Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present...Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.展开更多
A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear...A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.展开更多
传统的振动控制技术将初始辨识的系统频率响应函数贯穿使用于振动控制的过程中;针对液压振动台系统的时变特性,提出使用基于最小均方误差(least mean square,简称LMS)的自适应算法在线辨识系统的频响函数。平滑周期图功率谱估计法相对...传统的振动控制技术将初始辨识的系统频率响应函数贯穿使用于振动控制的过程中;针对液压振动台系统的时变特性,提出使用基于最小均方误差(least mean square,简称LMS)的自适应算法在线辨识系统的频响函数。平滑周期图功率谱估计法相对现代谱估计法分辨率较低,提出自回归(auto-regressive,简称AR)模型法对振动系统响应信号进行功率谱估计,利用尤利-沃克(Yule-Walker)方程求解AR模型参数,并给出AR模型阶次确定的方法。利用自行开发的基于DSP和ARM多处理器信号处理系统对功率谱复现进行软硬件仿真。结果表明,此方法对振动台功率谱进行复现,复现精度优于传统功率谱复现算法。展开更多
基金supported by the National Science Fund for Distinguished Young Scholars (11125209)the National Natural Science Foundation of China (10902068,51121063 and 10702039)+1 种基金the Shanghai Pujiang Program (10PJ1406000)the Opening Project of State Key Laboratory of Mechanical System and Vibration (MSV201103)
文摘Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
基金the National Natural Science Foundation of China(Nos.11772084 and U1906233)the National High Technology Research and Development Program of China(No.2017YFC0307203)the Key Technology Research and Development Program of Shandong Province of China(No.2019JZZY010801)。
文摘A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.
文摘传统的振动控制技术将初始辨识的系统频率响应函数贯穿使用于振动控制的过程中;针对液压振动台系统的时变特性,提出使用基于最小均方误差(least mean square,简称LMS)的自适应算法在线辨识系统的频响函数。平滑周期图功率谱估计法相对现代谱估计法分辨率较低,提出自回归(auto-regressive,简称AR)模型法对振动系统响应信号进行功率谱估计,利用尤利-沃克(Yule-Walker)方程求解AR模型参数,并给出AR模型阶次确定的方法。利用自行开发的基于DSP和ARM多处理器信号处理系统对功率谱复现进行软硬件仿真。结果表明,此方法对振动台功率谱进行复现,复现精度优于传统功率谱复现算法。
基金supported by the National Natural Science Foundation of China(21003009)Beijing Jiaotong University,China(2009JBZ019-4 and Undergraduates Innovating Experimentation Project)the Key Laboratory of Photochemical Conversion and Optoelectronic Materials, Technical Institute of Physics and Chemistry,Chinese Academy of Sciences~~
文摘由规范反应谱合成的地震动功率谱实用模型具有较高的工程应用价值.提出从功率谱零频含量特征和地面最大位移2个方面判断地震动功率谱实用模型低频段的合理性.以多国规范反应谱为目标谱合成地震动功率谱,对比分析各功率谱低频段的合理性.分析结果表明,由加速度反应谱合成的功率谱的合理性取决于反应谱的合理性,而合理的加速度反应谱在长周期(低频)段应随周期(T)的增长以T-2的速度下降.据此修正GB50011—2010反应谱,引入T-2下降段,并将起始下降周期初步定为2 s.
