In the dynamic impact response analysis of the structure，the dynamic amplification factor（DAF）is usually used to simplify the calculation of the dynamic response of the structure. However，the size of DAF in engineering structures is still controversial. In order to solve this problem，the analytical expression of DAF of multi-degree-of-freedom system（MDOF）is derived in this paper，and the precondition of DAF greater than 2.0 is analyzed. The accuracy of the analytical expression is verified by the single-degree-of-freedom（SDOF）and MDOF example models，and the reason why the DAF of the MDOF is greater than 2.0 is explained. Finally，based on the DAF analytical method proposed in this paper，the DAF distribution law of beam string under cable breaking impact is analyzed. The analysis results show that when the contribution of a first-order modal shape is opposite to the static response，the DAF of the beam string may be greater than 2.0. Even for the damping system，the DAF of the beam string may be greater than 2.0.

Bridge health monitoring data often encounter missing values due to sensor failures and other factors. Existing data recovery methods have not effectively utilized the temporal and spatial correlations in the data. In this paper，a multi-channel recovery method for bridge monitoring data based on temporal and spatial correlations is proposed. The original data is preprocessed using a Kalman filter to eliminate random errors. The preprocessed data is divided into training and testing sets，and training samples are constructed using a sliding window approach with masking. The data recovery issue is formulated as a time series prediction issue. Besides，an end-to-end LSTM network architecture is trained to leverage the temporal and spatial correlations in the historical data of the sensors which enables the recovery of missing data. The proposed method is validated using the measured deflection and cable force data from a suspension bridge，and the performance of single-channel and multi-channel data recovery is discussed. Compared to the traditional RNN models，results show that the proposed method achieves a 22% improvement in accuracy when the data missing rate is 60%. Moreover，the method effectively utilizes the temporal and spatial correlations among different channels，enabling simultaneous recovery of data from multiple channels.

In order to compare the seismic performance of different station-bridge combination systems under transverse seismic action，this paper takes an actual station-bridge separation system as the research object，designs a station-bridge integrated system combined with the actual situation，considers the nonlinear effect of bridge piers and supports，and the nonlinear sliding friction effect between expanded foundation，gravel cushion and metro station roof. A three-dimensional nonlinear dynamic model is established by using the finite element software MIDAS/Civil，and the dynamic response and pier damage of the composite system of two different stations and bridges under the cross-bridge seismic input are studied. The results show that under the unusual seismic lateral input，compared with the station-bridge integrated system，the station-bridge separation system can prolong the structural period and effectively reduce the dynamic response of the pier bottom and the supporting column of metro station. For the two combined station-bridge systems，the internal force response of the supporting column corresponding to the position of the pier is greater than that of other ordinary supporting columns. Under the lateral seismic input of the rare earthquake，compared with the stationbridge integrated system，the station-bridge separation system appears later in the plastic state，the final damage degree is lighter，the time of the support entering the nonlinear stage is later，and the overall deformation of the bridge pier is smaller. The seismic performance of the station and bridge separation system is better under the transverse earthquake action. However，in the actual project，attention should be paid to the increase of internal force caused by the transverse frame effect of the subway support column and the limit of the bridge foundation slip.

In order to clarify the collapse mode of multi-span simply-supported beam bridges of high-speed railway，a 10-span high-speed railway simply-supported beam bridge in northwest China is taken as the actual engineering background. Combined with the characteristics of double block ballastless track structure on the bridge，the track-bridge integration research model is established. The collapse mode of this kind of ballastless track bridge in high intensity earthquake zone is studied by using explicit integral method and energy method. The results show that the key parts of the destruction of high-speed railway multi-span simply-supported beam bridge mainly concentrate on the track area of the bridge expansion joint，the concrete area of the support and the support contact surface，and the bottom area of the pier. The energy ratio of the 10-span high-speed railway simply-supported beam bridge collapse discrimination is 89.33%. By coupling the track plate and the groove section at the bridge expansion joint to optimize the structural system，the integrity of the track and bridge connection is improved，so that the track at the bridge expansion joint avoids becoming the key part of the destruction at the early stage of the earthquake. The collapse time of structural system is prolonged by about 45%，and the probability of the beam falling is reduced，so that the overall collapse resistance ability of the bridge is improved.

Based on the seismic fragility method，this paper designed a random sampling procedure to investigate the effect of different amounts of input ground motions on the seismic fragility curves of underground structures in the cloud method. Taking a shallow-buried subway station with two-story and three-span as the research object，a non-linear dynamic interaction finite element model of the soil-underground structure was established，and 350 natural ground motions were selected as inputs to calculate the seismic response. The seismic fragility curves were constructed based on PGA-IDR finally. The results show that the amount of input ground motions has a greater effect on the PGA thresholds for each performance level of underground structures when the amount is less than 190. When the amount is greater than 190，the seismic fragility curves for minor and moderate damage to underground structures are not affected by the amount；when the amount is greater than 280，the curves for extensive damage and collapse are negligibly affected by the amount. When the underground structure is in an area with a low probability of strong seismic threat，this paper recommends 190 natural ground motions as inputs，otherwise，it should be 280.

In order to study the dynamic response characteristics of six-pile foundation with large diameter and variable section in different layers of liquefied soil，5010 waves with ground motion intensity of 0.15g，0.25g，0.35g and 0.45g are selected through indoor shaking table model test based on the solid project of Xiangan Bridge in Xiamen Second East Passage. The dynamic characteristics of saturated sand pore pressure ratio，pile acceleration，pile bending moment and pile top horizontal displacement of six pile foundations with large diameter and variable section are studied when the thicknesses of the liquefied soil layer are 30，40 and 50 cm. The results show that the acceleration and bending moment of six-pile foundation with large diameter and variable section change abruptly at the interface between variable section and soil layer under different thicknesses of saturated sand layer. Under the same soil thickness，with an increase of ground motion intensity from 0.15g to 0.45g，the pore pressure ratio of saturated sand，pile acceleration，horizontal displacement of pile top and pile bending moment all increase. Under the ground motion intensity of 0.15g，the stable value of pore pressure ratio of the six-pile foundation decreases with an increase of saturated sand layer thickness，but the horizontal displacement of pile top，pile acceleration and peak bending moment of the six-pile foundation gradually increase and increase. It is suggested that in the design of large diameter variable section pile foundation in liquefaction site，special consideration should be given to the dynamic response difference of six large diameter variable section pile foundation under different thickness of liquefied soil layer，and pay attention to the flexural performance of the interface between the variable section and soil layer，so as to ensure the seismic performance of the six pile foundation.

In order to solve the transverse vibration problem of two-span continuously modified Timoshenko beam on viscoelastic four-parameter foundation，a new vibration governing equation is established by combining two-span continuously modified Timoshenko beam with viscoelastic four-parameter foundation. By using the echo matrix method，bisection and golden section method，the relation and difference between the natural vibration characteristics of two-span（equal-span，unequal-span）continuously modified Timoshenko beam and single-span modified Timoshenko beam on viscoelastic four-parameter foundation are analyzed. The results show that for the modified Timoshenko beam on the viscoelastic four-parameter foundation，the natural frequency of each order of the single-span beam is less than that of the two-span continuous beam，the even-order natural frequency and attenuation coefficient of the single-span beam are the same as the odd-order natural frequency and attenuation coefficient of the two equal-span continuous beam，and the odd-order natural frequency of the unequal-span two-span continuous beam is less than that of the two-span continuous beam. The even-order mode shapes of two equal-span continuous modified Timoshenko beams are symmetrical with respect to the supports in the middle of the span，and the odd-order modes are antisymmetric with respect to the mid-span.

In this paper，we propose a general displacement field function method，which consists of the highly freely chosen basic function and a series of undetermined weighted coefficients to study the free vibration characteristics of GPLs/Al composite plate with an array cutouts. This general displacement field function method can solve the boundary constraint dependence when choosing the displacement field function to obtain the analytical solution in classical plate theory. There is a linear correlation between the weight coefficients. The system of linear equations is constructed based on the boundary constraints，thus the fundamental system of solutions can then be determined. By changing the system of linear equations as well as the fundamental system of solutions，the type of boundary constraint can be easily transferred. This proposed semi-analytic method not only solves the problem of assumed field function dependence on boundary constraints in the classical solution，but also has the superiority of fast conversion of boundary conditions. Meanwhile，by introducing the scatter integral method，a much more efficient and robust method is obtained other than the continuous integral method on the study of free vibration for the structure with an array cutouts. In this paper，we study the free vibration of GPLs/Al composite plates with a single and array cutouts. From the natural frequency and modal analysis，it is found that the generalized mass matrix and stiffness matrix of the open structure decrease synchronously when the cutouts distributed uniformly，and its free vibration characteristics tend to that of the complete plate.

A meshless method based on moving Kriging interpolation is used to study the dynamic behavior of multilayer nanoplates. A dynamical model of multilayer molybdenum disulfide（MoS₂）is established considering intra - layer stretching，interlayer shear and single layer bending. Compared with the results of molecular dynamics simulation，it is shown that the present model can predict the vibration behavior of multilayer MoS₂. The interlayer shear and slip of multilayer two-dimensional structures violate the prediction of classical plate theory，mainly due to the effect of interlayer shear and slip on the overall dynamic behavior of two-dimensional structures. The influence of different layer number and size on the frequency is investigated，and the influence of the three factors on the frequency is studied by changing the intralayer tensile stiffness，interlayer shear modulus and single layer bending stiffness.

Conveying can be achieved through the motion of objects on vibrating structural surfaces. With the rapid development of mechanical automation and intelligence，this technology is facing more requirements and challenges. This type of conveying equipment can generally be simplified as a motion model of bouncing balls on a vibrating thin plate surface. This article designs and builds an experimental platform for the dynamic behavior of a bouncing ball-thin plate system at a micro/macro-scale using an ideal ball-thin plate collision theoretical model. By using sound pressure sensors and data acquisition instruments to extract and process the sound signal of the ball hitting the thin plate，the effects of excitation frequency，amplitude，and ball mass on collision interval and strength are analyzed. The results show that the collision interval and collision strength between balls and thin plates are not fixed values，but exhibit a state with a single peak value. As the frequency and amplitude increase，the collision interval and collision intensity between balls and thin plates increase. Increasing the mass of the ball results in a decrease in both the collision interval and collision intensity，and such a change is a relative trend reflected by the mean，rather than a strictly absolute change. Specifically，it is found in the experiment that the waveform of the collision time between the ball and the thin plate is not instantaneous，but has a period of time effect，which is related to not only the coupling effect of the collision between the ball and the thin plate，but also the attenuation of the forced vibration of the thin plate under the impact of the ball.