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.

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.

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.

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.

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.

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.

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.

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°.

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.