Time-varying modal identification is important to obtain the dynamic characteristics of time-varying engineering structures and realize real-time vibration control and online health monitoring of structural systems. Aiming at the problems of measuring the excitation of engineering structures and low efficiency of time-varying modal identification，an output-only recursive identification method based on dynamic mode decomposition（DMD）is proposed in this paper. To extend the theory of the existing DMD method，this paper draws on the projection approximation subspace tracking algorithm and the sliding-window idea，and proposes a recursive format of the DMD method，which can update the system matrix and the proper orthogonal decomposition basis recursively，and can be further used for the output-only recursive modal identification of time-varying systems. A numerical example of a three-degree-of-freedom structural system with time-varying mass and an experimental setup of a liquid-filled cylindrical structural system with variable mass are respectively designed and built to validate the proposed method numerically and experimentally. The results demonstrate that the proposed recursive DMD method is able to accurately identify the modal parameters of the time-varying structures by only using the measured vibration response data，and has good output-only recursive identification capability.

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.

In order to study the influence of partially isolation on the dynamic characteristics and seismic performance，taking a dominate large terminal airport as a research object，a 3 dimensional finite element model using ABAQUS software is established. Based on this model，the structural vertical vibration modes，the effective mode mass，the vertical vibration acceleration，vertical deformation，component ductility，plastic damage and residual deformation are analyzed to reveal the influence of partially isolation on the dynamic characteristics and seismic performance. It’s demonstrated that partial isolation changes the vibration modes，increases the effective mode mass and magnify the vertical seismic load of the terminal building. At the same time，partial isolation filters the high frequency vibration，enlarges the low frequency vibration near the isolation frequency and increases the vertical acceleration and deformation. The plastic damage and residual deformation has been concentrated on the middle and end sections of innerspan beams.

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.

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%.

The analysis of seismic response at seabed sites is a crucial initial step in marine engineering construction. In this study，a fluid-solid weak coupling model is employed to replicate the interaction between seawater and the seabed. Specifically，four representative borehole sections along the proposed tunnel at Qiongzhou strait are chosen to investigate the influence induced by seawater，soft sediments，and bedrock earthquake motion on the seismic responses of the seabed site. A generalized non-Masing constitutive model（DCZ model）is utilized to account for the dynamic nonlinearity of the seabed soft soil. The findings indicate that the suppression effect of seawater on seismic motion in the seabed is limited to depths shallower than 50 m. Furthermore，the suppression effect is more pronounced in the vertical direction compared to the horizontal direction. Additionally，there is a positive correlation between the suppression effect of seawater on seismic motion at the seabed surface and the frequency response phenomenon characterized by high frequency suppression and low frequency amplification in the seabed seismic response. This correlation is influenced by the depth of the seawater. The mean lines of the horizontal and vertical spectrum β obtained by numerical calculation are higher than the design spectrum in the land code in several period ranges，and the possibility of adverse effects induced by seawater and seabed soft sedimentation on the seismic resistance of marine structures should be considered.

To establish the optimal design method of multiple tuned mass damper（MTMD）for the footbridge considering the vertical human-structure interaction，the parameters randomness of the mass-spring-damper（MSD）pedestrian model is simulated，and the vertical dynamic response of the random crowd-footbridge-MTMD system is calculated based on the pseudo-excitation method. Then，the effect of vertical human-structure interaction on the dynamic response of the footbridge-TMD system is demonstrated. Finally，based on the H₂ performance of the acceleration transfer function and response surface methodology of the coupled system，an optimal design method of MTMD for footbridge vibration control considering vertical human-structure interaction is established. The results show that the dynamic response calculation method of the coupled system avoids a large number of nonlinear time history analyses，and the power spectrum and root mean square of the coupled system response can be obtained efficiently. The vertical human-structure interaction makes the TMD detuning effect significant，and the reduction rate of TMD with 3% mass ratio decreases by 37.19% when the crowd density increases from 0.25 person/m² to 1.25 person/m². The proposed MTMD optimization design method for footbridge has an average mitigation rate of over 70% for footbridge acceleration response.

Currently，gear fault detection based on vibration，acoustic emission，and other signals requires the installation of additional sensors. This approach faces limitations in terms of sensor placement，high sensor cost，and difficulties in analyzing signals due to modulation effects in gear systems with variable transmission paths，such as planetary gearboxes. A method for diagnosing local gear faults using the built-in encoder of the servo motor is proposed in this paper. Using the output signal of the built-in encoder to extract the feature related to local gear faults. The encoder signal acquisition wiring is drawn from the built-in encoder of the servo motor，and a high-speed counter is used to record the time interval between the rising edges of the angular position pulses of the rotary encoder. The instantaneous angular speed（IAS）signal is calculated，and the IAS signal is analyzed and feature extracted in the angular and order domains to achieve local gear fault detection. Taking the planetary gearbox gear localized fault detection as an example，the proposed method is validated through experiments. Results show that using the built-in encoder of the servo motor can effectively achieve the detection of gear partial faults under low and variable speed conditions. This provides a new approach to fault detection of transmission units such as gearboxes in applications driven by servo motors.

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.

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.