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.

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.

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.

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 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.

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 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.

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.

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.

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.