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
The low frequency vibration response of a specimen in acoustic fatigue tests depends not only on the dynamic characteristics and the boundary conditions of the specimen itself, but also on the test unit which couples ...The low frequency vibration response of a specimen in acoustic fatigue tests depends not only on the dynamic characteristics and the boundary conditions of the specimen itself, but also on the test unit which couples the specimen to a given sound field. Further, the latter can even be dominant instead the former in some circumstances. This fact is shown in the paper by using the experimental results and the theoretical analysis of the acoustic-induced vibration of a boundary clamped rectangular thin plate. In analysing the systems of acoustic fatigue test, an approach of electro-mechano-acoustical analogous circuit is used. The application of the approach can give an estimation of the effects on the low frequency vibration modes of various parameters in a system quantitatively. This supplies a theoretical basis and a means for the rational layout of acoustic fatigue tests.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.
文摘The low frequency vibration response of a specimen in acoustic fatigue tests depends not only on the dynamic characteristics and the boundary conditions of the specimen itself, but also on the test unit which couples the specimen to a given sound field. Further, the latter can even be dominant instead the former in some circumstances. This fact is shown in the paper by using the experimental results and the theoretical analysis of the acoustic-induced vibration of a boundary clamped rectangular thin plate. In analysing the systems of acoustic fatigue test, an approach of electro-mechano-acoustical analogous circuit is used. The application of the approach can give an estimation of the effects on the low frequency vibration modes of various parameters in a system quantitatively. This supplies a theoretical basis and a means for the rational layout of acoustic fatigue tests.
