The camshaft is an important component that ensures the timely opening and closing of valve in marine diesel engines. Due to the poor contact lubrication state and excessive friction excitation，it is easy to cause larger interface torque on the camshaft. Considering the effects of transient excitation and interfacial friction，the tribo-dynamics model of the valve camshaft in V20 diesel engine is established. The forced vibration results of the camshaft are obtained，and the friction and lubrication performance of the cam-tappet pair is also analyzed under the fluctuating speed. The results show that，by thoroughly considering both the transient excitation and frictional excitation of each cam pair，the additional stress in each shaft section of the valve camshaft increases by about 4 MPa，while the transient speed fluctuation at the camshaft end increases by roughly ±30 r/min. Under the combined effects of speed fluctuation and surface roughness，the film thickness is dramatically reduced in some positions，especially in the cam base circle section where the film thickness decreases by about 0.3 μm. At the reverse motion position and nose of the cam，the temperature rise at the interface of the tappet exceeds the material’s scuffing temperature，thereby increasing the risk of scuffing wear.

Four multi-disk rotors with the same structure size are used as the research basis. The precision wire cutting method is used to prefabricate transverse cracks of different depths at different positions of the four rotors. The vibration characteristics of the cracked rotor system with changed crack parameters are tested and the relationship between the dynamic response characteristics of the cracked rotor and the crack location and crack depth is analyzed. The test results show that the 2× resonance phenomenon in the 1/2 critical speed zone and the 3× resonance phenomenon in the 1/3 critical speed zone are the typical characteristics of the rotating shaft crack failure. The 2× resonance peak value increases rapidly after the crack depth reached a critical point. While the 3× resonance peak value，which is different from the results of existing studies，drops abruptly after the crack depth reached a critical point. Also，there is a correlation between the critical depth that triggered an abrupt change in the peak 2× and 3× resonance and whether the crack location is at the root of the disc.

Rotor dynamic response sensitivity analysis is widely used in rotor model updating，parameter identification and structural optimization. In this paper，a first-order，second-order and mixed sensitivity analysis method for dynamic response of rotor system based on multi-complex domain perturbation method is proposed. The design parameters are perturbed in two complex directions respectively，and the motion equation of the rotor system in the double complex domain is obtained. Using the real matrix expression of the complex number，the complex motion equation is extended to obtain the equivalent real motion equation. By solving the equivalent real motion equation，the system response，first-order sensitivity and second-order sensitivity can be obtained simultaneously，and the Hessian matrix of dynamic response sensitivity can also be obtained. The numerical simulation analysis of single-disk rotor system and gas generator rotor system is carried out to verify the correctness of the rotor dynamic response sensitivity analysis method of multi-complex domain perturbation method. Compared with the traditional finite difference method，the multicomplex domain perturbation method shows insensitivity to the error caused by the perturbation step size，and the solution accuracy is higher.

The energy transfer efficiency and energy dissipation of coupled piecewise linear stiffness energy sink are studied. The equation of systematic slow-varying equations of the two-degree-of-freedom system coupled with the piecewise linear stiffness energy is derived by the complex variable-averaging method under 1∶1 internal resonance. The approximate expression of two extreme points of the slow-invariant manifold is obtained by using the polynomial approximation method，and the energy transfer efficiency equation and energy dissipation equation of the coupled piecewise linear stiffness energy sink system are obtained. The effects of piecewise gap and piecewise linear stiffness on energy transfer efficiency and the relationship between damping coefficient of the main structure and dissipation time are analyzed. The results indicate that the energy transfer efficiency of the system decreases as the piecewise gap of the coupled piecewise linear stiffness energy sink increases，while it increases with an increase of piecewise stiffness. Additionally，it decreases with an increase of the damping system of the main structure. Therefore，adjusting structural parameters，the piecewise linear stiffness energy sink can effectively mitigate vibrations within the main structure.

In order to grasp the influence of wear clearance of spherical pair on dynamic response characteristics of spatial parallel mechanism，a dynamic modeling and response analysis method for spatial parallel mechanism considering the wear of spherical joints is proposed. The 3SPS-S spatial parallel mechanism is taken as the research object. The wear model of the spherical joint clearance is established based on the Archard wear model，the worn ball head and ball socket are obtained by calculating the wear depth and surface geometric reconstruction，and the dynamic model of the parallel mechanism considering spherical joint wear is established. The numerical results are obtained by solving the above dynamic model. The change of dynamic response of mechanism before and after wear is compared and analyzed，and the influence of initial clearance value and load on dynamic response of mechanism after wear is obtained. The results show that the worn irregular clearance has adverse effects on the dynamic characteristics of the parallel mechanism，and the increase of clearance value and the introduction of load can reduce the stability of the parallel mechanism.

Ultra-long beam structure has large vibration frequency span. To control the wide frequency vibration of ultra-long beam structures，amplitude-enhanced dynamic vibration absorbers with damping are arranged periodically on the beam. The amplitude magnification device artificially magnifies the amplitude at the controlled point，thereby increasing the operating ability of the absorber. To be able to consider the effect of damping，a complex band structure analysis model is established，and a new complex band structure calculation method is proposed based on the artificial spring model and the energy method. This method is used to analyze the effect of amplification device type，absorber damping and magnification factor on the complex band structure in detail. The effect of the relative position of the connection points of the ungrounded magnification device on its vibration damping performance is studied. The results show that the magnitude amplification device type，absorber damping and magnification factor have great influence on the complex band structure. The suitably relative position can significantly improve the working ability of the ungrounded magnification device.

The vibration reduction efficiency of a tuned mass damper（TMD）is closely related to the inherent parameters of the structure and TMD. Accurate identification of the structure and TMD inherent parameters from the response of the structure-TMD coupling system is necessary for the evaluation of the vibration reduction performance of in-service TMD. This paper offers a parameter identification approach based on NSGA-Ⅱ（Nondominated sorting genetic algorithm）that can identify the parameters of‘bare structure’ and‘bare TMD’ from the coupled structure-TMD response in order to solve the issue of state evaluation of TMDs in service. The structure-TMD coupling equation is constructed. It is reduced and transformed into a two-degree-of-freedom system of the structure-controlled mode and TMD coupling. Two objective functions are constructed by means of the system state space matrix. The genetic algorithm is used to find the optimal solution corresponding to the minimum error between the theoretical value and the experimental value，so as to identify the modal parameters of the structure and TMD. The numerical simulation analysis of parameter identification of single-degree-of-freedom structure-TMD coupling system and multi-degree-of-freedom structure-TMD coupling system is carried out. The results show that the proposed method can accurately identify the inherent parameters of structure and TMD from the dynamic system response of the coupling system.

The axial compression of the landing gear strut can directly lead to the change of system stiffness and rotational inertia，but the effect of strut axial displacement is mostly ignored in existing models of nose landing gear shimmy. A nonlinear dynamic model of six-degree-of-freedom dual-wheel nose landing gear shimmy with axial displacement and longitudinal bending of struts is established. The bifurcation theory is applied to study the effect of introducing axial displacement on the shimmy region，and the maximum compression stroke of the buffer is combined with sliding speed，vertical load，and wheel rotational inertia，respectively. The combined parameters are analyzed by two parameter bifurcation. The fourth order Runge-Kutta method and fast Fourier transform are used to calculate the time-frequency characteristics in the stable shimmy region，and the interaction between the degrees of freedom of torsion，lateral bending，and longitudinal bending of the strut is studied. The results show that under certain conditions，considering the influence of axial displacement of the strut，the areas of torsional and lateral shimmy of the strut have a tendency to shrink. In the bistable region of double wheel nose gear shimmy，when the initial excitation is close to zero equilibrium state，the longitudinal shimmy occurs near 2 times the natural frequency of torsional vibration. When the initial excitation is far from the zero equilibrium state，longitudinal shimmy occurs near 2 times the natural frequency of lateral vibration.

In response to the galloping issue faced by ice-covered multi-split transmission lines，this study proposes a method based on the probability density evolution approach for dynamic tension stochastic analysis and reliability evaluation of such transmission lines. A stochastic analysis method for the dynamic tension in ice-covered multi-split transmission lines is established by integrating the finite element model with the probability density evolution technique. A tensile failure criterion for ice-covered multi-split transmission lines is developed by using the equivalent extreme value distribution method，and a framework for reliability evaluation of the transmission lines is constructed. Stochastic dynamic response analysis and reliability evaluation on a single-span ice-covered four-split transmission line are conducted. The analysis of the example shows that：The method in this paper can efficiently analyze the stochastic dynamic tension of the ice-covered four-split transmission line，and the stochastic dynamic tension is influenced by multiple modes after the transmission line enters the stable galloping stage；The tensile failure reliability probability of transmission lines during galloping does not exhibit a monotonous relationship with the increase of initial sag；The initial wind attack angle plays a crucial role in determining the tensile failure reliability probability of the transmission line，and the reliability of the transmission line is relatively low when the initial wind attack angle falls within the range of 20° to 60°.

The wind uncovering effect of the roof of a large-span terminal building is one of the important factors affecting its structural safety. Existing studies only consider the benign wind climate and static wind load effects，which are difficult to explain the real wind uncovering pattern and occurrence mechanism of the roof structure under the strong typhoon dynamic load. Based on WRF，CFD and LS/DYNA，this paper carries out the numerical simulation of continuous wind damage of a large-span terminal building under the action of typhoon. The wind field simulation of typhoon "Hegeby" was carried out firstly. The continuous wind uncovering process of the terminal roof under the typhoon was simulated by taking an international airport terminal building as an example，and the wind damage pattern and wind damage rate of the roof cover under different wind angles were compared and analyzed to reveal the wind damage mechanism of the large-span terminal building under the typhoon. The results show that the extreme wind pressure at the windward edge of the terminal roof is higher，and the effect of upward and downward pressure is obvious，and the maximum pressure difference coefficient is 12.41. When the critical wind speed is reached，the windward edge of the roof is partially lifted by the wind，and then the "chain effect" triggers the continuous wind damage of the roof，and the tearing direction of the roof is consistent with the incoming flow direction. The energy failure index K is given based on the law of internal energy change before and after the failure of roof units，which can be used to guide the design of large-span terminal building roofs against wind uncovering.

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.

W/Ta nanoscale metallic multilayer is a typical body-centered cubic/ body-centered cubic nanolayered composite，which is very promising for the application in nuclear fusion devices. Based on atomistic molecular dynamic（MD）simulations，we investigate the mechanical properties and plastic deformation mechanisms of W/Ta nanolayered composite under uniaxial tension，and further analyze the influence of modulation period on the mechanical response of W/Ta nanolayered composite. The results show that the W（110）/Ta（110）interface forms a misfit dislocation network，which can not only serve as the source for dislocation nucleation but also adsorb the dislocations in the metallic multilayer. The microstructure evolution analysis shows that，W/Ta nanolayered composite mainly experiences three deformation stages during stretching，i.e. linear elastic，plastic yield，and plastic flow stages. The dislocations firstly nucleate and propagate in the Ta layers，which leads to the sharp drop in the stress-strain curve. Subsequently，the dislocations in the Ta layers pass through the interfaces and enter into the W layers，and the propagation and slip of the dislocations in the W layers cause the yield of W layers. The yield of the sample is primarily determined by the Ta layers，and the plastic deformation in the flow stage is jointly governed by the dislocations and their evolution in both the W and Ta layers. With an increase of modulation period，the number of interfaces in the W/Ta metallic multilayer decreases，so that the nucleation of dislocations decreases as well as the amount of dislocations adsorbed by the interfaces decreases. In addition，the decreased number of the interface weakens the effect of hindering dislocations by interface. Therefore，the yield strength increases and the averaged plastic flow strength decreases.

The nonlinear dynamics of the bidirectional gear-driven friction nanogenerator（TENG）system is modelled by considering the time-varying meshing stiffness，time-varying support stiffness，transmission error，tooth side clearance and bearing clearance. The ode45 function is used to solve the vibration differential equations of system，and the time-varying meshing force diagram，time-frequency diagram，phase diagram，FFT spectrum diagram，Poincaré diagram，bifurcation diagram and three-dimensional spectrum diagram of the system are obtained，to explore the effect of the excitation frequency of the external load on the system dynamics characteristics. In addition，friction nano-generation technology is combined to obtain the output performance of TENG under different parameters，and to investigate the mechanism of the influence of external load excitation frequency and average engagement stiffness on the energy harvesting of the system. The results show that the bidirectional gear-driven friction nanogenerator mechanical transmission system has obvious nonlinear characteristics，and reasonable selection of the external load excitation frequency and meshing stiffness to avoid the control of unstable intervals can improve the mechanical energy conversion efficiency and increase the power generation capacity of TENG.

The transverse free vibration characteristics of a two-dimensional nanoplate with axial velocity are investigated based on the nonlocal strain gradient theory. The vibration control equations for the in-plane advection of the system are established according to the generalized Hamilton’s principle，and the intrinsic frequency of the nanoplate is derived by using complex modal analysis in the case of a four-ended simple support. The critical velocity of the system is determined by the equilibrium solution of the control equations，and the real and imaginary parts of the first-fourth-order modal functions are further analyzed for both the sub-critical and the supercritical velocities. The numerical results show that the scaling effect leads to a change in the self-oscillation frequency of the system at the micro- and nanoscale，and the nonlocal and strain gradient parameters have‘softening’ and‘hardening’ effects on the equivalent stiffness of the nanoplates，respectively，which affects the intrinsic frequency and the modal function of the nanoplates. This affects the intrinsic frequency and mode function of the nanoplates，and the higher order frequencies and vibration modes are more significantly affected by the size parameters.