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
In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncer...In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.展开更多
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.
基金supported by the National Natural Science Foundation of China (Grant No. 52105253)the State Key Program of National Science Foundation of China (Grant No.52235005)。
文摘In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.
