Aiming at the problem that the effectiveness and computation cost of the maximum second-order cyclic stationarity blind deconvolution （CYCBD） algorithm are affected by parameter setting，the crest of the harmonics spectrum （HSC） was used as an evaluation index to determine the length of the CYCBD filter adaptively，and the calculation cost of the optimization process was balanced by the method of encoder time series reconstruction. The bearing fault order is calculated and the cycle frequency is set according to it. The pulse number of time series reconstruction is determined according to the fault order. The central difference method （CDM） is used to calculate the instantaneous angular speed （IAS） of the reconstructed signal. The filter length of CYCBD was adaptively selected with the HSC as the evaluation index using the equal-step search strategy. The spectrum corresponding to the maximum HSC is calculated to achieve fault feature extraction. The simulation and experimental data analysis results show that the proposed method can adaptively select the filter length，which has an obvious effect on reducing the cost of the CYCBD algorithm，and is effective for rolling bearing fault feature extraction.

Base swing will bring additional gyroscopic moment and inertia load to the rotating machinery，affecting the vibration and stability of the rotor system and even endangering the rotor operation. In order to effectively control the vibration of the active magnetic bearing （AMB）-flexible rotor system under the base swing，a base acceleration feedforward algorithm is proposed in this paper. With the dynamic model and the parameters of the base swing，the optimal compensation current to suppress the vibration can be directly obtained by the proposed algorithm. Because of no iteration and simple structure，the algorithm has strong rapidity and practicality. Furtherly，to eliminate the influence of modeling error on the compensation performance，a method to correct compensating current is suggested. After that，the influence of the proposed algorithm on the rotor vibration in the spin speed range including the first bending critical speed is simulated. Finally，on the test platform，the effectiveness of the algorithm was verified when rotor in suspension without spin，constant speed and acceleration under the base swing. The theoretical and experimental results agree that the vibration perpendicular to the swing axis increases obviously due to the inertia load. The additional gyroscopic moment increases the vibration along the swing axis，and the rising amplitude grows along with the increase of the rotor spin speed. The algorithm proposed can efficiently suppress the rotor vibration under the base swing in the spin speed range including the first bending critical speed.

The magnetically suspended rotor applied to the moving carrier may be subject to the base motion excitation，causing the rotor vibration，and even cause friction and system instability. To explore the vibration response of the magnetically suspended rotor under the base excitation，the numerical simulation and experimental verification are conducted. The effect of the base excitation on the rotor is introduced into the differential equation of the rotor motion in the form of an additional generalized force. Considering the closed-loop control of the magnetic bearing，the dynamic model of the magnetically suspended rotor under base excitation is established. The influence of the excitation amplitude and frequency，the acceleration and shock width on the vibration response of the rotor is analyzed by numerical simulation. Finally，the base excitation experiments were conducted. The experimental results verify the accuracy of the magnetically suspended rotor model under the base excitation. The results show that the rotor vibration amplitude is proportional to the amplitude and square of frequency of the base harmonic excitation，the rotor vibration maximum is proportional to the base shock excitation acceleration. The proportional coefficient and differential coefficient of the magnetic bearing controller can suppress the rotor vibration brought by the base excitation.

A fast robust control strategy based on variable power log-reaching law is proposed for a class of manipulator systems with uncertain random oscillations in the mounting base. The uncertain dynamic model of the system is established based on Euler-Lagrange equation，and the oscillation term of the base in the model is regarded as the uncertain external disturbance force of the manipulator system. A new approach law of variable power logarithm function is proposed，which can realize the rapid approach of the system state far away from the sliding mode surface，and ensure the effective chattering suppression after approaching the sliding mode surface. On this basis，combined with a fast terminal sliding surface，a fast robust controller is designed，which can further improve the state convergence rate of the system. The finite-time convergence of the controller is proved based on Lyapunov stability theory. An experimental platform is built to further verify the effectiveness of the controller.

The large oscillation of the weight center on the sagittal plane can produce shock and oscillating force on the shoulders and back of the human body，which can cause muscle fatigue in the upper limbs. To alleviate the impact and oscillating force，a hip-joint driven backpack exoskeleton with adaptive adjustment of the weight-gravity center is proposed. Based on the five-bar model of the human body，the kinematic model of the gravity center in the human-weight system and the human-exoskeleton-weight system is established by the D-H method to analyze the trajectory of the gravity center. Based on the Newton-Euler method，the human dynamics model and the human-exoskeleton dynamics model are established. The changes in the human shoulder back forces and the lumbar，hip，and knee joint moments are obtained in the human-weight and human-exoskeleton-weight systems. Results are validated by the software OpenSim. Kinematics，dynamics，and software simulation show that the exoskeleton reduces the fluctuation of the gravity center，improves the torque distribution of each joint，and improves the load-bearing performance.

In this paper，the global dynamics of chaos and subharmonic bifurcation of an impacting system of cantilever beam supported by oblique springs under bilateral asymmetric rigid constraints are studied. It is difficult to study analytically the chaos and subharmonic bifurcation of the system because the stiffness term of the oblique spring support structure is a transcendental function. To do this，the stiffness term of the system is fitted by the approximation method，and the homoclinic orbit and its internal orbits of the approximate system are compared with the orbits of the original system. The threshold conditions for homoclinic chaos and subharmonic bifurcation are presented by applying the Melnikov method to the non-smooth impacting cantilever beam system. Moreover，the stability of the impacting subharmonic orbit is analyzed by combining characteristic multipliers of smooth manifolds with impact function，and the relationship between subharmonic bifurcation and chaos is analyzed. The effects of damping，excitation frequency，excitation amplitude and impact coefficient of restitution on chaos and subharmonic bifurcation are studied based on threshold conditions，which further verify the theoretical analysis.

In this paper，a method for calculating the vibration response of beams damped with constrained damping layer is presented. The indoor vibration experiment of I-beam was carried out，and the vibration response at different positions was measured. A numerical simulation model was established simultaneously based on the finite element method，and the natural frequencies and modal loss factors of I-beam were calculated accurately by using the modal strain energy method. Based on the above results，the modal superposition method was used for the harmonic response analysis，and the vibration response of the I-beam damped with constrained damping layer was obtained. The accuracy of the model was verified by comparing the measured and simulated results. The effects of design parameters （damping layer thickness and constrained layer thickness） on the natural frequency，modal loss factor and overall vibration acceleration level were analyzed. The results show that the vibration response of each component has a similar change rule. The overall vibration acceleration level of web is the largest，followed by the bottom，and the roof is the smallest. In general，the thickness of damping layer has little effect on the first 5 order natural frequencies of I-beam，but with the increase of the thickness of constrained layer，the first 5 order natural frequencies of I-beam decrease first and then increase. Increasing the thickness of damping layer and constrained layer can continuously improve the modal loss factor of I-beam，thereby reducing the overall vibration acceleration level effectively，and the vibration reduction effect of web is better than that of roof and bottom.

Based on the modified Timoshenko beam theory，the transverse vibration governing equation of the modified Timoshenko beam on the viscoelastic Pasternak foundation is established. The analytical solutions of the natural frequency and attenuation coefficient of the modified Timoshenko beam simply supported at both ends in the viscoelastic Pasternak foundation are derived with the reverberation-ray matrix method. The natural vibration characteristics of the modified Timoshenko beam on the viscoelastic Pasternak foundation under classical boundary conditions are calculated by dichotomy and golden section method. The effects of moment of inertia caused by shear deformation，beam length and different boundary conditions on the natural vibration characteristics of the structure are compared and analyzed. The results show that the natural frequency and attenuation coefficient of the modified Timoshenko beam on the viscoelastic Pasternak foundation are smaller than those of the classical Timoshenko beam； the shorter the beam，the more significant the influence of the moment of inertia caused by shear deformation on the natural frequency and attenuation coefficient of the structure，and the influence on the higher order is obviously greater than that on the low order； the stronger the boundary constraint condition，the more obvious the vibration energy attenuation.

The nonlinear dynamic systems exhibit particular behaviors when subjected to combined deterministic and stochastic excitation. A semi-analytical method for calculating the nonstationary response of a fractional nonlinear oscillator subjected to combined excitation is proposed. Representing the system response as a sum of a deterministic component and zero-mean stochastic component leads to two equivalent sub-equations for the differential equation of motion. The time-varying harmonic balance method is used for the nonstationary solution of the deterministic differential sub-equation，while the statistical linearization method is utilized for obtaining an equivalent linear substitution for the stochastic sub-equation. A semi-analytical solution of the equivalent linear equation is obtained by the Prony-SS and Laplace transform technique. The unknown deterministic/stochastic response components are obtained by solving the derived nonlinear algebraic equations simultaneously. Monte Carlo simulations demonstrate the applicability and accuracy of this method.

The advanced transfer path （ATPA） method is used to study the vibration transfer characteristics of the computer mainframe package from each cushion pad to key components under different vibration levels of random vibration through experiments，the analysis of the vibration contribution of the cushion pad and optimal design of vibration reduction are carried out. The results show that the measured vibration response of the two key components of the computer mainframe is consistent with the synthetic response of the ATPA method，which verifies the correctness of the ATPA theory for the analysis of the vibration transfer characteristics of the product packaging system； when the area of each cushion pad is the same， the two cushion pads on the same side of the key components of the computer mainframe play a decisive role in its acceleration response， thus being the key cushion pads； the cushion area of the key cushion pad affects the acceleration response PSD peak value and frequency range of the key components. With the increase of the cushion area，the acceleration response PSD peak value of key components gradually decreases； when the cushioning area of the key cushion pad is more than doubled，the reduction effect of the acceleration response PSD peak value tends to be saturated，the resonance peak becomes smooth，and the vibration response energy is dispersed over a wider frequency range. The vibration reduction optimized design keeps the non-key cushion pad unchanged and only increases the cushion area of the key cushion pad. The research results provide a reference for the vibration reduction design of the product.