the superposition of modal contribution functions[J].Journal of Sound and Vibration,2008,315:58-64.
[11]吴崇健,陈志刚,徐志云.均匀有限杆纵向振动谐响应的WPA解法[A].2005年船舶结构力学学术会议论文集