Based on a large depot project in Chongqing，the vibration and secondary noise characteristics and human comfort of the over-track buildings induced by metro operation in the depot are studied. The vibration characteristics of the depot are analyzed by field measurement. Combined with the numerical simulation method，the finite element model of the track-soil-depot-over-track buildings is established based on the metro-track coupling theory and the finite element theory. The vibration and secondary noise characteristics of the top buildings under train excitation are analyzed and evaluated. The combined annoyance model of vibration and secondary noise is constructed by combining psychology and fuzzy mathematics to analyze the human comfort，and the annoyance is used as the evaluation index. The results show that under the train operation，the vibration level of the throat area is the highest，and the vibration stability for different areas of the depot is as follows：the inner area > the throat area > the upper cover area. As the lateral propagation distance increases，the maximum Z vibration level of the platform decreases approximately linearly. The vibration peak of each building on the top is 12.5~20 Hz，and the main frequency band of secondary noise is 63~80 Hz. The vibration and secondary noise of each building attenuate with the increase of floors，but the vibration and secondary noise of residential building are amplified after 12 floors. The vibration of each building on the upper cover do not exceed the standard，but the secondary noise exceeds the standard in the commercial building，and the maximum exceeding value is 4.9 dB（A）. The annoyance results obtained by the joint annoyance model are in good agreement with the standard evaluation results，but the annoyance can refine the influence of vibration and secondary noise on human comfort. The model calculation shows that although the first floor of the residential building meets the standard limit，the joint annoyance is above 0.6 at night，and the evaluation using the joint annoyance rate model is more demanding.

Reconstructing the sound field environment inside the aircraft cabin during actual flight in a laboratory environment can provide a means for analyzing the acoustic environment inside the aircraft cabin，subjective evaluation，and noise reduction design. Based on the principle of sound pressure matching，this paper adopts a regularization method based on the L-curve method to solve the problem of inverse transformation of ill conditioned matrices. The effectiveness of the method in solving ill conditioned problems and improving reconstruction accuracy is demonstrated through simulation examples. Independently designed and built an aircraft cabin sound field reconstruction system. Conduct flight tests on transport aircraft，measure the noise at the pilot’s ear position under typical flight conditions，and use it as the target sound field. By using the sound pressure matching method，the full flight profile sound field reconstruction was achieved through the aircraft cabin sound field reconstruction system. Through sound field reconstruction experiments and subjective evaluation experiments，it shows that the reconstruction error in each frequency band of the one-third octave band is within 3 dB （A），and the subjective auditory fidelity and restoration are relatively high，providing support for subsequent analysis and subjective evaluation of the aircraft cabin acoustic environment.

In response to the challenging issue of low-frequency continuous spectrum reduction and isolation of ship equipment vibration，a vibration reduction method based on surface wave energy attenuation is proposed. Taking the rubber-fiberglass composite vibration system as an example，the damping characteristics of rubber surface waves are calculated using the finite element method. The influence of parameters such as thickness，damping coefficient，and Young’s modulus on surface wave attenuation is preliminarily explored. Experimental tests on rubber surface wave attenuation are conducted to validate the effectiveness of the surface wave attenuation method. The results demonstrate that the surface wave effect has a good vibration reduction performance，especially at high frequencies. The surface wave attenuation effect strengthens with increasing medium thickness，but not in a completely positive correlation. Reduction of the medium’s elastic modulus enhances the attenuation effect noticeably. Increasing damping is beneficial for surface wave attenuation. Compared to full-coverage rubber layers，local coverage of rubber layers on top of the isolating foundation provides better vibration reduction benefits.

In view of the light weight，small space and small amplitude requirements of electronic equipment for vibration isolation structure，the paper focuses on the isolation of low frequency vibration from its base. By introducing the cross-braced configuration，a concave cross braced plate model is proposed，the influence law of structural parameters on its low frequency vibration isolation performance is illustrated. Then，based on the design concept of cross-bracing，a concave sandwich phononic crystal structure model is proposed，and the influence mechanism of geometric parameters on its frequency response characteristics is revealed. After geometric parameter optimization and experimental verification，the vibration isolation structure model has excellent vibration attenuation characteristics in the low and wide frequency band. In 100~500 Hz，the attenuation efficiency of acceleration power spectral density above 70%. In 35~80 Hz，and 500~2000 Hz，the attenuation efficiency of acceleration power spectral density above 40%. Working displacement of the vibration isolation structure under 3 times standard deviation confidence is less than 3 mm. Therefore，it is suitable for the isolation of low frequency random vibration. In addition，the model has broad application prospects owing to its advantages of light weight，small volume，large bearing capacity and strong universality.

The riser bundle system is an important equipment to explore oil and gas in ocean engineering. Under ocean flows，upstream and downstream risers in tandem will experience vortex-induced vibrations and wake-induced vibrations，respectively，which seriously threatens the structural fatigue life. To predict the vibration responses of a downstream flexible riser，this paper develops a semi-empirical frequency-domain prediction method for wake-induced vibrations based on the classical vortex-induced vibration prediction method of a single flexible riser. Considering the wake shielding effect on the downstream riser due to the existence of the upstream riser，the reductive wake velocity becomes the flow velocity to excite the vibrations of the downstream riser. Then，the upstream-to-downstream diameter ratio is utilized to determine whether the frequency capture occurs. The added mass coefficient of the downstream riser will be adjusted when the frequency capture occurs，otherwise it is 1 constantly. Subsequently，the prediction is based on the resonance condition. The excitation coefficients from a series of forced oscillation tests of a rigid cylinder are approximate to be the wake-induced force coefficients. According to the balance between the modal structural damping force and the modal hydrodynamic force amplitudes，the modal amplitude can be non-iteratively solved. Afterwards，the wake-induced vibration displacements can be calculated based on the mode superposition method. By comparing prediction results with the experimental results，the proposed method can basically correctly predict the dominant frequency，displacement，strain and fatigue damage of the wake-induced vibration for the downstream flexible riser. Therefore，the present method is conducive to the multiple-riser system design in practical engineering.

Based on the three-dimensional elasticity theory，the smooth stochastic response model of three-dimensional sandwiched cylindrical shells is established by using the unified series method and the pseudo-excitation method （PEM）. The cylindrical shell subdomains are divided according to the interlayer property differences of the sandwich material，and the kinetic energy，strain energy，boundary potential energy and smooth random excitation work of each subdomain are established by using three-dimensional elasticity theory combined with the virtual excitation method. The mechanical coordination conditions between the layered subdomains are converted into coupling condition energies by the coupling penalty function method，and then the overall energy generalization of the sandwiched cylindrical shell is obtained by superposing the energies of each subdomain. The displacement components of each subdomain are constructed using a unified level expression and solved by combining the Rayleigh-Ritz method to obtain the stochastic response of the three-dimensional sandwiched cylindrical shell structure. The correctness of the stochastic response model is verified by comparison with literature and finite element results. Finally，the effects of thickness-to-radius ratio，lay-up angle of laminated-functional gradient sandwich material and power-law index on the random response of three-dimensional sandwiched cylindrical shell are analyzed.

The parameters design and vibration control of the system of Spar-floating offshore wind turbine （S-FOWT） coupled tuned mass damper-inerter （TMDI） under the joint wind-wave loads are studied in this paper. The theoretical model of 15-DOF Spar-FOWT with high fidelity is established based on multi-body dynamics modeling method and compared with FAST from both cases of damped free vibration and forced vibration. The damping efficiency of the FOWT-TMDI system under wind and wave loads is analyzed. In order to obtain the global optimal system parameters，the surrogate model method is used to optimize the time-varying and fully-coupled system. An example analysis shows that the model of 15-DOF Spar-FOWT has high fidelity which accurately secures the global dynamical characteristics of the wind turbine system. Meanwhile，the TMDI optimized by the proposed method has the expected control effect and the desired objective of “reduction in mass and stroke” is achieved. Compared with TMD，in addition，the TMDI has anticipative efficiency of the vibration reduction while reducing 75% of the mass and reducing about 80% of the damper stroke.

The Bagley-Torvik（B-T） equation is a differential equation of motion with fractional （3/2）-order derivative terms that is applied to describe the motion of a rigid plate in Newtonian，viscous fluid. In this paper，we develop non-stationary analytic solutions of the B-T equation whose inhomogeneous term is a stochastic process. The B-T equation is transformed into a half-order state-space equation in matrix form and eigen-analysis is performed to obtain complex eigenvalues and eigenvectors. Subsequently，the generalized coordinate transformation is introduced to decouple the equation into a system of independent 1/2-order differential equations which are solved by Laplace transform to obtain the solution in generalized coordinates； The generalized coordinate solution is converted into a natural coordinate solution to obtain the impulse or step response function. When the inhomogeneous term of the equation is a stochastic process，the Laplace transform can be used to derive the time-varying frequency response function from which the analytical solution of the non-stationary stochastic response can be obtained by relying on the relationship between the excitation and the response power spectral density. The correctness of the method is verified by numerical cases using the Spanos-Solomos fully non-statoionary stochastic excitation as an example.

Environmental vibration energy is a kind of renewable and clean energy with abundant reserves and wide distribution. Through energy harvesting technology，the mechanical energy in the environment is converted into electrical energy to power low-power electronic devices and wireless sensor networks，which is an effective solution to break the limitations of traditional power supply methods. In this paper，the bursting oscillation and energy capture efficiency of a mechanical nonlinear multistable piezoelectric cantilever beam device are studied under low frequency excitation. By analyzing the potential energy of the system，it can be seen that the system has multi-stable characteristics with the change of system parameters. According to the fast and slow dynamic analysis method，the external excitation term is regarded as a slow variable and control parameter to adjust the dynamic behavior of the fast subsystem，and the time history diagram，phase diagram and transition phase diagram of the system are obtained. The motion state and energy capture performance of the system under low frequency excitation are analyzed by numerical method. The results show that the system exists bursting oscillation under low frequency excitation，and the system has good energy capture characteristics when the system is bistable. In addition，the time-delay feedback control can control the clustering phenomenon and ensure the stable operation of the system.

The disturbance induced by the rotation of dual axis flex solar wing is the important factor which impacts satellite attitude and pointing accuracy and stability of satellite precise payload. The flexible multibody system method based on recursive formulation is proposed to solve the dynamics problem induced by satellite dual axis flexible solar wing rotation. The satellite dynamics equations are established by considering orbit mechanics，satellite configuration，solar wing flexibility and solar array drive assembly and momentum wheels. As an example of a satellite with dual axis solar wing，the research on multibody dynamics simulation of satellite electromechanical coupling is developed，and the simulated attitude angle and angular velocity of satellite are compared with the corresponding telemetry data. The research shows that the simulated attitude angle and angular velocity of satellite agree well with the corresponding telemetry data，which proves the correctness of the model，The rotation of flexible dual axis solar wing will produce big disturbance torque and attitude angle，the control torque needs to be distributed to momentum wheel assembly for the accurate simulation results，and the disturbance torque of floating satellite caused by the rotation of solar wing was obtained by simulation，which can give the reference condition of ground test verification of solar wing rotation.

In order to solve the engineering problems of strict convergence condition of traditional decentralized algorithm and huge computation amount of centralized algorithm in vibration active control of complex systems，this paper combines network topology cooperation strategy and FxLMS algorithm to design a novel active vibration control algorithm based on network topology cooperation，and selects a simplified airframe model of a helicopter as the controlled object. The simulation study of active vibration control with a scale of 20×20 （20 actuators and 20 error sensors） is carried out. The results show that the algorithm based on network topology can achieve the same vibration reduction effect as the centralized algorithm while significantly reducing the computation amount，which is an advantage that the decentralized algorithm and the centralized algorithm do not have. The mean vibration decreases about 34.3 dB under single-frequency control，and about 12.6 dB under multi-frequency control. At the same time，the characteristics of secondary path coupling are properly simplified，which is conducive to the value of convergence coefficient，and the effectiveness and superiority of this algorithm for active vibration control of helicopter complex system are fully verified.

Statistical energy analysis （SEA） is a widely used method for analyzing the high-frequency dynamic response of mechanical structures. The reasonable division of subsystems is one of the critical basises for SEA. In this paper，an automatic identification method of SEA subsystem based on order-reduced modal energy density and hierarchical cluster analysis is developed. First，the structural modal energy densities in the high-frequency band are obtained through the discrete finite element model. Then，the main features of the modal energies are extracted through the proper orthogonal decomposition. The similarity of the modal energy density between different elements is analyzed by hierarchical cluster analysis. Finally，the number of statistical energy analysis subsystems and the corresponding structural elements are identified. The T-shaped plates，I-shaped plates，and engine combustion chamber are taken as simulation models to verify the effectiveness of the proposed method. Simulation results show that the coupling relationship between components，the number of subsystems，and corresponding elements can be automatically identified by the proposed method. Then，the SEA model can be established efficiently and accurately.

Active magnetic bearings （AMBs） are ideal bearings for high speed and high power rotating machinery for its adjustable stiffness and damp. In this paper，a dynamic model of AMBs-flexible rotor system is established. Aiming at suppressing vibration displacement of the rotor system in passing through the first bending critical speed region，a control which combines a decentralized PID controller and input second filter in series is designed and the controller performances are simulated. The experiments in simulated rotation and real acceleration operations are carried out in a platform of AMBs-flexible rotor system. The rotor system can smoothly pass through its first bending critical speed region and the maximum rotor vibration displacement in acceleration operation is less than half of backup bearing gap. The rotor vibration displacement and current responses of the rotor in different unbalances are measured in order to analyses the influence of the rotor unbalance on vibration characteristics of AMBs-flexible rotor system. It is shown that the proposed controller can make the rotor system smoothly pass through its first bending critical speed region. The rotor imbalance has a significantly influence on the control performance and stability of AMBs-flexible rotor system. The experiment results give a support on the high-performance control strategy of AMBs-flexible rotor system.

A milling unbalance correction method based on a discrete vector model is proposed to address the issue of poor performance of traditional dynamic balancing methods when the initial unbalance of the micro motor rotor is large. A discrete vector model is established based on the parameters of the milling cutter and rotor，and the corresponding relationship between the equivalent cutting mass and cutting depth under second time cutting is obtained by integrating the discrete points of the edge curve. By comparing with the 3D model simulation data，it is verified that the deviation rate of the model is low. Experimental verification shows that when the initial unbalance on one side of the rotor exceeds 100 mg，a total weight removal rate of over 90% can be achieved，and the equivalent mass of the remaining unbalance on one side can be controlled below 10 mg. All rotors meet the G1 accuracy level. This indicates that this proposed method can improve the dynamic balance accuracy of the micro motor rotor when the initial unbalance of the micro motor rotor is large.

Research on magnetically levitated rotors has been heavily influenced by studies on slender shaft magnetic levitated rotors. In the study on a certain magnetically levitated flat rotor for a centrifugal pump structure，both experiments and finite element analysis revealed that the support characteristics of the radial permanent magnetic bearings，with the same dual-ring structure，exhibited the significant differences from the known experience when applied to flat rotors. The translational stiffness and torsional stiffness showed substantial variations. This paper analyzes the variations in translational and torsional stiffness of permanent magnetic radial bearings for flat rotors based on changes in the bearing’s structural dimensions. Based on the analysis，a flat rotor magnetic levitation structure is proposed，which can increase and adjust the torsional stiffness of the permanent magnetic bearings，while also allowing for a rational ratio between translational and torsional stiffness. A finite element analysis is used to identify the structural conditions that yield maximum translational and rotational stiffness. The effectiveness of the proposed methodology is subsequently validated.

To investigate the effect of waviness on the slippage and vibration characteristics of the full ceramic bearing，displacement excitation and thermal deformation are coupled to propose the dynamic waviness model. The Hertz contact theory and time-varying displacement excitation are combined to obtain the calculation method of time-varying contact stiffness coefficient，and the stiffness coefficient is analyzed in detail. The effects of time-varying contact stiffness coefficient and time-varying displacement excitation are also taken into account to model the slipping dynamic of the full ceramic bearing. The effects of rotational speed and waviness on the slippage and nonlinear vibration characteristics of the full ceramic bearing are analyzed. The results show that an increase in rotational speed，waviness amplitude and wave number all lead to an enlarged contact stiffness coefficient between the ball and the raceway. The contact stiffness coefficient is more sensitive to changes in wave number. The increase in rotational speed can exacerbate slippage. Both the increase in waviness amplitude and wave number can have the effect of inhibiting slippage. However，the waviness amplitude and wave number can be too large resulting in abnormal vibration of the inner ring. The maximum fundamental frequency deviation between simulation and test is 2.75 Hz，the maximum error is 0.37%. This research can be used for the optimal design of the full ceramic bearing structures as well as for health monitoring.

During real-time hybrid simulation（RTHS） of nonlinear specimens，the interaction between the specimen and the loading system can lead to variations in the specimen’s behavior，consequently affecting the time delay in the servo system. Online estimation of the system’s time delay enables the application of an adaptive time-delay compensation method for controlling time-varying systems. Nevertheless，during the initial stages of parameter identification，the estimated values frequently exhibit notable fluctuations，which can have a detrimental impact on the effectiveness of control. To this end，a two-stage adaptive time-delay compensation method driven by the inverse model for RTHS is proposed. Firstly，the inverse model controller of the system is used to perform coarse compensation to eliminate the test error caused by the main time delay. Then，the adaptive delay compensation method based on recursive least squares is used to compensate the remaining delay to further control the accuracy. By using the two-story shear frame as the prototype and the self-centering viscous dampers as the specimens，a time-delay compensation RTHS is carried out simultaneously on the two experimental substructures. Numerical simulations and experimental results show that the control accuracy of the proposed method is higher than that of the single-stage time-delay compensation method，and it can be applied to RTHS involving multiple experimental substructures.

In order to obtain more accurate and refined dynamic characteristics of the flat boom tower crane，the field test of the dynamic response of the typical freestanding flat boom tower crane was carried out considering the influence of lifting positions，lifting heights （rope lengths） and lifting weights. The test results show that the vibration along the boom axial direction and vertical direction has good synchronization. However，the response correlation between the horizontal direction of the vertical boom and the axial and vertical direction of the tower crane boom is relatively low. The natural frequencies identified by the half-power bandwidth method and the SSI-COV method are basically the same，with the difference of lifting positions，rope lengths and lifting weights，the natural frequencies of flat boom tower crane will fluctuate around the natural frequency under no load. There are some differences in the identification results of the damping ratio between the two methods，in most working conditions，the damping ratio identified by the SSI-COV method is smaller than that identified by the half power bandwidth method. Based on orthogonal test analysis，the influence of the above factors on the natural frequency and damping ratio of the tower crane is not significant，and there is no main effect. In addition，the finite element model of the flat arm tower crane is optimized，and the frequency of the updated model is in good agreement with the test results. The boom vibration mode function under no-load condition was fitted，the amplitude distribution along the boom length exhibits an approximately linear，however，when the lifting weight appears at the end or root of the boom，the boom vibration mode may show an obvious nonliner characteristics.

Existing bridges undergo time-varying load effects and resistance degradation during service. The complex loads and diverse failure modes make the existing bridges face greater risks in service. Therefore，it is urgent to make time-dependent reliability assessment for the service bridges. The classical time-varying reliability analysis method is more complex and difficult as the number of random variables increases. In this paper，probability density evolution theory is introduced to solve the above problem，which is more advantageous for solving the reliability of complex structures with multiple random variables. The dynamic reliability of the existing bridge in serviceability limit state and ultimate limit state is analyzed by considering the bridge resistance degradation and load effect increase，as well as the time-varying factors such as shrinkage and creep effect of concrete bridges. The accuracy and computational efficiency for this method are compared with the Monte Carlo method，and the effectiveness of the proposed method is verified.

Post-tensioned prestress，self-centering brace and shape memory alloy （SMA） are the main ways to realize the self-centering of the structures. However，the construction of post-tensioned prestress is complex，the concentrated force generated by self-centering brace may cause joint damage，and the SMA is expensive. The disc springs are preloaded to provide the self-centering force. A self-centering rebar splice is developed to connect the longitudinal rebars in the reinforced concrete structures. The calculation method of the stiffness，preload and effective stroke of the self-centering rebar splice is established. Four rebar splices with different preload force，stiffness and effective stroke are designed and manufactured，and the mechanical properties of the rebar splices are tested. The parameters of the rebar splice adopting the Bouc-Wen model are identified based on particle swarm optimization algorithm. The results show that the self-centering rebar splice has a stable half-flag hysteretic curve and excellent self-centering performance. The Bouc-Wen model can accurately describe the hysteretic characteristics of the rebar splice，and the fitting data are in good agreement with the test data.

Focusing on a type of cable-bracing inerter system that utilizes positive and negative teeth ball screws to achieve self-balancing properties，this paper explores the prospect of its application in high-rise or super high-rise structures with complex deformation characteristics of bending and shearing. This paper develops a simplified model for the dynamic analysis of bending-shear structures based on the modified Timoshenko beam theory in order to take into account the accuracy and computational efficiency of the simulation of the original structural dynamic characteristics. Three types of cable layout schemes are proposed for the cable-bracing-self-balancing inerter system，and the appropriate cable layouts for the structures with different bending-shear deformation ratios are verified. A quantitative metric is proposed to optimize the anchorage position for structure-specific modal control. The accuracy of the optimization results is confirmed in the time and frequency domains through the application of fixed-point theory for single-modal control. The following conclusions can be derived. The higher the percentage of bending deformation of the structure is，the more effective the vertical connection of the cables will be，and the more effective the diagonal connection will be as the percentage of shear deformation increases. With regard to structure-specific modal control，the optimized anchorage position and fixed-point theory methods can significantly increase the damping efficiency of the inerter system.

In order to achieve rapid construction and reliable connection of precast RC frames，a sleeve-type fully-bolted joint is proposed. The ends of the prefabricated components are reinforced with a steel sleeve-concrete combination. High-strength bolts are pre-built in the sleeve area，and the precast components are rapidly installed using a connection plate. A total of four test specimens were designed for different thicknesses of connecting cover plates. The horizontal hysteresis test study obtained the damage mode，load-displacement hysteresis curve，ultimate bearing capacity，ductility and energy dissipation capacity of this type of joint. The results show that the new joint has a 43% higher ultimate load，70% higher initial stiffness and nearly 50% higher ductility than the cast-in-place joint，and the equivalent viscous damping coefficient is increased by about two times，which shows better seismic performance. Strain analysis reveals that the cover plate at the joints shows a “stress increase”，but the effect on the overall performance is not apparent. As the thickness of the connection plate increases，the squeezing effect of the sleeve on the concrete increases. Therefore，a connection stiffness ratio of 1.6 is more reasonable. Finally，based on the test results，a trifold moment-turning angle model is established，and the calculated results agree with the test values.

In practice，earthquakes typically involve a mainshock followed by a series of aftershocks，and their occurrence is highly unpredictable. The mainshock damages the structure，and the aftershocks worsen the response and damage of the structure. However，no studies have investigated the effects of stochastic seismic sequences on AP1000 nuclear power plants. This paper proposes an analytical framework for studying the dynamic response and reliability of AP1000 nuclear power plants under stochastic main aftershocks. Stochastic main aftershock sequences are generated using the physical stochastic function model of ground motions，narrow-band harmonic group superposition method，and Copula function. The dynamic response of the AP1000 nuclear power plant is analyzed by using ABAQUS software. The direct probability integration method （DPIM） is used to obtain the probability density function of the maximum displacement response in the horizontal direction of the shielded building，and its dynamic reliability is calculated. The results show that the acceleration and relative displacement of the top of the shielded building and the steel containment vessel have increased to varying degrees after the aftershock，compared with experiencing the mainshock only. Additionally，the damage area between the water tanks and the vents has expanded. The aftershocks could cause further damage to the nuclear power plant. The dynamic response of nuclear power plants exhibits a high degree of randomness due to the stochastic ground motions. Aftershocks can reduce the reliability of nuclear power plants to varying degrees under different thresholds.

According to certain selection criteria，this paper selects 8 mainshock-aftershock events and 560 mainshock-aftershock sequences from NGA-West2 ground motion database，uses ASK14 ground motion prediction equation to carry out residual analysis on the mainshock-aftershock sequences，obtains the intra event residual of mainshock-aftershock sequences at each station，and standardizes them. According to the geostatistical semivariogram method，the exponential semivariogram model and the manual fitting method are used to calculate the spatial autocorrelation of the spectral acceleration period of the mainshock-aftershock sequence. Since the Pearson linear correlation coefficient can better measure the linear relationship between the fixed-distance variables，the Pearson linear correlation coefficient is used to calculate the cross-correlation of the normalized intra-event residuals between different spectral acceleration periods of the mainshock-aftershock sequence without considering the spatial cross-correlation. According to Markov’s hypothesis，the spatial information is introduced into the calculation of the cross-correlation，and then the expression of the change of the spatial cross-correlation with the spatial distance （h） is obtained. The results show that the mainshock is significantly different from aftershocks in terms of spatial autocorrelation and cross-correlation characteristics，and aftershocks generally have higher spatial correlation in the long-period stage. Neglecting the spatial correlation between the mainshock and aftershocks or using the characteristics of the mainshock to replace the characteristics of the aftershocks will adversely affect the research on earthquake hazard analysis，damage assessment，and the synthesis of main and aftershock sequences.

Compared with the in-plane seismic performance，the out-of-plane seismic performance of reinforced concrete shear walls is weak and usually neglected，which leads to an inadequate study of the out-of-plane damage mechanism of shear walls and a lack of clear protective measures，and the overall seismic performance of shear wall structure is also unsafe，which needs urgent attention. In order to compare the similarities and differences in seismic performance of reinforced concrete shear walls when subjected to in-plane and out-plane loads in different directions and to clarify the key influencing factors，low cyclic loading tests are conducted on typical shear wall specimens in-plane and out-plane directions，and the macroscopic test phenomena，hysteresis curves，skeleton curves，stiffness degradation curves，energy dissipation capacity and ductility in both directions are compared and analyzed. The moment-curvature simulations of shear wall sections in both in-plane and out-plane directions are analyzed，and the results obtained from multiple sets of constitutive models are compared with the experimental results. Combined with the finite element variable parameter analysis，the effects of parameters such as axial pressure ratio，wall thickness，height-to-width ratio and concrete grade on the seismic performance of in-plane and out-plane are analyzed. Based on the endurance time analysis，the time-history response of structural displacement with seismic magnitude is studied. The results show that the seismic performance of shear walls outside the face is significantly weaker than that inside the face，and the bearing capacity is only 1/20~1/15 times of the latter，among which the wall thickness and height-width ratio are the main parameters affecting the seismic performance inside and outside the face. The out-of-plane nonlinear analysis of the cross-section can be performed more accurately and quickly by using the principal structure model proposed in this paper and some traditional principal structures. In the seismic design of shear walls，especially for the single directional wall with less structure，both in-plane and out-of-plane seismic performance should be ensured，and the thickness and aspect ratio of shear walls should be reasonably controlled. Wall damage assessment by using elastic-plastic energy dissipation difference rate has the characteristics of obvious differentiation and reasonable threshold value.

Based on the Biot’s poroelastic model and the Euler-Bernoulli beam equations，the dynamic response of extended helical pile foundations with multiple helixes is studied. The equivalent stiffness model is used to simulate the helixes on the helical pile. With the utilization of the integral transform，the variable separation methods，and the impedance matrix transfer method，the analytical solution to the dynamic response of helical piles with multiple helixes is derived. Through the comparisons with the simplified analytical solutions and the experimental results，the correctness of the proposed model is justified. Finally，with the presentation of a comprehensive parametric study，some dominant impact factors on the dynamic responses are revealed，and the optimal design scheme is suggested accordingly. The main conclusion of this study can be concluded as：An increase of the extension ratio of helix will increase the complex impedance and resonance frequency at the pile top of the helical pile. An increase of the ratio of helix spacing to width will increase the complex impedance of the pile top，but the effect on the resonance frequency is not significant. An increase of the vertical static load at the top of the pile will significantly reduce the complex impedance and resonance frequency at the pile top. The helix inclination has an optimal range in the effect of complex impedance of the pile top.

The principle of the hydraulic drifter is introduced，and the process of drilling into rocks by the drifter is established as a physical model of rock with three-degree-of-freedom dry friction. The concept of rate of penetration （ROP） is introduced. The stick and non-stick modes are studied，explaining the differences between these two types of motion. The periodic trajectories of the nonlinear piecewise smooth dynamical system mathematical model are segmented. By using the pseudo-arclength continuation method and Floquet theory，the angular frequency and amplitude of the hydraulic force are taken as control parameters to obtain stable periodic trajectories and the point of maximum ROP. Bifurcations such as period-doubling bifurcation，saddle-node bifurcation，and torus bifurcation are discovered. The data acquisition system for drilling rocks with a hydraulic drifter is introduced，and the displacement and velocity of the piston obtained from the model and experiments are compared. The results indicate that to make the drifter work on the period-1 trajectory，the range of angular frequency should be ω<6.814，and the range of amplitude should be 0.03<a<3.051. There is a strong correlation between the experiments and the model，and compared with the experiment，the piston in the model undergoes deceleration before colliding with the drill tool，adding an impact deceleration stroke.

Based on the basic principle of variational method and limit equilibrium method，the stability of soil slope under earthquake action is analyzed accurately. Combining the limit equilibrium method of slope stability analysis and the pseudo-static method，the auxiliary functional under constraint conditions is constructed by introducing Lagrange multiplier into the equilibrium equation of sliding soil. The first order ordinary differential equations with the basic unknowns of potential sliding surface，normal stress of sliding surface，force of sliding body，safety factor and Lagrange multiplier are obtained by using Euler equation. The coupled nonlinear differential equations are solved numerically by using the shooting method，and an accurate solution for slope stability analysis under seismic action is obtained. The effectiveness of the model and method is verified by numerical examples.