Study On Excitation Transmission Characteristics Of Non Gaussian Random Vibration And Its Frequency Domain Equivalent Method

Structural fatigue failure caused by random vibration widely exists in railway,aerospace and other fields.In recent years,rail transit is in a period of rapid development,and the speed of high-speed EMUs is faster and faster.At the same time,the incentive is more and more complex.In the past,the non Gaussian excitation and non Gaussian stress response were processed according to the Gaussian method.However,with the increase of excitation magnitude and complexity,such an evaluation method will reduce the reliability of the structure.Therefore,this paper generates non Gaussian excitation with different parameters,studies the transmission characteristics of different non Gaussian excitation in different structures,and puts forward three frequency domain equivalent methods: rain flow counting equivalent method,GMM equivalent PSD method and GMM weighted equivalent method.Firstly,the modal characteristics of aluminum alloy specimens are obtained through frequency sweep test and modal simulation.It is determined that the first-order modal frequency is 31 Hz and the second-order modal frequency is 178 Hz.Then the non Gaussian excitation with different kurtosis is generated through the nonlinear transformation model,and the excitation frequency is divided into two cases according to whether the excitation frequency includes the first-order modal frequency of the specimen.When the non Gaussian excitation frequency includes the first-order modal frequency of the specimen,it is found that the stress response of the specimen is a sinusoidal signal with variable amplitude,and the frequency is 31 Hz,that is,the first-order modal frequency of the specimen.The kurtosis of stress response is 3,which belongs to Gaussian signal.It shows that the non Gaussian excitation is not transmitted to the stress response.After calculating the damage results by rain flow counting,it is found that the damage under non Gaussian excitation with different kurtosis has no obvious increasing trend.Secondly,the non Gaussian excitation is adjusted between the first and second modal frequencies of aluminum alloy specimens.It is found that the stress response power spectrum is basically consistent with the theoretical solution of the linear system,which is a broadband distribution.In this case,with the increase of excitation kurtosis,the damage caused by stress is also increasing.At the same time,it is found that the stress response is also a non Gaussian signal,and the greater the kurtosis of the excitation,the greater the kurtosis of the stress,and the kurtosis of the stress is less than that of the excitation.Then the excitation is applied to the complex structure,and it is found that the frequency coverage of the stress response is basically consistent with the excitation.In this case,the kurtosis of the stress is also close to the kurtosis of the excitation,and the damage of the stress increases with the increase of the kurtosis of the stress.Then non Gaussian excitation with different skewness is generated.Similarly,the excitation is divided into two categories: including and excluding the first modal frequency of aluminum alloy specimens.When the excitation includes the first modal frequency of the structure,the kurtosis and skewness of the excitation can not be transmitted to the stress response,nor does it affect the damage of the structure.When the excitation does not include the first-order modal frequency of the specimen,the deflection is transmitted less,and has no obvious effect on the damage of the structure.Kurtosis is the main factor affecting the damage.For the three equivalent methods,the rain flow counting equivalent method has better equivalent effect when the excitation kurtosis is small,and there will be insufficient equivalence when the excitation kurtosis becomes larger;GMM equivalent PSD method has better effect when the excitation contains low-frequency components;When the excitation lacks low-frequency components,the phenomenon of insufficient equivalence will appear;GMM weighted equivalent method has a good equivalent effect for simple structures,but it is not suitable for practical engineering.It is only used as a method to verify the theory.