The bushing element is established for dynamic modeling of rolling linear guideway joints based on the movement characteristics of guideway. The effectiveness of the bushing element is verified by the numerical and experimental examples. Base on the fact that the guideway joint has significant influence on the dynamic performance of the whole structure，the model updating technique combined with the substructure method is proposed for parameter identification of bushing element. A simulation example of dumbbell structure is used to verify the effectiveness of the proposed parameter identification method. Based on the simulation example，a dumbbell structure with single slider rolling guideway is used for bushing element parameter identification and model verification. The effectiveness and universality of the bushing model is verified by a rolling linear guideway structure which contains four sliders. The engineering application of the bushing element is verified by the structure of rolling linear guideway moving platform of special ring welding machine. The results show that the bushing model is simple for application，the dynamic modeling error for single slider rolling linear guideway is within 5% and the error for four sliders rolling guideway system is within 12%，and the error of engineering structure of moving platform with four sliders is about 11%.

The axle-box bearing is a key component of high-speed trains，and the wheel-rail excitation caused by complex braking conditions leads to extremely complex vibration and contact characteristics of axle-box bearings and it is unclear until now. Therefore，a rigid-flexible coupled dynamics model of a high-speed train considering braking systems and axle-box bearings is established. Moreover，the braking system，axle-box bearing and vehicle system are dynamically coupled via the nonlinear friction of the braking interface，wheel-rail interactions，nonlinear contact of the axle-box bearing and suspension systems. Further，the field tests are conducted to verify the effectiveness of the established model. Based on this，the vibrations，bearing internal force，and contact characteristics of axle-box bearings under different braking conditions are systematically studied. The results indicate that train braking increases the longitudinal force of the axle-box bearings on the first and second wheel-set，and enhances the longitudinal vibration. The vertical vibration of the axle-box is slightly influenced by braking. In addition，when the train brakes，the friction between disc and pad makes the pitch motion for bogie frame，causing changes in the primary suspension force on the first and second wheelset，resulting in a decrease in the vertical force of axle-box bearing on the first wheel-set，an increase in the vertical force of the axle-box bearing on the second wheel-set，and ultimately an increase in the maximum roller-raceway and contact stress of the axlebox bearing on the second wheel-set.

The dynamic behavior of the Duffing-van der Pol oscillator with fractional-order derivative and parametric excitation is studied in this paper. The effects of various parameters on the amplitude-frequency curves of the system under the combined action of viscous inertia（1≤p≤2）and parametric excitation are analyzed. The system is analyzed by the averaging method，and the fractional-order derivative is treated by the concepts of equivalent linear damping and equivalent mass. The approximate analytical solution of the system is obtained and compared with the numerical solution. The curves of the two solutions agree well with each other to a large extent，which proves the correctness of the analytical solution. The influences of system parameters on the amplitude-frequency curve are analyzed. It is found that the resonance peak value，resonance frequency，resonance region，the range and the number of multivalued solutions are all affected by the system parameters. Through analysis，it is found that the external excitation amplitude and the coefficient of fractional-order derivative can suppress the effect of parametric excitation to some extent.

In order to accurately study the nonlinear dynamic characteristics of NW（internal and external meshing planetary gear train）wind power transmission system，this paper considers factors such as random wind speed，time-varying support stiffness，ring gear flexibility，time-varying meshing stiffness，transmission error，tooth flank clearance，and bearing clearance. A nonlinear dynamic model of the NW planetary gear-bearing system is established. Time history，FFT spectrum，Phase diagram，and Poincaré maps are used to describe the nonlinear characteristics of the system，and bifurcation diagrams and the maximum Lyapunov exponent are used to describe the influence of excitation frequency and meshing stiffness on the nonlinear behavior of the system in more detail. The results show that the NW planetary gear-bearing system has rich nonlinear characteristics. In a specific range of excitation frequencies，the system can enter a chaotic motion state，leading to instability. However，within a certain range of meshing stiffness，the system can operate stably.

A spectral geometry-incremental harmonic balance method（SGM-IHBM）is proposed to study the nonlinear vibration characteristics of functionally graded porous（FGP）beams with geometric nonlinearities. The geometrically nonlinear strain-displacement relationship of the beam structure is obtained according to the Von-Karman theory，and the Lagrange energy function of the FGP beam is derived based on the Timoshenko theory. The spectral geometric series are used to characterize each displacement component of the beam structure，and the linear modal components are introduced to establish the nonlinear reduced-order equations of the FGP beams，and then the incremental harmonic balance（IHB）method is used to trace the dynamical response solution of the reduced-order model of the FGP beams. The correctness of the nonlinear model in this paper is verified by comparing the SGM-IHBM solution with the literature solution，and then the effects of porosity，thickness，and excitation amplitude on the nonlinear vibration characteristics of FGP beams are analyzed.

In order to accurately identify cable force in complex boundary conditions，a new method of cable force identification using machine vision and generalized regression neural network（GRNN）is proposed. Machine vision technologies，such as the phase-based motion amplification algorithm and sub-pixel edge detection algorithm，are used to extract the vibration displacement time history data and identify the frequency through the cable vibration video to realize multi-point non-contact synchronous measurement of cable vibration deformation. A sample dataset is generated using the finite difference method. The smoothing factor of GRNN is obtained by the sparrow search algorithm（SSA），and a SSA-GRNN cable force prediction model is constructed，establishing the correspondence between frequencies and cable force under complex boundary conditions. The obtained frequency information is input into the model for cable force recognition. Taking a single cable as an example，the numerical simulation of the cable in complex boundary conditions and the cable test under artificial excitation condition are carried out. The results show that the cable force identification using machine vision and GRNN can accurately identify frequencies through vibration video，and improve the recognition accuracy of the cable force in complex boundary conditions.

To enhance the accuracy of instantaneous frequency（IF）identification for non-stationary response signals of time-varying structures，a locally optimized multi-synchrosqueezing-short time fractional Fourier transform（LOMS-STFRFT）algorithm is proposed in this paper. Firstly，the local rotation parameters of the short time fractional Fourier transform（STFRFT）are optimally selected in this method. Subsequently，the time-frequency coefficient matrix projected to the fractional domain is obtained through STFRFT. After that，IF estimation and multiple iterations are performed on the time-frequency coefficient matrix. The time-frequency coefficient matrix is reassigned by the multi-synchrosqueezing operator，and IF curves are then extracted via the local mode maxima method. The accuracy of the proposed method is validated through a numerical example of a multi-component signal and a linearly time-varying cable test. The results demonstrate that the proposed LOMS-STFRFT algorithm behaves better than traditional multi-synchrosqueezing transform on IF identification of non-stationary signals from time-varying structures.

Control algorithm is a key factor to improve the performance for reducing helicopter vibration. In this paper，according to the multi-frequency characteristics of helicopter vibration，both the response separator and controller are constructed utilizing the adaptive notch filter to establish the adaptive dual-notch control of helicopter structural response. The response separator separates each frequency component from the error response to update the control input of each harmonic independently in time domain. Utilizing a dynamic similarity model of helicopter airframe，simulations and experimental studies of the proposed adaptive dual-notch control algorithm are carried out. The results show that the adaptive dual-notch control algorithm has good control performance and faster convergence rate under the multi-frequency excitations，and it can enhance the robustness of active vibration control system by increasing the critical convergence step size.

A nonlinear enhanced bellows-type hydraulic inerter-based antiresonance vibration isolator is proposed for low-frequency line spectra vibration isolation. The nonlinear dynamic model of the enhanced system and the quasi-static model with bistable negative stiffness are established. The influence of parameters such as geometric dimensions and elastic coefficients on the nonlinear stiffness characteristics of the system is studied. It is found that the structure with negative stiffness enhancement only regulates the extent of nonlinear stiffness without changing the load-bearing capacity or static deformation. Subsequently，an estimation analysis of vibration isolation performance is conducted. The vibration transmissibility of the degraded linear system under force excitation is studied，and the effects of non-dimensional parameters，including the inertial mass ratio，effective area ratio，and damping ratio，on the transmissibility characteristics are analyzed. The dynamic response is solved by using the averaging method，and the analytical solution steps for the transmissibility of the nonlinear enhanced system are given based on the equivalent linearized stiffness. The analytical results are validated by comparing them with numerical simulation results，showing small relative errors，and thus can be used for design purposes. A comparative study is conducted on the transmissibility characteristics of the nonlinear negative stiffness enhanced hydraulic inerter-based vibration isolation system. The results indicate that the introduction of a bi-stable negative stiffness can lower the resonance and anti-resonance frequencies of the isolation system. By designing appropriate inertial mass parameters，it is possible to achieve superior wideband isolation effectiveness in the low-frequency range.

To reduce the starting isolation frequency of the isolator，enhance adaptability to different vibration sources，and achieve superior vibration suppression effects compared to traditional passive isolators，this study proposes a high static-low dynamic stiffness（HSLDS）isolator with asymmetric stiffness structure employing electromagnetic coils nested with permanent magnets. It can adjust the system stiffness according to changes in vibration source frequency，thereby realizing semi-active vibration isolation. The incremental harmonic balance method is employed to obtain the displacement transmissibility characteristics of the system under different excitations and currents. Based on the system model of the isolator，a semi-active control strategy is proposed in this study，which can adjust the system stiffness according to changes in vibration source frequency. An experimental test platform was constructed for experimental research. The results show that the proposed HSLDS isolator can reduce the starting isolation frequency by 19.25%. Introducing the semi-active control strategy can attenuate the maximum acceleration amplitude by 54.7%.