含单面限位局部非线性结构的主频响应分析
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摘要
对于含单面限位的大型局部非线性结构,其主频响应特性往往与限位的位置、大小和数量密切相关。研究含单面限位局部非线性结构的主频响应分析方法,采用非线性控制中的描述函数来表征单面限位非线性的频域特性;通过逆阵更新方法进行降维处理,极大地提高了频域响应的计算效率;搭建含单面限位约束的实验梁结构,在不同激励幅值和间隙大小情况下,测量约束梁结构的频响曲线。数值仿真与实验结果获得了较好的一致性,验证了所提出的局部非线性结构主频响应分析方法的有效性。
For large-scale nonlinear structures with local single-sided limitation,the fundamental frequency response characteristic is often closely related to the position and size of the limitation. The analysis method for nonlinear structures was mainly studied. The frequency domain characteristics of nonlinearity were characterized by the describing function first appeared in the nonlinear control. The inverse matrix updating method was used to reduce the processing dimension,which greatly improves the computational efficiency of frequency domain response. The numerical method Runge-Kutta was adopted to verify the effectiveness of the method. The first-order frequency response curve of a T-shaped beam was analysed by simulations and experiments.
For large-scale nonlinear structures with local single-sided limitation,the fundamental frequency response characteristic is often closely related to the position and size of the limitation. The analysis method for nonlinear structures was mainly studied. The frequency domain characteristics of nonlinearity were characterized by the describing function first appeared in the nonlinear control. The inverse matrix updating method was used to reduce the processing dimension,which greatly improves the computational efficiency of frequency domain response. The numerical method Runge-Kutta was adopted to verify the effectiveness of the method. The first-order frequency response curve of a T-shaped beam was analysed by simulations and experiments.
引文
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[2]王军文,李建中,范立础.桥梁中抗震限位装置设计方法的研究[J].土木工程学报,2006,39(11):90-95.WANG Junwen,LI Jianzhong,FAN Lichu.A study on the design method of seismic restrainers for bridges[J].China Civil Engineering Journal,2006,39(11):90-95.
[3]KRISHNA I R P,PADMANABHAN C.Experimental and numerical investigations of impacting cantilever beams part 1:first mode response[J].Nonlinear Dynamics,2012,67(3):1985-2000.
[4]CHEN J E,ZHANG W,GUO X Y,et al.Theoretical and experimental studies on nonlinear oscillations of symmetric cross-ply composite laminated plates[J].Nonlinear Dynamics,2013,73(3):1697-1714.
[5]ERKAYA S,DOGˇAN S,ULUS.Effects of joint clearance on the dynamics of a partly compliant mechanism:numerical and experimental studies[J].Mechanism&Machine Theory,2015,88:125-140.
[6]阎绍泽,陈鹿民,季林红,等.含间隙铰的机械多体系统动力学模型[J].振动工程学报,2003,16(3):290-294.YAN Shaoze,CHEN Lumin,JI Linhong,et al.Dynamic modeling of multibody system with clearance joints[J].Journal of Vibration Engineering,2003,16(3):290-294.
[7]厉行军,赵建华,张春辉.带限位的隔离系统抗冲击性能分段建模法研究[J].兵器装备工程学报,2016(8):29-32.LI Xingjun,ZHAO Jianhua,ZHANG Chunhui.Research on subsection modeling method of shock resistance performance of the single stage vibration-isolating system with displacement restrictors[J].Journal of Sichuan Ordnance,2016(8):29-32.
[8]程长明,彭志科,孟光.一类非线性系统的随机振动频率响应分析研究[J].力学学报,2011,43(5):905-913.CHENG Changming,PENG Zhike,MENG Guang.Random vibration frequency response analysis of nonlinear systems based on volterra series[J].Acta Mechanica Sinica,2011,43(5):905-913.
[9]MAEZAWA S,FURUKAWA S.Superharmonic resonance in piecewise linear systems[J].Bulletin of the Japanese Society Mechanical Engineers,1973,16:931-941.
[10]SHAW S W,HOLMES P J.A periodically forced piecewise linear oscillator[J].Journal of Sound and Vibration,1983,90(1):129-155.
[11]MOUSSI E H,BELLIZZI S,COCHELIN B,et al.Nonlinear normal modes of a two degrees-of-freedom piecewise linear system[J].Mechanical Systems&Signal Processing,2015,64/65:266-281.
[12]吴志强,雷娜.分段线性系统的振动性能分析[J].振动与冲击,2015,34(18):94-99.WU Zhiqiang,LEI Na.Analysis of vibration performance of piecewise linear system[J].Journal of Vibration and Shock,2015,34(18):94-99.
[13]卢绪祥,刘正强,黄树红,等.含间隙碰撞振动系统的非线性振动特性[J].动力工程学报,2012,32(5):388-393.LU Xuxiang,LIU Zhengqiang,HUANG Shuhong,et al.Nonlinear vibration characteristics of a vibro-impact system with clearance[J].Power Engineering,2012,32(5):388-393.
[14]ONESMUS M,JOHN K,BERNARD I.Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints[J].Nonlinear Dynamics,2013,73(1/2):259-273.
[15]林道福,余永丰,华宏星.带限位器的浮筏隔振系统的冲击响应分析[J].噪声与振动控制,2004,24(1):6-9.LIN Daofu,YU Yongfeng,HUA Hongxing.The shock response analysis of a raft isolation system with restrictors[J].Noise and Vibration Control,2004,24(1):6-9.
[16]GELB A,VANDER VELDE W E.Multiple-input describing functions and nonlinear system design[M].New York:McGraw-Hill,1968.
[17]WORDEN K,TOMLINSON G R.Nonlinearity in structural dynamics:detection,identification and modelling[J].Institute of Physics Publishing,2002,216(3):383.
[18]SHERMAN J,MORRISON W J.Adjustment of an inverse matrix corresponding to changes in the elements of a given column or given row of the original matrix[J].Annals o Mathematical Statistics,1949,20(4):621-622.
[19]云永旺,王珺,陈力奋,等.基于逆阵更新方法的局部非线性结构频响分析[J].动力学与控制学报,2015,13(3):177-183.YUN Yongwang,WANG Jun,CHEN Lifen,et al.Frequency response analysis for local nonlinear structures using an inverse matrix updating method[J].Journal of Dynamics and Control,2015,13(3):177-183.
[20]WILLIAM R M.Mean value methods in iteration[J].Proceedings of the American Mathematical Society,1953,4(3):506-510.
[21]WANG J,CHEN L F,GUO Q W.Iterative solution of the dynamic responses of locally nonlinear structures with drift[J].Nonlinear Dynamics,2017,88(3):1551-1564.