The magnetically suspended rotor applied to the moving carrier may be subject to the base motion excitation，causing the rotor vibration，and even cause friction and system instability. To explore the vibration response of the magnetically suspended rotor under the base excitation，the numerical simulation and experimental verification are conducted. The effect of the base excitation on the rotor is introduced into the differential equation of the rotor motion in the form of an additional generalized force. Considering the closed-loop control of the magnetic bearing，the dynamic model of the magnetically suspended rotor under base excitation is established. The influence of the excitation amplitude and frequency，the acceleration and shock width on the vibration response of the rotor is analyzed by numerical simulation. Finally，the base excitation experiments were conducted. The experimental results verify the accuracy of the magnetically suspended rotor model under the base excitation. The results show that the rotor vibration amplitude is proportional to the amplitude and square of frequency of the base harmonic excitation，the rotor vibration maximum is proportional to the base shock excitation acceleration. The proportional coefficient and differential coefficient of the magnetic bearing controller can suppress the rotor vibration brought by the base excitation.

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.

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 this paper，a method for calculating the vibration response of beams damped with constrained damping layer is presented. The indoor vibration experiment of I-beam was carried out，and the vibration response at different positions was measured. A numerical simulation model was established simultaneously based on the finite element method，and the natural frequencies and modal loss factors of I-beam were calculated accurately by using the modal strain energy method. Based on the above results，the modal superposition method was used for the harmonic response analysis，and the vibration response of the I-beam damped with constrained damping layer was obtained. The accuracy of the model was verified by comparing the measured and simulated results. The effects of design parameters （damping layer thickness and constrained layer thickness） on the natural frequency，modal loss factor and overall vibration acceleration level were analyzed. The results show that the vibration response of each component has a similar change rule. The overall vibration acceleration level of web is the largest，followed by the bottom，and the roof is the smallest. In general，the thickness of damping layer has little effect on the first 5 order natural frequencies of I-beam，but with the increase of the thickness of constrained layer，the first 5 order natural frequencies of I-beam decrease first and then increase. Increasing the thickness of damping layer and constrained layer can continuously improve the modal loss factor of I-beam，thereby reducing the overall vibration acceleration level effectively，and the vibration reduction effect of web is better than that of roof and bottom.

Aiming at the low accuracy of traditional empirical formulas in complex site environment，a predictive model for peak blasting vibration velocity based on grey wolf optimization support vector regression （PCA-GWO-SVR） with principal component analysis （PCA） feature selection is proposed. Based on the monitoring data of blasting excavation of dam abutment trough on the right bank of Baihetan Hydropower Station，the blasting center distance，maximum single-shot charge quantity，elevation difference，longitudinal wave velocity，bore spacing and bore row distance are selected as input parameters，and the characteristic values are selected by data dimension reduction of PCA，and the six selected features are dimensionally reduced to four characteristics with higher correlation. Support vector regression （SVR） is improved by grey wolf optimization algorithm （GWO） to obtain the optimal parameters. Parameters are input into the SVR model for evaluation. The research results show that the PCA-GWO-SVR algorithm has better agreement with the predicted values and the measured values of Sadowski formula，improved Sadowski formula，SVR，PCA-SVR，GWO-SVR. The predicted results are more accurate and can predict the peak value of blasting vibration of slope more effectively，which provides help for safety control of blasting construction of slope.

Based on the modified Timoshenko beam theory，the transverse vibration governing equation of the modified Timoshenko beam on the viscoelastic Pasternak foundation is established. The analytical solutions of the natural frequency and attenuation coefficient of the modified Timoshenko beam simply supported at both ends in the viscoelastic Pasternak foundation are derived with the reverberation-ray matrix method. The natural vibration characteristics of the modified Timoshenko beam on the viscoelastic Pasternak foundation under classical boundary conditions are calculated by dichotomy and golden section method. The effects of moment of inertia caused by shear deformation，beam length and different boundary conditions on the natural vibration characteristics of the structure are compared and analyzed. The results show that the natural frequency and attenuation coefficient of the modified Timoshenko beam on the viscoelastic Pasternak foundation are smaller than those of the classical Timoshenko beam； the shorter the beam，the more significant the influence of the moment of inertia caused by shear deformation on the natural frequency and attenuation coefficient of the structure，and the influence on the higher order is obviously greater than that on the low order； the stronger the boundary constraint condition，the more obvious the vibration energy attenuation.

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.

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.

In this paper，the characteristics of structural response and modal parameters of Shenzhen New World Center （height 238 m） are analyzed based on the field data during five typhoons in the last 10 years. The field results are further compared with the wind tunnel test results when the roughness exponent α is 0.22，0.30 and 0.35 respectively. The field results show that the building exhibits obvious crosswind vibration when reaching its maximum vibration amplitude，and the corresponding vibration is in the north-south direction. The measured maximum acceleration is 17.28 cm/s²，which meets the requirement of residential comfort. During the five typhoons，the modal frequencies are shown to be evidently amplitude dependent and time-varying，and it is more reasonable to describe the variation of modal frequency with time than the variation with amplitude. The modal frequency first decreases with time and reaches its minimum at the peak wind speed，and then returns to the normal value. The modal damping ratios tend to be scattered in the middle- and low-amplitude region，and rise slightly with increase in the amplitude. The maximum damping ratios in the alongwind and crosswind directions are 1.9% and 1.2%，respectively. The wind tunnel test results for α=0.35 are in good agreement with the field measured results，indicating that the wind tunnel test results for terrain category C are conservative.

Based on the measured acceleration response under Typhoon Kompasu，the modal parameters of the 356 m Shenzhen Meteorological Gradient Tower （SMGT） are identified. The Non-dominated Sorting Genetic Algorithm Ⅱ（NSGA-Ⅱ），which is a fast and elitist genetic algorithm，is applied to update the finite element （FE） model of SMGT. The results show that the vibration modes of SMGT are very dense，and the involvement of cable vibration modes is obvious. The fundamental frequencies of SMGT in X and Y directions are 0.614 Hz and 0.603 Hz，respectively，and the damping ratio of the first 3 order bending modes are about 1%~2%. The tower density and cable elastic modulus have a significant effect on the modal frequency and mode shape of SMGT，the lineic mass of high-rise cable and tower elastic modulus also have a certain influence，while the cable tension has a relatively low influence on the modes of SMGT. The wind-induced response of the updating FE model is higher than that of initial model，and closer to the actual measurement，which verifies the accuracy of the updating FE model.