The electromagnetic performance of phased array antenna is greatly affected by the phased array antenna surface deformation. How to apply the strain measurement data of sparse fiber grating strain sensors to sense the shape of antenna array is the key to realize structural health monitoring and electromagnetic performance control. This paper proposes a virtual sensing method for structural deformation under complex experimental modes. In this method，the complex mode transformation is first used to process the complex mode data obtained from modal testing to obtain the corresponding real displacement modes，and then the full field expansion of finite real displacement modes is realized using mode expansion；Combining the extended real displacement modal and finite element modal data，two virtual sensing equations named CMT-SEREP（complex mode transformation-system equivalent reduction expansion process）and CMT-LC（complex mode transformation-local correspondence），which characterize the relationship between sparse measured strain information and the full field displacement of the structure，have been derived to achieve the real-time estimation of the deformation shape of the antenna structure from sparse measured strain information. Using the developed large phased array antenna array deformation experimental platform，experimental verification of different sensing methods was carried out under three deformation working conditions. Experimental results show that the proposed method can reconstruct the full field displacement of the antenna array structure using sparse strain measurement information，and the sensing accuracy of CMT-LC is higher than that of CMT-SEREP. Compared to the traditional modal method，the relative percentage error of deformation sensing using CMT-LC method has been reduced by at least 6.105%. This method is not only suitable for deformation sensing of non-proportional damping antenna structures，but also suitable for other complex engineering structures，and it has a great application potential.

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.

An axisymmetric finite element-boundary element coupled computational method is proposed for the dynamics of cylindrical shells with endplates in water. Due to the periodic characteristics of the structure，the movement of the cylindrical shell and end plate can be determined by examining their meridional movement，and the meridians are discretized into several elements for further analysis. By using the energy method，the elemental matrices are obtained and assembled into the global matrices. Then the discrete schemes for structural motion with the finite element is established. Considering the axisymmetric characteristic of the fluid，an axisymmetric boundary element on the meridians is established and the calculation format for fluid-elastic forces on the finite elements is given. The fluid forces are then converted into an equivalent nodal force at the nodes and the effects of the fluid are evaluated by the added mass，damping，and stiffness matrices. By combining the structural motion and the schemes of fluid-elastic forces，an axisymmetric finite element-boundary element coupling method is developed to solve this fluid-structure coupling problem. The calculated results presented in this paper demonstrate good agreement with existing theoretical solutions and commercial analysis software，validating the accuracy of present method. Moreover，this method exhibits higher computational efficiency compared to commercial analysis software. It allows for direct determination of the mass and stiffness matrices of cylindrical shells in fluid，facilitating fast calculation of forced vibration. Based on this method，the wet frequencies and stability characteristics of complex cylindrical shells with end plates in axial flow are analyzed. The results show that the end plates will change the flow velocities on the cylindrical shell and make it more easily to instability.

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%.

The fuzzy domain of traditional fuzzy control is fixed，and the control efficiency will decrease when the dynamic characteristics of the controlled structure or external excitation changes. On the basis of traditional fuzzy control algorithms，a variable universe fuzzy control is designed. The variable universe fuzzy control takes the error and error rate of the controlled structure as input，and the scaling factor as output，achieving adaptive adjustment of the fuzzy domain of the main fuzzy controller. A two-story steel frame structure with a magnetorheological damper as the control device was constructed，and the variable universe fuzzy control system with the displacement and velocity of the first floor as inputs was developed in the dSPACE real-time simulation system. Shaking table tests under different intensities of seismic motion and different additional mass conditions were conducted. The results show that variable universe fuzzy control can adaptively adjust the fuzzy domain，effectively reducing structural displacement，velocity，and acceleration response. When the added mass of the controlled structure and the peak ground acceleration change，the control effect of variable universe fuzzy control is better than that of fuzzy control and OFF passive control.

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.

Inerters and negative stiffness devices can improve the energy dissipation performance of vibration absorbers. An increasing number of applications of them in novel high-performance vibration suppression have been witnessed. In this paper，analytical parametric optimization analyses on the tuned inerter mass systems with negative stiffness（NS-TIMS）are performed. A unified model of governing equations and transfer functions for NS-TIMS under different installation locations，application scenarios（such as inter-layer vibration absorption，and base isolation）and excitation types is established. Based on the fixed-point theory，the optimal parameters of NS-TIMS considering both H_∞ and H₂ norms are analytically derived. Considering typical application conditions，the analytical formulas are further analyzed and simplified. Consequently，the design formulas for the optimal parameters of NS-TIMS based on the“equivalent inertial mass ratio” are proposed. The application scopes of the design formula are discussed. Through numerical cases on the practical examples of wind-induced vibration control and seismic base isolation，the effectiveness of the design formulas considering the actual structural damping ratio and spectral characteristics of stochastic excitations is verified. It is also revealed that NS-TIMSs have superior performances in both high flexible structure vibration absorption and auxiliary base vibration isolation.

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.

To improve the whole seismic performance of the frame structure，especially the beam-column joint，a new seismic reinforcement method is proposed for reinforced concrete frame structure with adding a web-type plate. The internal force optimum can be achieved by setting the web-type plate at a certain region between frame beams，and the bending moment of the beam-column joint will decrease. A multiple seismic defense lines frame structure can be formed with the web-type plate. A typical frame structure of 10 stories is designed as a case study. The effects of the layout，linear stiffness ratio，and reinforcement of the web-type plate on the structural performance are analyzed. The reinforcement ratio of the web-type plate to the column and beam is proposed. The seismic analysis shows that the lateral stiffness of the structure is improved，meanwhile the bending moment of the beam-column joint is reduced. The optimum layout position of the web-type plate is 0.3 and 0.7 of the beam span，and the suggested linear stiffness ratio of the web-type plate to column and beam are 0.7~1.5 and 3.5~7，respectively. Further，a suggested reinforcement ratio of the web-type plate is given by nonlinear parametric analysis to ensure that the plate yields first as designed. The nonlinear dynamic time-history analysis of an actual engineering project that seismic upgrading with the web-type plate is undertaken. The analysis results show that the lateral displacement，and the inter-story drift ratio of the structure with web-type plate are reduced. Compared with the structure before upgrading，the plastic hinges are reduced. The seismic performance of the frame structure reinforced with the web-type plate is improved. The analysis verify that the proposed strengthening method with web-type plate was reasonable and feasible.

The influence line is an important parameter of the elastic mechanical state of the bridge structure，which can effectively reflect the resistance and deformation resistance of the structure，and is expected to be used to evaluate and predict the elastic-plastic response during earthquakes. Taking the influence line of a three-span steel plate composite continuous beam bridge as the model correction target，the bridge model correction research is carried out based on BP neural network. With the expectation of Beta distribution as the earthquake damage index，the overtaking probability expression of the bridge model under various performance levels is fitted，and the seismic vulnerability of the continuous beam bridge structure before and after the finite element modification is analyzed and compared. The results show that the relative error between the measured value and the calculated value can be reduced from 38% to less than 10%，and the earthquake damage index of the modified finite element model is lower than that of the initial model. By incorporating the Beta distribution to weight and integrate different performance levels，the structural vulnerability matrix can be transformed into a seismic damage index，thereby accounting for the damage consequences of different failure levels and providing a more comprehensive representation of the seismic performance of the bridge structure.

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.

Based on the three-dimensional finite element slope dynamic analysis model which is validated through the test data of 1：7 indoor physical model for live tree stump，the attenuation characteristics of additional dynamic stress on live tree stump slopes，the stress response characteristics of taproot and lateral root of live tree stumps，and the influence of live tree stumps on slope stability are studied. The dynamic stability mechanism of live tree stump slope is explored. The research conclusion is as follows. The peak value of vertical dynamic soil pressure calculated by the three-dimensional finite element dynamic analysis model is close to the measured results of the indoor physical model. The method and calculation results of the three-dimensional finite element dynamic analysis model of the live tree stump slope established through Midas GTS NX are reliable. The peak value of additional dynamic stress on the slope is affected by the superposition effect of train axle load. The higher the train movement speed，the greater the peak value of vertical dynamic stress. The additional dynamic stress in the ballast layer is the largest，it rapidly decays and diffuses downwards showing a semicircular arc shape. Only small dynamic stresses are transmitted to the two rows of live trees on the upper slope. The degree to which the shear resistance of the taproot of live tree stumps varies at different positions，and the taproot at the foot of the slope is subjected to greater shear stress compared to the taproot at the shoulder of the slope. The taproot is similar to the anti-slide pile to exert its shear resistance ability. The side roots of live tree stumps growing inside the slope are similar to anchor rods，while the side roots growing outside the slope are similar to supports，and they form an anchor-support effect that synergizes with the main root to play a sliding resistance role. The existence of live tree stumps leads to a redistribution of stress in soil，and the shear stress concentration near the live tree stumps. The live tree stumps hinder the transmission of shear stress in soil，inhibit the connectivity of plastic zones，and improve slope stability. The degree of influence on the horizontal dynamic displacement of the slope is related to its distance to the location of the dynamic load，and the closer the distance，the greater the impact. The live tree stumps can reduce the horizontal dynamic displacement at various points on the slope，but the reduction at the foot of the slope is the greatest. The live tree stumps can significantly improve the stability of slopes under train power，and their slope safety factor can be increased by 15%~20%. The potential sliding surface of the live tree stump slope presents a circular arc shape，and the live tree stump moves the plastic zone towards the deep soil layer，thereby improving the stability of the slope. The research results can provide certain guidance for the application of live tree stumps in roadbed slopes.

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.

For cross domain diagnosis of the label spaces of source domain and target domain are partially overlapped，that is to say，both the target domain and the source domain contain the classes that the other does not have，a cross domain adaptive fusion diagnosis method based on weighted adversarial learning is proposed. As entropy can be used to reflect the characteristics of the shared known classes and unknown classes，two convolutional neural networks with the same structure are introduced to carry out entropy-based weighted adversarial training，which is aim to enhance the ability to identify the shared known classes by extracting the domain-invariant features，as well as the binary cross schemes of the source domain and target domain sample outputs are used to isolate the unknown classes. In addition，the fully connected layer hidden features of these two convolutional neural networks are taken as the input of two label transfer models，and the probability outputs of these three diagnostic models are fused by voting rule. The failure test bench data of mechanical transmission components under variable working conditions and the damage data of selfpriming centrifugal pump are used for analysis and verification，the experimental results show that the proposed cross domain adaptive fusion diagnosis method can distinguish the shared known classes and unknown classes in the target domain more accurately.