The vibration reduction characteristic of rotor system with active elastic support dry friction damper is studied in this paper. The dynamic model of rotor system is established and a 2D friction model of contact surface in dry friction damper us built. The transient and steady state dynamic responses of rotor system are obtained after dynamic equations being solved by utilizing Newmark-HHT numerical integration method. The steady state vibration signals of dry friction damper rotor system under different normal load are compared，meanwhile the transient dynamic responses of rotor system before and after turning on dry friction damper are studied. Experimental test rig for rotor system and dry friction damper are set up. The vibration signals of rotor while passing the first-second critical speed regions are measured and analyzed. Then the experimental vibration signals are compared with simulation vibration responses to verify the vibration reduction effect，and the vibration attenuation characteristic of dry friction damper on rotor system under different working conditions is studied. The results show that the active elastic support dry friction damper could only attenuate rotor’s vibration within a certain normal force. Finally，the results could provide theoretical guide for vibration control strategy on rotor system.

A magnetorheological elastomer （MRE） vibration absorber is designed to suppress the vibration of industrial robotic milling in order to solve the low frequency chatter problem. The magnetorheological effect of MRE with different mass ratio is studied by using the unique rheological characteristics of MRE. The number of turns of coil and the current in the absorber are determined by theoretical calculation and numerical simulation. It is found that the designed MRE absorber has frequency shift characteristics in the range of 17.35~45.21 Hz through modal simulation and shaking table sweeping excitation experiment. The mapping relationship between natural frequency of absorber and current is established，which is verified by experiments in the milling process of KUKA KR500 robot. The results show that the robot is prone to chatter at its low order natural frequency under low rotational speed machining conditions，and the chatter suppression of the robot is realized by MRE absorber. Compared with the condition without vibration absorber，the peak-to-peak value of the vibration acceleration in the X direction of the robot spindle is reduced by 70.7%，and the root-mean-square value is reduced by 64.7% after being electrified. The peak-to-peak value in the Y direction is decreased by 54.7%，and the root-mean-square value is decreased by 49.9%. In addition，the machining surface quality of workpieces after milling has also been significantly improved.

In order to improve the dynamic output performance and environmental adaptability of the tri-stable piezoelectric energy harvester （TPEH），a new flexible tri-stable piezoelectric energy harvester （FTPEH） with double flexible auxiliary beams for real-time adjusting the potential well depth and barrier height is proposed. Based on the traditional magnetic coupling tri-stable piezoelectric energy harvester，two auxiliary flexible beams with the same structure and size are introduced，and the two external magnets are fixed at the tip ends of the two auxiliary flexible beams. When the harvester is excited by the external excitation，the two auxiliary beams oscillate with slight amplitude in the horizontal direction，thus the horizontal distance between the external magnets and the tip magnet of the piezoelectric cantilever beam can be adjusted in real-time，so as to tune the potential energy well depth and barrier height，resulting in improving the dynamic output performance and environmental adaptability. The electromechanical coupling dynamic model describing the dynamic responses of the new tri-stable piezoelectric energy harvester is established based on Euler Bernoulli theory and Hamilton principle，and the influences of system parameters on the nonlinear magnetic force and dynamic performance are simulated and analyzed. Compared to the traditional tri-stable harvester，the new tri-stable harvester has a wider bandwidth of inter-well motion and lower excitation for jumping from intra-well motion to inter-well motion.

The harmonic vibration produced by the gear meshing in the helicopter’s main reducer is one of the main sources of noise in the helicopter cabin. Designing vibration-isolating gearbox struts to suppress vibration transmission to the airframe can effectively reduce cabin noise. The piezoelectric stack actuators periodic strut （PSAPS），composed of periodically arranged piezoelectric stacks and metallic materials，demonstrates ‘mechanical filtering’ characteristics within specific frequency bands，serving as a passive vibration control method. By adjusting the driving voltage of piezoelectric stacks in PSAPS to achieve variable stiffness characteristics，active vibration control is enabled. In order to study the electromechanical coupling relationship between active vibration control and passive vibration control of PSAPSs，a specialized PSAPS configuration is developed to address helicopter gear meshing noise suppression，and the electromechanical coupling dynamic model of PSAPSs with the form of transfer matrix is established for the mechanical filtering characteristics of periodic structure and elastic wave propagation in piezoelectric stack. In frequency domain，the force and velocity at both ends of the PSAPSs，the driving voltage and current，the geometrical parameters of the strut and the material parameters are coupled in this model. In this paper，the maximum attenuation rate of the PSAPS can be obtained under the limitation of the maximum driving voltage and current of the piezoelectric stack by using this model. The influence of rubber damping loss factor，excitation force，and cell number in PSAPS on the required driving voltage and current for active control is analyzed in this article.

Existing S-transform-based load spectrum editing methods for automotive components suffer from the problem of lack of adaptivity in time-frequency resolution，which affects the time-frequency aggregation of load spectrum energy and leads to poor editing results. To solve this problem，based on the theory of generalised S-transform （GST），the application of GST method in the field of automobile components load spectrum editing is explored. The GST method is used to perform time-frequency analysis of the mount load spectrum to obtain the distribution information of the load energy on the time and frequency axes. The accumulative power spectral density （APSD） of the load spectrum is calculated，and a genetic algorithm is used to determine the threshold value of the APSD in order to identify the time segments of the load spectrum with smaller damage contributions. The time segments of the load spectrum with small damage contributions are identified and removed，and the remaining load time segments are spliced to obtain a compressed load spectrum. Comparing with the load spectrum editing method based on S-transform，it is found that the time compression of the compressed load spectrum obtained based on the GST method is larger，and the compressed load spectrum basically matches with the original load spectrum in terms of statistical parameters，power spectral density，rainflow counts，fatigue life and damage distribution. The results show that the GST method is suitable for editing the load spectrum of automotive components. It can provide an effective means to improve the efficiency of durability bench tests of automotive components.

In order to improve the intelligence of fastener disease diagnosis，a fastener condition diagnosis method is proposed based on vehicle dynamic response data and generalized demodulation time-frequency analysis combined with sparrow search algorithm-support vector machine （SSA-SVM） model. The acceleration signals of the normal and abnormal sections of the fastener are collected，and the short-time Fourier transform and the maximum overlapping discrete wavelet packet transform are used to preprocess the signal data. The generalized demodulation time-frequency analysis method is used to decompose the signal，and the effective value，energy contribution rate and wavelength of the main information components are calculated as the characteristic index. The characteristic index is trained by the joint SSA-SVM model to construct the classification model. The results show that the accuracy of the method is 97.50%，and several evaluation indicators are used to verify that its effectiveness and accuracy can meet the actual needs.

To accurately extract fault feature information under strong background noise，a multi-scale improved differential filter （MIDIF） is proposed for rotating machinery fault diagnosis. The rotating machinery vibration signal is decomposed into a series of multi-scale improved differential filter signals using MIDIF. In view of that the MIDIF filtered signals exhibit varying extents of validity in revealing fault features，a weighted reconstruction method using correlation analysis is proposed in which the weighted coefficients are counted and distributed to the corresponding MIDIF filtered signals to highlight the effective MIDIF filtered signals and weaken the invalid ones. The weighted coefficients are multiplied with the MIDIF filtered signals under different scales to produce transient impulse components. The fault types of rotating machines are inferred from the fault defect frequencies in the envelope spectrum of the transient impulses. The results show that MIDIF is more accurate in extracting fault features than multi-scale average combination different morphological filter （ACDIF） and multi-scale morphology gradient product operation （MGPO），and that it provides an effective method for rotating machinery fault diagnosis.

Based on the problems of poor interpretability，as well as parameter increase and memory consumption caused by blind stacking layers in traditional fault diagnosis method based on deep learning，Neural ordinary differential equation （NODE） is introduced into mechanical fault diagnosis，the network structure of NODE for machinery fault diagnosis is constructed. In the constructed structure，the derivatives of the parameterized hidden states of the neural network are used to replace the discrete sequences of the specified hidden layers. By constructing a nonlinear relationship between fault data and fault types，an ordinary differential equation solver （ODE solver） is used to complete the classification of different fault types，and an end-to-end fault diagnosis model is formed. The proposed method is applied to mechanical fault diagnosis to build a specific NODE network model，and the classification task of different fault categories is accomplished through the input of fault data. The constructed model is applied to the fault diagnosis of spindle bearing in the aircraft engine，and compared with the fault diagnosis method based on residual network model. The experimental results show that the constructed model and residual network model have satisfactory accuracy. However，the constructed model not only reduces the memory consumption，but also reduces the number of model parameters by almost five times.

Aiming at the problems of bearings working in complex environments，where fault data are difficult to obtain in large quantities and the serious imbalance between the ratio of normal data and fault data resulting in insufficient in-depth model training and low diagnostic accuracy，a bearing fault diagnosis method based on LSGAN-Swin Transformer is proposed. The least-squares generative adversarial network is utilized to expand the imbalanced or lack of bearing dataset，and the windowed self-attentive network is introduced for bearing fault state identification. The proposed method is validated by using two date sets，and compared with SGAN and WGAN respectively. It is demonstrated that LSGAN generates data training models with higher accuracy. The proposed Swin Transformer （Swin-T） model is compared with CNN，AlexNet and SqueezeNet under small sample conditions，and the accuracy is improved by 34.85%，13.45%，and 12.95%，respectively. The classification effect of the model is evaluated by t-SNE visualization，and the results show that the LSGAN-Swin-T model can still meet the requirements in fault diagnosis better when the number of training samples is small，which provides a new idea for the research of bearing fault diagnosis under unbalanced data.

To solve the problem that the early weak fault diagnosis effect based on feature mode decomposition （FMD） is susceptible to the filter length L，frequency band segment K and mode decomposition number n，a diagnostic method is proposed in which a genetic algorithm is used to optimize the preset parameters of FMD，and the kurtosis，envelope entropy and modified adaptive envelope spectrum characteristic energy ratio as the comprehensive objective function. The method uses genetic algorithm to compare the comprehensive objective function values of each component signal decomposed by FMD under different preset parameters，and selects L，K and n corresponding to the maximum value as the preset parameters of FMD. The bearing fault type is determined by the envelope spectrum characteristics of the signal processed by FMD. The open bearing fault data of Western Reserve University and University of Cincinnati show that this method has good anti-noise ability and effective early fault diagnosis ability.