Milling vibration problems can increase tool wear and reduce part machining accuracy，the suppression of which is a hot research topic in the field of milling. In order to suppress forced vibration in milling and enhance the stability of the machining system，a spindle-tool system is proposed based on electromagnetic actuators technology. The electromagnetic actuators are mounted in the spindle-tool system and acts on the toolholder position，using its controlled electromagnetic force for vibration suppression. Firstly，the structure and working principle of the system is described and the milling dynamics of the system is modelled. Secondly，based on the working principle of electromagnetic actuators，a PD controller is designed and the dynamic model and controller are simulated and verified. Finally，machine vibration signals are collected and external excitation experiments are carried out on a rotor test bench simulating tool process. Simulation and experimental results show that the spindle-tool system based on electromagnetic actuators under PD control law can effectively suppress the forced vibrations during the milling process.

Aiming at the problem of the multi-order modal vibration of flexible wind turbine tower，a self anchored damping cable is designed in this paper，which converts the angular displacement of tower bending vibration into linear displacement，and drives the damper to dissipate energy and reduce vibration. Firstly，the tower-damper-cable vibration equation is established，and the analytical solution of the additional damping ratio provided by the damper cable for the first two-order bending vibration of the wind turbine tower is obtained. Then，the relationship between the damper viscosity coefficient and the additional damping ratio provided by the damper cable for the first two-order modal vibration of the wind turbine tower is analyzed through model experiment. The results show that the damping cable can provide a large additional damping ratio for the first two-order bending vibration of the tower，and the analytical solution of the additional damping ratio is in good agreement with the experimental results. Finally，based on the theoretical calculation formula of additional damping ratio，the influence of parameters on the damping performance of damping cable is analyzed.

In order to solve the problem of seismic design of continuous beam bridge in which the longitudinal seismic inertia force is only carried by the fixed pier，the seismic potential of the movable pier is fully exerted with the same section as the fixed pier. Based on the principle of wrap rope，the mass rotation wrap rope device excited by additional mass inertia force is developed to realize the cooperative force of fixed pier and movable pier and limit the relative displacement of beam end. Based on the working principle and structural characteristics of the device，the restoring force model of the device is proposed，and through a 3-span regular continuous beam bridge，the finite element model of the whole bridge is established. The effects of additional mass，friction coefficient and initial relaxation coefficient on the vibration reduction performance of continuous beam bridge are systematically analyzed. The results show that the effect of mass rotation wrap rope device on reducing the seismic response of fixed pier and lifting the movable pier to participate in the longitudinal whole cooperative force of continuous beam bridge is obvious. The influence of parameters of different seismic wave input characteristics is slightly different，but reasonable design parameters of the device will produce a more obvious effect of shock absorption.

In order to finely and continuously adjust the damping of a spring-suspended sectional model （SSSM） system in the wind tunnel test，a double-sided permanent magnet plate-type eddy current damper （ECD） device is developed in this paper. First，the basic structure of the ECD is introduced and its design points are analyzed. Then，the rationality of the structure for the ECD is analyzed by using the electromagnetic finite element steady-state analysis method，its working range is predicted，and the influence of the motion speed and position offset of the conductor plate on its working performance is analyzed. Finally，the relationship between the vertical and torsional additional damping ratio provided by the ECD to the SSSM system is derived，and the linear characteristics of the eddy current damping and the cooperative adjustment ability of the damper to the vertical and torsional additional damping of the SSSM system are verified by experiments. The study shows that the double-sided permanent magnet plate-type ECD can provide continuously adjustable linear viscous damping for the SSSM system with different scaling ratios，and the damping coefficient is stable and not easily affected by the front-back，left-right and up-down position offsets of the model，which is also suitable for the wind tunnel test of the SSSM system with large bending-torsional coupling vibration. By installing two dampers symmetrically along the diagonal of the SSSM system，the vertical and torsional damping ratios of the SSSM system can be cooperatively adjusted，which provides conditions for the fine study of the bending-torsional coupling wind-induced vibration of the SSSM system.

This article investigates the optimization problem of a novel base isolation system by introducing a passive network consisting of one damper，one spring and one inerter and a grounded element with negative stiffness. The dynamic equations of the system are established and the frequency response function in the dimensionless form is derived. Since it is found that the amplitude-frequency response curves pass through four fixed-points，the extended fixed-point method is utilized to solve the parameter optimization problem. The explicit expressions of the optimal inertance-to-mass ratio，the optimal natural frequency ratio，and the optimal corner frequency ratio of the system are derived by adjusting the four fixed points to the same height. The expression of the optimal damping ratio is calculated by letting the amplitudes of the three invariant frequencies among the four fixed points to the same amplitudes as those of the four fixed-points. A necessary and sufficient condition for the system with optimal parameter values to be stable is derived by utilizing the Hurwitz stability criterion. Compared with other three optimal isolation systems，the optimal isolation system in this article can provide better H_∞ performance and better output responses in the multi-storey building vibration system.

Inerter element is a mechanical element whose inertia force is proportional to the relative acceleration between its terminals. This kind of specific inertia force is not involved in classical theory of Structural Dynamics. From the point of view of inertial and non-inertial reference frame，the inerter element is proposed as a real inertial force element. The difference between the real inertial force of inerter element and the virtual inertial force of classical mass element is also explained. In order to illustrate the differences between inerter-based technology and classical structure control technologies，the vibration mitigation mechanisms of classical technologies are elaborated firstly. Based on the mechanical relationship of inerter element and inerter system，the concepts of inerter element，inerter system and structure with inerter system are defined and explained. From the point of motion equations and energy equations of structures with inerter systems，the enhancement mechanism of inerter-based technology is revealed. The characteristics of inerter-based technology，involving dynamic negative stiffness，lightweight tuning and targeted modal control，are also described，which provides an alternative way for high-performance control of structure. On this basis，the theoretical design framework of inter-story，lightweight-tuned and isolated structures with inerter systems are given，performance-oriented optimal design namely，which can provide reference for the practical design of structure with inerter system.

Due to the lack of research on the dynamical response of the inerter system based on non-stationary seismic excitation，an analytical solution for the time-varying variance of the dynamical response of a multi-degree-of-freedom energy-consuming structure with series-parallel layout Ⅰ inerter system （SPIS-Ⅰ） is proposed. According to the constitutive relationship of the SPIS-Ⅰ，the dynamic equations of the energy dissipation structure，and the impulsive non-stationary seismic excitation，we decouple the inertial energy dissipation structure into first-order systems using complex modal analysis and the virtual excitation method. It is convenient to obtain the unified solution of the structural response quantities such as displacement，velocity，inter-story shear force，etc. The quadratic decomposition method is used to transform the time-varying power spectral density function of the unified solution into a linear combination of the complex modal eigenvalues of the inertial-capacitated energy-consuming structure，the modal coefficients，the time-varying modal strength coefficients，and the quadratic product containing the squared term of the circular frequency. On this basis，an analytical solution for the time-varying variance of the response of the energy-consuming structure under non-stationary seismic excitation is derived by utilizing the characteristics that the non-stationary modes spectral moments have an analytical solution in the infinite integration interval. The accuracy of the proposed dynamic response power spectrum and time-varying variance is verified by using the sudden white noise excitation to analyze the dynamic response of the structure. At the same time，the dynamic response of the frame structure based on the sudden Kanai-Tajimi model is studied，and the influence of the parameters of the inertial system on the damping effect is analyzed. The proposed method can be applied to analyze the seismic response of linear structures under other non-stationary modulation functions.

In this paper，the strong earthquake records of 13 soil stations within 41 km from the fault of the 2008 Wenchuan 8.0 magnitude earthquake are selected. These records are combined with the strong earthquake records of 29 calculation points obtained by using the stochastic finite fault method simulation. Moreover，nonlinear least squares fitting is performed by using three near-fault ground motion attenuation models and the fifth-generation ground motion parameter zoning map attenuation model to obtain the peak ground motion acceleration of the Wenchuan earthquake near-fault. The attenuation relationships are obtained and analyzed by considering ±1 times standard deviation and correlation coefficients for reliability. The results show that there are some differences in the attenuation relations obtained by different attenuation models. The peak acceleration obtained by the Shao Guangbiao model is low. The prediction results of Wang Guoquan model has a large deviation for other magnitude earthquakes because the magnitude term is not considered. Besides，the peak acceleration of the fifth-generation ground motion parameter zoning map attenuation model is low.

Tianjin Metro Line 6 is adjacent to Beiyangyuan Campus of Tianjin University，and the train operation may cause adverse vibration effects on important infrastructures of the campus. In this paper，the National Facility for Earthquake Engineering Simulation of Tianjin University，which is close to the line，is taken as the research object. Firstly，the site vibration test is carried out on the sites distributed along the line and the adjacent constructions，through which the vibration attenuation law along the site and the vibration level of the control points in the constructions are studied. Furthermore，a whole process finite element model of tunneling-site-facility constructions is established，and the vibration simulation analysis of site and facility constructions is carried out considering whether the protected river exists or not （actually there is a protected river）. The vibration isolation efficiency of the protected river is emphatically discussed. The research shows that the vibration impact of the operation of Tianjin Metro Line 6 on the large-scale earthquake engineering simulation research facilities of Tianjin University meets the limit requirements of the code. Affected by Tianjin soft soil and the protected river，the vertical acceleration attenuation of the site is significant，and the attenuation rate reaches 97.33% from 0m to 80 m. The design of the mass concrete foundation of the facility and its bottom pile foundation is helpful to the vibration control of the foundation itself. Due to the presence of protected river，the amplitude of the site and the large shaking table foundations was reduced by 40.87% and 27.97%，and the frequency spectrum of the site showed obvious “double peak” phenomenon in 0~20 Hz and 40~80 Hz bands.

To establish a 3D metro train-FST coupling model in the frequency domain，the key problem of the rail displacement at each moving wheel-rail contact point caused by all moving wheel-rail forces needs to be solved firstly. The matrix of the TFC establishes the relationship between them. Based on the established 3D discrete supported floating slab track model in the frequency domain，a method to calculate the TFC is put forward in this paper. Based on the relationship between the fixed and moving coordinate systems，the TFC to a moving point on FST can be written as the integration of the rail displacement response at a fixed point in the frequency domain caused by a moving harmonic load. After calculating the TFC of the 3D FST，some conclusions are obtained. At each excitation frequency，the TFC of a moving wheel-rail force to each wheel-rail contact point is the largest at the point of the force itself. Due to the moving of the wheel-rail force，there is a certain difference between the TFC of the front axle wheel-rail force to the rear axle wheel-rail contact point and that of the rear axle wheel-rail force to the rear axle wheel-rail contact point. In the same bogie，the TFC of the left wheel-rail force of the front axle to the right wheel-rail contact point of the same axle is similar to the TFC of that force to the left wheel-rail contact point of the rear axle. It is advisable to use a 3D model to finely analyze the dynamic characteristics of floating slab tracks.

Vehicle transport is an important part of logistics transport. It is of great significance to study the response of cargoes in the process of vehicle transport. Considering the coupling effect between cargo and vehicle bottom，an 11-degree-of-freedom vehicle-cargo coupling model is established. The relationship between three-way response is compared，and the influence of different road levels and cargo-related parameters （load，stiffness，damping） on the system response is taken into consideration. The results show that the coupling effect of vehicle-cargo significantly affects the system response. The influence of rotation in transportation cannot be ignored. The vibration response of cargo increases with a decrease of load，stiffness and damping. The worse the road condition is，the bigger the vibration response of cargo and vehicle bottom will be. The research results are of great significance and value for the design of vehicle-cargo transportation system.

Extracting sensitive damage features from structural response signals is crucial for damage identification methods based on pattern classification. To this end，a hybrid network that combines a deep belief networks （DBN） and a long-short term memory （LSTM） network is proposed through a hybrid learning mechanism to utilize the merits of both networks in the aspects of extracting high-order abstract features and considering data sequence correlations. First，transmissibility data from response signals are sequentially input into the DBN to achieve the initial data compression and feature extraction，reducing the redundant information in the responses. Then，the extracted feature sequences are input into the LSTM network to consider the correlation between the different responses for acquiring the relevant sensitive damage features. Finally，a classification layer with the Softmax function is used to classify the features output by the LSTM network. Thereby，different structural damage patterns can be identified. The damage identification results on a three-dimensional experimental steel frame demonstrate that the hybrid learning mechanism can better train the network parameters，and the fine-tuning on the whole hybrid network contributes to the subsequent damage feature classification. Under the pollution of numerical or measured noises，the hybrid network can still effectively perform the data compression，feature extraction and classification. The various damage scenarios of the experimental frame are well identified.

The star-shaped negative Poisson’s ratio structure is used as the core of sandwich panels. The dynamic model of a sandwich plate is established，and the equivalent elastic parameters of sandwich layer are derived. The equations of motion of sandwich plates are derived based on Hertz theory，first order shear deformation theory and Hamilton principle. Then，the equations of motion are solved by navier method. The contact force of the impact model is obtained through the spring-mass model with two degrees of freedom，and the lateral displacement of the sandwich plate after impact is calculated by Duhamel integral. The predicted results of plate contact force and lateral displacement are compared with the published papers to verify the accuracy. Meanwhile，the low-velocity impact response of star-shaped negative Poisson’s ratio sandwich panels is also compared with the negative Poisson’s ratio concave hexagonal honeycomb sandwich panels，and the influence of the parameters of sandwich panels is also discussed. When the impact velocity increases，the maximum contact force and the maximum lateral displacement of the sandwich plate also increase，while the duration of the impact response decreases. The greater the thickness ratio of the sandwich plate is，the better the impact performance of the sandwich plate will be. The smaller the side length ratio of cell is，the better the impact performance of sandwich plate will be. The increase of the cell concave angle enhances the impact performance of the sandwich panel. This study can provide some reference for the study of impact resistance of negative Poisson’s ratio metamaterial structures and sandwich panels.

The rod string is a thin rod string composed of a coupling and a rod connected by threads. The research on the dynamic behavior of the sucker rod string is the basis to prevent the failure of the sucker rod string and reduce the operation cost of the oil well. In view of the coupling vibration of rod string，it is proposed that the torsional torque generated by the friction force between the rod and tubing is the excitation of torsional vibration. Considering the influence of friction force on the coupling vibration of rod string，a simulation model of the coupling vibration of rod string in one directional well with initial bending is established under the conditions of displacement excitation at the top，load excitation at the bottom，trajectory excitation at the curved hole and tubing constraint. The four-order Runge-Kutta method is used to solve the simulation model and to simulate the dynamic behavior of the rod string. The simulation results show that： both longitudinal and transverse vibration simulation results are affected by the coupling vibration of the rod string. The effect on longitudinal vibration is not obvious. The contact force between the rod and the tubing in the inclined section of the oil well is high，and the collision in the compressed section of the rod string is serious. Hence，the inclined section of the oil well and the compressed section of the rod string are dangerous points for eccentric wear. Under normal preload conditions，the torsional vibration of the rod string is not sufficient to cause the rod string to trip. However，when the preload force of the coupling drops below the maximum torque of the rod string，torsional vibration may cause the rod string to trip. The research provides a theoretical basis for analyzing the failure mechanism of pumping rods，improving the working life of pumping rods and optimizing the design of pumping rods.

Brake disc bolts are important to ensure the braking reliability and the operation safety of electric multiple units （EMU）. Based on the load test technique of braking disc bolts， an experiment was conducted on the wheel-mounted braking disc bolts of the Chinese high-speed train to obtain the data of the dynamic loads，including the tensile load，the radial bending moment and the circumferential bending moment. By establishing a finite element model of the wheel-mounted braking disc bolts with the wheel-rail contact，the bolt loads under high-speed rotation are simulated and compared with test results. According to the test results and the simulation results，it indicates that the braking disc bolt loads are closely related to the operating speed of EMU. The higher the operating speed is，the bigger the variation of the bolt load will be. The loads of the braking disc bolt change periodically with the wheel rotation. When the wheel rotates once，the bolt load changes once. Meanwhile，there are some small waves on each load signal，which is caused by the wheel-rail excitation. With an increase of the operation speed，the vibration of wheel increases，and the bolt load fluctuation also increases. The results of the finite element model show that the values and directions of the radial bending moments at different positions are inconsistent. Due to the asymmetry of the wheel structure，the radial bending moment at the left cross section of the bolt is bigger than that of the right cross section.

Based on the strain gradient nonlocal Biot theory，the analytical solution of the dynamic response of the tunnel lining under the action of P-wave is obtained by using the wave function expansion method and the boundary conditions between saturated soil and lining with the deeply buried circular lining as the research object. The influence of non-local parameters and size factors on the dynamic stress concentration factor （DSCF） is investigated for different incident P-wave frequencies. The results show that when the incident wave frequency is low，the non-local parameters and size factor have almost no effect on the DSCF. As the incident wave frequency increases，the effects of the non-local parameters and size factor on the DSCF become more and more obvious. The non-local parameters are negatively correlated with the DSCF，and the size factor is positively correlated with the DSCF. The maximum dynamic stresses in the lining appear on the right side of the lining. With an increase of frequency，the DSCF in the lining shows obvious radial direction and the dynamic stresses in the lining appear in the right side of the lining. The maximum dynamic stresses in the lining all appear on the right side of the lining，With an increase of frequency，the DSCF in the lining shows obvious fluctuation along the radial direction，and the non-local parameters and size factor have little influence on the distribution pattern of the cyclic stresses in the lining.

In this paper，the timing transmission gear of a certain type of domestic marine 20V diesel engine is taken as the research object. Aiming at solving the problem of frequent broken teeth fault，considering the influence of various types of internal and external comprehensive excitation，the lumped parametric bending-torsion coupling dynamic model of multi-branch gear transmission shaft system of diesel engine is established. Based on Newmark step-by-step integration method，the forced vibration response is predicted，and the accuracy of the model is verified by the actual test data. Considering the influence of dynamic load，the traditional tooth root bending stress load spectrum is modified，and the strength fatigue check of the faulty gear is carried out. The results show that the peak value of the response energy at the driven timing gear of the fuel supply cam end of the diesel engine is 5.2 times that of the peak value of the response energy at the flywheel end，which indicates that the speed fluctuation at the driven gear of the timing gear is too large and the torsional vibration characteristics are poor. At this time，the bending fatigue safety factor of the tooth root is only 1.35，which is in the general reliability range and is prone to tooth breakage. Based on the engineering practice experience，the vibration optimization design scheme of the fault gear transmission system is proposed to improve the bending fatigue safety factor of the fault gear by 1.61 to ensure the safe and stable operation of the shafting. The research results reveal the mechanism of timing gear tooth breaking fault from the perspective of dynamics，provide some theoretical guidance for accurate prediction of tooth root bending stress and performance optimization，and provide theoretical support for vibration response analysis and vibration and noise reduction of diesel engine timing gear shaft system.

The incipient fault characteristics of planetary gearbox are weak and difficult to effectively identify under strong background noise interference and variable working conditions. To address these issues，an improved feature mode decomposition （IFMD） algorithm is proposed to extract the weak fault characteristics of planetary gearbox under time-varying speed conditions. Firstly，for the key input parameters of the FMD algorithm，such as the number of decomposition mode n，the number of filter K，and the length of filter L，which need to be set manually and lack adaptability，an adaptive scale space spectrum segmentation method is proposed to determine the required number of decomposition modes n. On this basis，the Spectral Gini Index （SGI） is used as the objective function，and particle swarm optimization algorithm is used to automatically determine the optimal filter number K and filter length L. Subsequently，the IFMD is applied to perform optimal modal decomposition on the fault signal under the optimal parameter combination，and the decomposed component with the highest SGI value is selected as the sensitive modal component. Finally，significant fault feature orders are extracted from the envelope order spectrum of sensitive component to accurately diagnose the fault type and location of planetary gearbox. The analysis results of variable speed simulation signals and engineering experimental data indicate that compared to the PSO-VMD method，MED method，SGMD method，and fast spectral kurtosis method，the proposed method can extract weak fault information more clearly and comprehensively，thereby improving the characterization ability and diagnostic accuracy of early fault features of planetary gearbox under time-varying speed conditions.