It is usually difficult to establish the dynamic model of a launch vehicle that accurately describes its time-varying characteristics. Therefore modal identification techniques are particularly necessary to obtain the time-varying dynamic characteristics of launch vehicles under flight conditions. Aiming at the problem of in-flight modal identification of launch vehicles，an output-only recursive identification method based on the time-dependent autoregressive moving average model is developed by using exponentially weighted mechanisms to track the time-varying characteristics. Without measuring the natural excitation forces，the proposed method can accurately and quickly identify the time-varying modal parameters of launch vehicles by exclusively using the measured response signals. Taking the CERES-1 launch vehicle as an example，time-varying modal parameters before liftoff and during the flight phase are accurately estimated by processing the flight telemetry data. Identification results are consistent with the variation of the finite element analysis results，demonstrating the high achievable accuracy of the proposed method. The proposed in-flight modal identification method can obtain the full-cycle modal information of launch vehicles，which meets the engineering requirements for the finite element model updating and attitude control system design.

The large number of aero-engine rotor components and the large computational volume of high-dimensional complex models lead to difficult dynamic analysis and long computation times，which are disadvantageous to the efficiency of rotor structure design and dynamics verification. Based on the component modal synthesis method，a novel multi-stage modal reduction strategy is proposed for the modal reduction of a large complex system with many components. The internal freedom degrees of each sub-structure are reduced in parallel using fixed interface modal reduction，while the couplings between the substructures are retained completely. By defining a new level of substructure through substructure combination，the multi-stage modal reduction is applied to an additional reduction，and the hybrid mode synthesis is subsequently combined to construct the branch mode and significantly reduce the dimensionality of the rotor FEM model. Meanwhile，the dynamic characteristics of key substructures and the key dynamic characteristics of the vibration system are preserved. This computational strategy is used to establish a low-dimensional reduced model of a missile engine rotor system，and the reduced model is used to improve the efficiency of rotor dynamics analysis and accelerate the design optimization of bearing stiffness parameters. The results show that the time required for rotor dynamics analysis is reduced by 99.5%，and the accuracy error does not exceed 0.1% compared with ANSYS calculations. The computational strategy can be used for rapid analysis of multi-component high-dimensional complex systems.

In the process of maneuvering flight，the aeroengine will bear very harsh working conditions，leading to irregular transient vibrations that can result in failure. In this paper，the effect of a semi-active magnetorheological damper （MR damper） on the dynamic characteristics of a rotor system under maneuvering flight is investigated. The finite element model of the rotor system with MR damper under maneuvering flight is established using the finite element method. The Newmark-β numerical method is used to solve the dynamic equations，and the dynamic characteristics of the rotor system during maneuvering flight are studied. On this basis，considering the effects of MR damper on the transient，the steady state responses of the rotor system under maneuvering flight are analyzed. The results show that transient impact is caused at the beginning and the end of maneuvering flight，which stimulates the first order modal response of the rotor system. The MR damper with suitable current can effectively suppress the amplitudes of transient and steady-state responses of the rotor system during maneuvering flight. In addition，due to the large eccentricity of the journal in maneuvering flight，the MR damper is prone to produce nonlinearity.

In pursuit of the ideal power-to-weight ratio，supercritical transmission shaft systems are increasingly used in the design of helicopter structures，which leads to the generation of violent vibrations driving through its critical speed. To suppress the excessive transcritical vibration，dry friction dampers are usually employed. In this study，a supercritical transmission shaft system with a dry friction damper is investigated. The governing equations are established and the boundary characteristics of various rub-impact responses of the system under eccentric excitation of the transmission shaft are analyzed. Firstly，the nonlinear governing equations of the damper/shaft system are constructed. Secondly，typical response characteristics are determined using frequency sweep，and the boundaries of impact occurrence and stability conditions for the synchronous full annular rub are solved using analytical methods. Finally，the derived response boundaries are verified by the Runge-Kutta method，and the relationship between the response boundaries and the system parameters is further explored.

Taking aircraft brakes as the research object，the problem of aircraft brake induced vibration was studied. Aiming at the influence of disc friction characteristics caused by the complex braking environment during aircraft skidding，a nonlinear dynamic analysis model of brake disc set was established considering the properties of the hydraulic system and disc material，with the model interface reserved for the development of new material technology. From the perspective of practical engineering research value，the influence of the above parameters on the stability of the system is studied by using numerical simulation，bifurcation theory，and other nonlinear analysis methods by considering key factors such as wheel speed，hydraulic system equivalent damping，brake disc surface damping and brake disc friction characteristics as control variables，and the range of structural parameters to keep the system stable is determined. It is convenient to parameterize the structure for rapid analysis and design. Based on the results of the model analysis，part of the causes of brake vibration were revealed，and corresponding optimization measures for vibration reduction were put forward from two aspects of structural parameters and brake control law. Then a comprehensive analysis method for aircraft brake induced flutter was formed，which provided a theoretical reference for the initial stage of aircraft brake design.

The band gap characteristics of periodic structures provide a new idea for the field of seismic isolation in civil engineering，among which the one-dimensional periodic foundation structure has garnered significant attention due to its simple structure and economical applicability. In this paper，by studying the vibration characteristics of the one-dimensional periodic base structure，an approximate analytical solution for calculating the one-dimensional rubber-concrete periodic base band gap is derived，and on this basis，a one-dimensional rubber-concrete periodic foundation optimization design method based on the resonance zone of the superstructure is proposed. Numerical examples in the frequency domain and time domain show that the periodic foundation designed by this optimization method can ensure a good damping effect of its superstructure in a wide and continuous frequency range.

Due to the existence of a deep seawater layer in marine sites，its influence on the seabed ground vibration characteristics and the seismic response of marine structures is significant and should not be ignored in the seismic analysis of marine structures such as cross-sea bridges. Therefore，to determine the influence of the seawater layer on the seismic response of the structure，the study establishes the seismic fluctuation analysis model based on the seismic fluctuation theory for the coupled seawater-seabed-stayed bridge. In addition，considering that the marine environment may pose a threat to the durability of the damping members，the study proposes a new type of cable-stayed bridge damping system using Bulking Restrained Brace（BRB）with excellent durability as the longitudinal damping member，and takes the Qingzhou Channel Bridge as the engineering background to verify the seismic response by comparing it with the floating system cable-stayed bridge model. The feasibility of the new type of seismic damping system considering the influence of the marine environment is verified. The study optimizes the location and equipment parameters of the BRB. The design method of BRB as a longitudinal damping member for cable-stayed bridge is further determined. It is found that the hydrodynamic effect generated by seawater under the seismic action will amplify the seismic response of the super⁃ structure of the cable-stayed bridge. By comparing the seismic response of the structure under different working conditions，it is confirmed that the best overall seismic damping effect of the bridge is achieved when the BRB is installed at the pier and tower locations simultaneously. Besides，the parameters such as yield bearing capacity of BRB also have a great influence on the seismic performance of cable-stayed bridges.

The seismic safety evaluation of existing urban buildings （groups） is faced with multiple technical development of efficient analysis，rapid evaluation and quantitative determination. Considering the evolution of structural performance during the long-term service life，the safety evaluation of in-service buildings requires design and measurement information on the structures as well as regional ground motions to calibrate the real conditions of the structures，which can ensure the accuracy of the performance evaluation results within an acceptable timeliness. Based on the equivalent nonlinear single-degree-of-freedom model and the authors’ recent research on data-driven performance assessment index，this study proposes a method to map the global conditions of the structure with the measurement modal information and assess the seismic safety of the target building using the regional dataset of measured ground motion further. Based on the field testing and the HAZUS technical manual，the procedure of establishing the equivalent nonlinear single-degree-of-freedom representing the existing building is described. Two structural condition evaluation indicators are proposed，combined with multivariate engineering performance parameters，and the relationship between the deformation of an equivalent model and different seismic performance levels is further established. A high-rise regular RC frame structure located in Gongxian，Sichuan Province is considered as an example，the seismic safety of this building subjected to 10 local earthquakes measured from 2019 to 2022 is evaluated.

Tuned viscous mass damper （TVMD） is widely recognized as one of the promising inerter-based devices. This study focused on investigation of the effective damping ratio enhancement effect and optimal design of TVMD for building structures under seismic excitations. The TVMD control performance for the structural inherent damping energy dissipation power was regarded as an effective damping ratio added to the primary structure. Further，a theoretical expression of the TVMD effective damping ratio was derived based on the random vibration theory. To make the application of TVMD more valuable，TVMD was expected to obtain a larger effective damping ratio compared to the viscous damper （VD） with the same damping coefficient，which was defined as the effective damping ratio enhancement effect. The effective damping ratio enhancement factor was introduced for the quantitative evaluation of the enhancement effect on the damping ratio. Both the effective damping ratio and the effective damping ratio enhancement factor were considered as optimization objectives，and a closed-form solution of TVMD optimum design parameters was therefore proposed. Analysis results showed that the proposed closed-form solution had an excellent applicability and stability. The TVMD mass ratio and damping ratio were recommended to be less than 0.3 and 0.1，respectively，for the sake of the best efficiency of the damping ratio enhancement effect. A 7-story steel benchmark model was taken as an engineering example to illustrate the TVMD optimal design process and to verify the validity and superiority of the proposed closed-form solution. It was found that the deformation of the damping element for TVMD designed by the proposed closed-form solution was amplified remarkably，demonstrating the desired effective damping ratio enhancement effect. Most importantly，compared to the traditional closed-form solution，the best advantage of the proposed closed-form solution is to ensure that TVMD control performance is better than VD with the same damping coefficient，regardless of control efficiency problem.

The longitudinal linkage of the floating slab track （FST） has weakness due to the dynamic effects of FST longitudinal linkage，which are not adequately considered in the track design. By introducing the method of equivalent density and equivalent foundation coefficient to simplify the model of the base of a steel-spring-FST system，a three-dimensional finite element model of vibration characteristics analysis of prefabricated short and cast-in-situ FST system is established. In the proposed model，the influence of the rail，shear hinge，and foundation under the slab on the vibration characteristics of the floating slab structure is fully considered. The modal analysis and harmonic response analysis are analyzed with a focus on the dynamic effect characteristics of the longitudinal connecting slab of the FST system. The results show that： The modal shape of the FST in the low frequency band of 1~200 Hz mainly shows four types of motion： rigid body motion，bending，bending-torsion combination and torsion； For the prefabricated slab track system，the frequency band in which the floating slab dominates the vibration characteristics of the system conforms the system modal analysis and harmonious response analysis； For the cast-in-situ slab track system，when the frequency is within 32.6~57.8 Hz，the frequency band is the transition band，where the dominant role of the FST in the vibration characteristics of the system is weakened； The lower-order bending modes generated by the coupled slab dynamic effect are expressed as rigid body motion modes in the prefabricated slab system； for the FST composed of N_s slabs，the number of additional modes around each order of bending mode frequency of a single slab caused by the coupled slab effect is N_s/2‒1.

Π-shaped composite deck is an elastic bluff body，which is susceptible to aerodynamic instability. In the present study，a cable-stayed bridge with a Π-shaped composite deck is taken as the research object，and the vortex-induced vibration （VIV） and the aerodynamic countermeasures are investigated by using the small-scale wind tunnel tests and computational fluid dynamics （CFD） method. The wind speed range of the VIV for the Π-shaped composite deck is determined via the wind tunnel test. After that，several VIV mitigation measures are investigated. The computational fluid dynamics （CFD） method is used to study the mechanism of VIV and vibration suppression by aerodynamic measures. The results indicate that the VIV in the original section is caused by the interaction of the periodic shedding of the vortex in the wake area and the vortex evolution on the upper and lower surfaces of the girder； After adopting three different aerodynamic measures，the flow can pass through the section more smoothly，so as to mitigate the VIV effectively，except for the upper inverted L-shaped guide plate at the wind attack angle of +3°. This study can offer guidance on the wind-resistant design of a cable-stayed bridge with a Π-shaped composite deck.

The power generation of single-axis PV trackers system is significantly higher than that of the fixed photovoltaic system，making them widely used in recent years. The single-axis PV tracker is prone to torsional aerodynamic instability in the strong wind condition due to its low torsional stiffness，resulting in structural damage. In order to understand the occurrence conditions and mechanism of this vibration further，the present study investigates the influence of structural natural frequency，tilt angle，damping ratio and other parameters on torsional aerodynamic instability through wind tunnel tests with elastic support. The variations of aerodynamic damping and aerodynamic stiffness with wind speed and tilt angle are focused. The result shows torsional aerodynamic instability of single-axis PV trackers shows strong aerodynamic coupling effect. The aerodynamic damping and aerodynamic stiffness are significant parameters that can influence aerodynamic instability，which are sensitive to wind speed and tilt angle with self-excited vibration characteristics. The increase in torsional stiffness can effectively limit the amplitude at certain tilt angles and improve the critical wind speed of the structure at various tilt angles. The unstable tilt angle is approximately located in the range of -15°~20°. It is suggested that a large tilt angle can be used to avoid aerodynamic instability in strong wind. When a small tilt angle is inevitable，higher critical wind speed corresponds to a 0° tilt angle.

In recent years，acoustic black hole （ABH） has shown an extremely broad application prospect in the fields of structural vibration and noise suppression，acoustic wave control，energy recovery，etc，due to its excellent performance. However，the truncation of ABH edge will lead to the existence of non-zero reflection coefficient，thus weakening the acoustic black hole effect. In this paper，the constrained layer damping is introduced into ABH plates. Under the framework of Rayleigh Ritz method，Gaussian function is selected as the basis function，and the distribution of basis function is determined according to the shape of ABH plate to avoid the singularity of mass matrix and stiffness matrix. A semi analytical model of ABH plate with constrained layer damping is established. By comparing with the results of finite element analysis，the correctness of the semi analytical modeling method is verified. The influence of structural parameters of constrained layer damping on the bending vibration characteristics of ABH plate is studied，and the damping mechanism and energy dissipation of constrained layer damping are revealed. The experiment further verifies the damping effect of ABH plate with constrained layer damping. The research provides a design reference for the application of constrained layer damping in ABH structures.

In this paper，a two-dimensional analytical model for composite beams is first proposed through the equivalent transformation of the cross-section. Based on the mixed variational principle，the dynamic state equations are derived through finite element meshing and interpolation along the length of the beam，with frequency contained nodal displacements and their energy-conjugated stresses as element nodal variables. The differential quadrature method （DQM） is introduced to discretize the equations along the height of the beam，and natural frequencies of composite beams under different axial forces and boundary conditions are obtained. This method was verified by numerical examples about natural frequencies of three beams，i.e. a concrete-wood composite beam，a concrete beam with a corrugated steel web and steel-concrete composite beam. Since the proposed method is based on the two-dimensional theory，it can provide benchmarks for beam theories and error analyses.

Environmental vibration is one of the non-periodic and random broadband excitations. It is of great significance to study the characteristics of vibration energy harvesters under environmental vibrations. In this paper，the modified stochastic averaging method is used to solve the following parameters of piezoelectric beam with a variable cross-section： steady-state probability density function of equivalent amplitude，displacement and velocity，joint probability density function of displacement，and velocity and steady-state mean square output voltage. Then the study investigates the energy acquisition efficiency of a piezoelectric beam with a variable cross-section under Gaussian white noise excitation. The results show that when the load resistance reaches a certain value，the variable section piezoelectric beam with a section coefficient β>0 can produce better steady-state mean square output voltage than the constant section piezoelectric beam with β=0； when the section coefficient β>0，with the increase of the reciprocal of the product of resistance and capacitance，the mean square voltage of the variable-section piezoelectric beam shows a gradually decreasing trend. The trend shows the following rules： when the reciprocal value of the resistance and capacitance reaches a certain value，the larger the β value is，the higher the mean square voltage will become； with the increase of the noise intensity，the mean square voltage of the variable-section piezoelectric beams shows a trend of increasing gradually； when the noise intensity reaches a certain value，the larger the β value is，the higher the mean square voltage will become. The research results in this paper can provide a theoretical basis for the design and application of the variable-section piezoelectric cantilever energy harvesting system.

The supercritical carbon dioxide power cycle system has a very positive effect on the realization of energy saving and emission reduction goals. In this paper，a calculation model is proposed for a foil gas dynamic pressure bearing structure. By fitting the non-ideal state gas supercritical carbon dioxide，the relationship between density and pressure is established. Based on the heat transfer model and the gas lubrication energy equation，the temperature rise of the bearing gas film is analyzed. The Reynolds equation of the lubricating gas is corrected in combination with the turbulent effect in the actual operation process，coupled with the mechanical analysis model，Reynolds equation and energy equations，the static characteristics of foil gas dynamic pressure bearings are analyzed，and compared with air as a medium to analyze the influence of different system parameters and turbulence parameters on the bearing characteristics. The results show that compared with air，the foil gas dynamic pressure bearing using supercritical carbon dioxide as the lubricating gas has a higher bearing capacity，and within a certain range，the bearing capacity can increase with the increase of bearing diameter and width，eccentricity，the rotational speed and the reduction of the bearing clearance. For the turbulent influencing factors，within a certain range，the bearing capacity can increase with the increase of the local Reynolds number and turbulence coefficient，aerodynamic viscosity，density for ambient gas and the decrease of ambient temperature.

At present，many rolling bearing fault diagnosis methods based on convolutional networks have the disadvantages of poor diagnosis effect and poor generalization ability under the influence of noise signals and load variations. Aiming at these problems，an improved convolutional capsule network fault diagnosis method of rolling bearing under variable operating conditions is proposed. This method designs a multi-scale asymmetric convolution module，in which asymmetric convolution layers of different scales to extract features from the input data to maximize the extraction of feature information in the data and reduce the number of parameters effectively. In this module，the channel attention mechanism is introduced to better extract useful channel features and improve the feature extraction ability of the method in this paper. By improving the fully connected layer in the network to the fully connected layer of the capsule，the capsule can avoid the loss of characteristic information in the space in the process of outputting vector feature information. Case Western Reserve University bearing dataset and Southeast University gearbox dataset are used to verify the diagnostic performance of the proposed method and compare with other deep learning methods. The experimental results show that the proposed method has a better generalization and performance.

The windowed synchronous averaging （WSA） is commonly applied to the fault detection of planetary structures since it can overcome the problem of time-varying transfer path. However，it is unsuitable for the fault feature extraction of the planet gear at the first stage in a two-stage planetary gearbox due to the vibration coupling caused by the two-stage planetary structures. To address the issue，an angle compensation synchronous averaging scheme is proposed in this paper. In the proposed scheme，the speed fluctuation of the observed vibration is eliminated by equal-angle resampling. The second-stage interference from the sun gear at the second stage is constructed by applying the synchronous averaging to the resampled vibration based on the angle compensation strategy. The second-stage interference is removed by subtracting it from the resampled vibration. The corresponding envelope signal is extracted by the envelope analysis from the residual vibration. The WSA is utilized to construct the synthetic envelope signal of the planet gear at the first stage. The envelope synchronous averaging is used to suppress the asynchronous interference and extract the fault feature of the planet gear. According to the experimental results of a two-stage planetary gearbox test rig，the effectiveness of the proposed method is verified.