In order to study the seismic effectiveness of the most commonly used support method for fixing figurine cultural relics，the full-scale shaking table tests of the seismic system （two types of figurine replicas with typical size and vulnerable materials and fixed measures of supports） were carried out. The seismic responses of the cultural relic replicas and the interaction between the cultural relic replicas and supports under different working conditions were obtained. The influence of the key body shape parameters of figurines，the clamping position of metal supports，the support size，the installation gap between cultural relic replicas and fixed measures on the movement state of cultural relics was discussed. The seismic effectiveness of support measures was evaluated and reasonable suggestions were put forward. It provided the necessary basis for the optimal design of fixed method for this type of cultural relics with the principle of safety and minimum intervention. The results showed that all the floating figurine replicas were overturned，which had a great risk of damage. The rocking responses of figurine replicas were effectively reduced after independent supports were used for fixation. As the ratio of the center of gravity height to the base width of the figurine replicas increases，along with the increase in their mass，the obvious plastic deformation or even the root fracture occurred in the case of smaller supports，resulting in overturning and damage of figurine replicas. At the same time，with the increase of the size of the supports，the improvement of the fixation effect was limited. Based on the principle of minimum intervention for cultural relics，and considering the seismic safety and the art exhibition，the support size should be optimized. The rocking responses of figurine were controlled to some extent when its shoulder was fixed by the support，however，with the increase of the fixed position，the sliding response of the figurine was more obvious. The surface of the figurine was easily damaged because of the interaction between the support and the figurine. When the gap between the two was filled with silica gel cushion，the rocking and sliding responses of figurine replicas were reduced by nearly 40% and 50% respectively，the strain at the root of the support was reduced by nearly 40%，and the strain at the contact area between the figurine and the support was reduced by nearly 60%，which effectively improved the seismic effectiveness of support measures.

The advanced transfer path （ATPA） method is used to study the vibration transfer characteristics of the computer mainframe package from each cushion pad to key components under different vibration levels of random vibration through experiments，the analysis of the vibration contribution of the cushion pad and optimal design of vibration reduction are carried out. The results show that the measured vibration response of the two key components of the computer mainframe is consistent with the synthetic response of the ATPA method，which verifies the correctness of the ATPA theory for the analysis of the vibration transfer characteristics of the product packaging system； when the area of each cushion pad is the same， the two cushion pads on the same side of the key components of the computer mainframe play a decisive role in its acceleration response， thus being the key cushion pads； the cushion area of the key cushion pad affects the acceleration response PSD peak value and frequency range of the key components. With the increase of the cushion area，the acceleration response PSD peak value of key components gradually decreases； when the cushioning area of the key cushion pad is more than doubled，the reduction effect of the acceleration response PSD peak value tends to be saturated，the resonance peak becomes smooth，and the vibration response energy is dispersed over a wider frequency range. The vibration reduction optimized design keeps the non-key cushion pad unchanged and only increases the cushion area of the key cushion pad. The research results provide a reference for the vibration reduction design of the product.

Base swing will bring additional gyroscopic moment and inertia load to the rotating machinery，affecting the vibration and stability of the rotor system and even endangering the rotor operation. In order to effectively control the vibration of the active magnetic bearing （AMB）-flexible rotor system under the base swing，a base acceleration feedforward algorithm is proposed in this paper. With the dynamic model and the parameters of the base swing，the optimal compensation current to suppress the vibration can be directly obtained by the proposed algorithm. Because of no iteration and simple structure，the algorithm has strong rapidity and practicality. Furtherly，to eliminate the influence of modeling error on the compensation performance，a method to correct compensating current is suggested. After that，the influence of the proposed algorithm on the rotor vibration in the spin speed range including the first bending critical speed is simulated. Finally，on the test platform，the effectiveness of the algorithm was verified when rotor in suspension without spin，constant speed and acceleration under the base swing. The theoretical and experimental results agree that the vibration perpendicular to the swing axis increases obviously due to the inertia load. The additional gyroscopic moment increases the vibration along the swing axis，and the rising amplitude grows along with the increase of the rotor spin speed. The algorithm proposed can efficiently suppress the rotor vibration under the base swing in the spin speed range including the first bending critical speed.

Base-isolation system would undergo considerable great displacement subjected to strong earthquake. According to recent research progress，the hybrid control strategy combining variant tuned mass damper （VTMD） with base-isolation system has been proved to be effective in reducing such great displacement demand. However，large tuned mass is required to achieve better control performance，which may be difficult to realize in practical application. Employing the mass-amplification effect of the inerter device，a variant tuned mass damper inerter （VTMDI） is proposed in this study by inserting the inerter device in parallel with the dashpot in the VTMD and is attached to the isolation level in the base-isolated structure. Due to the stochastic nature of seismic ground motions，investigation into the optimum design of the VTMDI are conducted based on the framework of random vibration. It is demonstrated that the traditional optimization strategy，taking the inter-story drift of isolated superstructure as the optimization objective，is not cost-effective. Thereby，a novel optimization strategy consisting of two step optimization procedure is proposed. In this two-step optimization strategy，the optimization objective in the first step is taken as the control effect of the base-isolated structure equipped with the VTMDI compared with that of the corresponding base-isolated structure with the same dashpot，and then the optimization objective in the second step is to minimize the inter-story drift of isolated superstructure. And the dynamic time-history analyses show that both optimization strategies can effectively reduce the horizontal deformation in the isolation level and inter-story drift in the superstructure，and the excessive strokes of the tuned mass are also avoided. However，the two-step optimization strategy is more cost-effective than the traditional optimization strategy.

In allusion to inadequate research on damage identification of multi-tiered reinforced soil retaining wall，a large shaking table test of two-tiered reinforced soil retaining wall was carried out. The time domain identification method was used to analyze the dynamic response characteristics of the model under horizontal seismic loading，and the distribution laws of the natural frequency and damping ratio of the upper and lower retaining walls were expounded. The corresponding relationship between the structural damage degree and the natural frequency and damping ratio was explored. The results show that the natural frequencies of the upper and lower retaining walls are basically the same before loading，and the damping ratio decreases with the increase of wall height. With the accumulation of loading conditions，the natural frequency gradually decreases and the damping ratio gradually increases. The distribution curves of natural frequency and damping ratio are fitted by polynomial method. The comparative analysis shows that when the natural frequency decreases by 0~15.41% and the damping ratio increases by 0~299.35%，the structure is basically intact. When the natural frequency decreases 15.41%~18.92% and the damping ratio increases 299.35%~360.07%，the structure is slight damage. When the natural frequency decreases by 18.92%~21.29% and the damping ratio increases by 360.07%~398.21%，the structure is in the middle damage stage； when the natural frequency decreases by 21.29%~29.60% and the damping ratio increases by 398.21%~532.99%，the structure is destroyed.

The traditional Tuned Mass Damper （TMD） has many issues，such as large additional mass requirement，limited installation space restrictions and large motion stroke required when the mass block vibrates. Based on the principle of translation-rotation mutual transformation and conservation of kinetic energy，the rotary inertia virtualizing translational mass based Tuned Mass Damper （RTMD） is proposed in this paper. The conceptual design of RTMD control system is carried out，and the motion equation of RTMD control system is established with the reference of a single degree of freedom system. The influence law of RTMD control system parameters on the vibration control effect of structure is analyzed. It is discovered that the control effect is closely related to the system’s physical mass ratio，inertial mass ratio，damping ratio，and such regulations can be applicable to general multiple degrees of freedom systems. The correctness of the design parameters of the RTMD control system and the realizability of the control system are verified by shaking table test of the design model. The results of time domain analysis and frequency domain analysis show that the dynamic response obtained from shaking table test is consistent with the dynamic response of numerical simulation，which verifies the correctness of the established theoretical equations of RTMD control system.

Large heavy-duty bearings have special working conditions. Under low speed conditions，the impact duration is prolonged，the system response amplitude is reduced，and the fault information is easier to be covered by noise. Acoustic emission technology has been widely used in the field of structural health monitoring and equipment condition detection because of its sensitivity to weak damage. The spatial localization method in acoustic emission technology can be used to accurately locate faults of large bearing with low speed and heavy load. The localization effect depends on the accurate arrival time of signals. The identification and accurate separation of each acoustic emission event is a major challenge at present. Gate recurrent unit network （GRU） can consider the internal in sequence data and extract temporal correlation features，which has certain advantages in signal processing. Akaike information criterion （AIC） can effectively identify two different stochastic processes. In this paper，an acoustic emission signal time of arrival picking method based on GRU and AIC is proposed. The results based on the lead and test data show that the proposed method has great potential in determining the large，heavy-duty，low-speed bearings acoustic emission signal arrival time by comparing with the traditional AIC，threshold discrimination and short term averaging/long term averaging.

The nonlinear dynamic systems exhibit particular behaviors when subjected to combined deterministic and stochastic excitation. A semi-analytical method for calculating the nonstationary response of a fractional nonlinear oscillator subjected to combined excitation is proposed. Representing the system response as a sum of a deterministic component and zero-mean stochastic component leads to two equivalent sub-equations for the differential equation of motion. The time-varying harmonic balance method is used for the nonstationary solution of the deterministic differential sub-equation，while the statistical linearization method is utilized for obtaining an equivalent linear substitution for the stochastic sub-equation. A semi-analytical solution of the equivalent linear equation is obtained by the Prony-SS and Laplace transform technique. The unknown deterministic/stochastic response components are obtained by solving the derived nonlinear algebraic equations simultaneously. Monte Carlo simulations demonstrate the applicability and accuracy of this method.

In this paper，the global dynamics of chaos and subharmonic bifurcation of an impacting system of cantilever beam supported by oblique springs under bilateral asymmetric rigid constraints are studied. It is difficult to study analytically the chaos and subharmonic bifurcation of the system because the stiffness term of the oblique spring support structure is a transcendental function. To do this，the stiffness term of the system is fitted by the approximation method，and the homoclinic orbit and its internal orbits of the approximate system are compared with the orbits of the original system. The threshold conditions for homoclinic chaos and subharmonic bifurcation are presented by applying the Melnikov method to the non-smooth impacting cantilever beam system. Moreover，the stability of the impacting subharmonic orbit is analyzed by combining characteristic multipliers of smooth manifolds with impact function，and the relationship between subharmonic bifurcation and chaos is analyzed. The effects of damping，excitation frequency，excitation amplitude and impact coefficient of restitution on chaos and subharmonic bifurcation are studied based on threshold conditions，which further verify the theoretical analysis.

A damage identification method of laminated rubber bearing based on its natural frequency is proposed in this paper. Through the periodic structural characteristics of laminated rubber bearings and the characteristic waveguide nano method of the periodic structure，the relationship between the natural frequency and the change of overall shear modulus of the basic periodic unit is deduced，and the sensitivity identification equations of the rate of natural frequency change to unit damage is established. The identification equation set is solved by the constrained optimization method. The damage identification of the laminated rubber isolation bearing based on the change of natural frequency is therefore realized. The example of the calculation model considers the influence of the upper structure on the rubber bearing at the bottom layer，which makes the calculation model more in line with practical engineering. The effectiveness and accuracy of the damage identification method proposed in this paper is verified by the three-dimensional finite element numerical siulation analysis.