The harmonic vibration produced by the gear meshing in the helicopter’s main reducer is one of the main sources of noise in the helicopter cabin. Designing vibration-isolating gearbox struts to suppress vibration transmission to the airframe can effectively reduce cabin noise. The piezoelectric stack actuators periodic strut （PSAPS），composed of periodically arranged piezoelectric stacks and metallic materials，demonstrates ‘mechanical filtering’ characteristics within specific frequency bands，serving as a passive vibration control method. By adjusting the driving voltage of piezoelectric stacks in PSAPS to achieve variable stiffness characteristics，active vibration control is enabled. In order to study the electromechanical coupling relationship between active vibration control and passive vibration control of PSAPSs，a specialized PSAPS configuration is developed to address helicopter gear meshing noise suppression，and the electromechanical coupling dynamic model of PSAPSs with the form of transfer matrix is established for the mechanical filtering characteristics of periodic structure and elastic wave propagation in piezoelectric stack. In frequency domain，the force and velocity at both ends of the PSAPSs，the driving voltage and current，the geometrical parameters of the strut and the material parameters are coupled in this model. In this paper，the maximum attenuation rate of the PSAPS can be obtained under the limitation of the maximum driving voltage and current of the piezoelectric stack by using this model. The influence of rubber damping loss factor，excitation force，and cell number in PSAPS on the required driving voltage and current for active control is analyzed in this article.

In order to consider the effect of liquid sloshing in an annular water tank on mechanical performance of a two-stage variable damping TMD，taking an actual high-rise structure as an example，a global model considering the water tank as a particle and the liquid-solid coupling model of the water tank under the full water state and the non-full water state are established by ABAQUS software. The seismic responses of the two-stage variable damping TMD under different liquid-solid coupling states are compared and analyzed. The results show that the amplitude and maximum damping force of the two-stage variable damping TMD considering liquid sloshing are larger under larger seismic excitation，and the sloshing effect of liquid inhibits the full development of the second-stage damping energy consumption of the two-stage variable damping TMD. With the increase of seismic excitation，the maximum base shear force of the liquid-solid coupling model is larger than that of the particle model，and the relative increase amplitude increases accordingly.

Based on the problems of poor interpretability，as well as parameter increase and memory consumption caused by blind stacking layers in traditional fault diagnosis method based on deep learning，Neural ordinary differential equation （NODE） is introduced into mechanical fault diagnosis，the network structure of NODE for machinery fault diagnosis is constructed. In the constructed structure，the derivatives of the parameterized hidden states of the neural network are used to replace the discrete sequences of the specified hidden layers. By constructing a nonlinear relationship between fault data and fault types，an ordinary differential equation solver （ODE solver） is used to complete the classification of different fault types，and an end-to-end fault diagnosis model is formed. The proposed method is applied to mechanical fault diagnosis to build a specific NODE network model，and the classification task of different fault categories is accomplished through the input of fault data. The constructed model is applied to the fault diagnosis of spindle bearing in the aircraft engine，and compared with the fault diagnosis method based on residual network model. The experimental results show that the constructed model and residual network model have satisfactory accuracy. However，the constructed model not only reduces the memory consumption，but also reduces the number of model parameters by almost five times.

In order to improve the dynamic output performance and environmental adaptability of the tri-stable piezoelectric energy harvester （TPEH），a new flexible tri-stable piezoelectric energy harvester （FTPEH） with double flexible auxiliary beams for real-time adjusting the potential well depth and barrier height is proposed. Based on the traditional magnetic coupling tri-stable piezoelectric energy harvester，two auxiliary flexible beams with the same structure and size are introduced，and the two external magnets are fixed at the tip ends of the two auxiliary flexible beams. When the harvester is excited by the external excitation，the two auxiliary beams oscillate with slight amplitude in the horizontal direction，thus the horizontal distance between the external magnets and the tip magnet of the piezoelectric cantilever beam can be adjusted in real-time，so as to tune the potential energy well depth and barrier height，resulting in improving the dynamic output performance and environmental adaptability. The electromechanical coupling dynamic model describing the dynamic responses of the new tri-stable piezoelectric energy harvester is established based on Euler Bernoulli theory and Hamilton principle，and the influences of system parameters on the nonlinear magnetic force and dynamic performance are simulated and analyzed. Compared to the traditional tri-stable harvester，the new tri-stable harvester has a wider bandwidth of inter-well motion and lower excitation for jumping from intra-well motion to inter-well motion.

The fifth generation “seismic ground motion parameters zonation map of China” （GB 18306―2015），which was promulgated and implemented in China，introduced the vary rare earthquake effect for the first time. However，the current seismic design specifications still adopt the three-level defense principle. The seismic design for vary rare earthquake has become one of the urgent issues that need to be addressed in structural seismic design. Based on the identification method of continuous wavelet transform，this paper selects 12 pulse-like ground motions and 12 non-pulse seismic motions recorded in the Turkey mega earthquake on February 6，2023. The incremental dynamic analysis （IDA） is conducted on continuous pipelines and ductile iron pipelines to evaluate their seismic fragility. The fragility analysis results are compared with the failure probability obtained by empirical statistical method. The results show that the effect of pulse-like ground motions significantly increases the probability of serious structural damage for buried pipelines with different forms. Compared with continuous pipelines，ductile iron pipelines are more prone to damage underground motions，and are more sensitive to the pulse-like ground motion. The empirical statistical results based on actual seismic damage data are slightly lower than the failure probability of pipelines under non-pulse earthquake motion，but significantly underestimate the damage of buried pipelines under pulse earthquake motion. In this paper，the failure probability of different types of buried pipelines under pulse-like seismic motions is given，and the research results can provide a strong theoretical basis for the risk assessment and seismic design of buried pipelines under very rare and pulse-like ground motions.

Existing S-transform-based load spectrum editing methods for automotive components suffer from the problem of lack of adaptivity in time-frequency resolution，which affects the time-frequency aggregation of load spectrum energy and leads to poor editing results. To solve this problem，based on the theory of generalised S-transform （GST），the application of GST method in the field of automobile components load spectrum editing is explored. The GST method is used to perform time-frequency analysis of the mount load spectrum to obtain the distribution information of the load energy on the time and frequency axes. The accumulative power spectral density （APSD） of the load spectrum is calculated，and a genetic algorithm is used to determine the threshold value of the APSD in order to identify the time segments of the load spectrum with smaller damage contributions. The time segments of the load spectrum with small damage contributions are identified and removed，and the remaining load time segments are spliced to obtain a compressed load spectrum. Comparing with the load spectrum editing method based on S-transform，it is found that the time compression of the compressed load spectrum obtained based on the GST method is larger，and the compressed load spectrum basically matches with the original load spectrum in terms of statistical parameters，power spectral density，rainflow counts，fatigue life and damage distribution. The results show that the GST method is suitable for editing the load spectrum of automotive components. It can provide an effective means to improve the efficiency of durability bench tests of automotive components.

Time-delay has significant influence on the performance of control systems and the stability of controlled structures，which，to a certain degree，limits the application of active control techniques in practical engineering. Although the time-delay classical optimal control method can consider the influence of time-delay，the time-delay problem needs to be transformed into a delay-free problem through introducing an augmented state vector associated with the control forces within the time-delay interval. Therefore，the augmented Riccati equation needs to be solved，leading to a large amount of computational cost for the design of control law. This paper is devoted to developing a time-delay explicit optimal control method of structures. The explicit time-domain expressions of dynamic responses are first established for the system with time-delay control. On this basis，the time-delay explicit optimal control law can be analytically derived from an unconstrained linear quadratic optimization problem. As the effect of time-delay control force on structural dynamic responses can be readily considered with the aid of the explicit time-domain formulation，the time-delay explicit optimal control law can be derived without augmented treatment of the state vector and solving of the Riccati equation. A numerical example involving a three-storey shear-type structure with an active controller subjected to seismic excitation is presented to investigate the effect of time-delay and validate the feasibility of the proposed method.

There are a large number of ultra-large slope bridges in the rack railway line，and the settlement of bridge piers is difficult to avoid. It leads to the decrease of the smoothness of the railway line and threaten the safety and smoothness of the train. To solve this problem，based on the theory of vehicle-rack（track）-bridge dynamic interaction and gear dynamics，a coupled dynamic model of mountain vehicle-rack（track） -bridge system is established. The dynamic model considers the nonlinear meshing behavior of gear-rack and nonlinear contact behavior of wheel-rail in detail. The meshing behavior of gear-rack and the dynamic characteristics of vehicles under three different pier settlement modes （single pier settlement，continuous pier settlement and spaced pier settlement） are investigated，and the influence of different pier settlement modes on the vibration of vehicles is compared. The results show that the influence of pier settlement on the rack railway system is mainly reflected in the vertical and longitudinal acceleration of the vehicle，and the main frequency of vibration is 1~2 Hz and 8~9 Hz respectively. The effects of single pier settlement on the basic vibration characteristics of the rack-bridge system are similar to those of double pier settlement. But compared with double pier settlement，the effects of single pier settlement on the longitudinal acceleration of the vehicle are more significant，and the fluctuation of the meshing frequency is also significantly increased. Pier settlement will cause the increase of gear offset，and then lead to the instability of gear-rack meshing. When pier settlement is 6 mm，the problem of meshing apart begins to appear，which seriously threatens the operation safety of vehicles.

The vibration reduction characteristic of rotor system with active elastic support dry friction damper is studied in this paper. The dynamic model of rotor system is established and a 2D friction model of contact surface in dry friction damper us built. The transient and steady state dynamic responses of rotor system are obtained after dynamic equations being solved by utilizing Newmark-HHT numerical integration method. The steady state vibration signals of dry friction damper rotor system under different normal load are compared，meanwhile the transient dynamic responses of rotor system before and after turning on dry friction damper are studied. Experimental test rig for rotor system and dry friction damper are set up. The vibration signals of rotor while passing the first-second critical speed regions are measured and analyzed. Then the experimental vibration signals are compared with simulation vibration responses to verify the vibration reduction effect，and the vibration attenuation characteristic of dry friction damper on rotor system under different working conditions is studied. The results show that the active elastic support dry friction damper could only attenuate rotor’s vibration within a certain normal force. Finally，the results could provide theoretical guide for vibration control strategy on rotor system.

To address the problems of large number of random variables and time-consuming computation in the simulation of non-stationary non-Gaussian stochastic processes，a fast computation method of non-stationary non-Gaussian stochastic processes is proposed based on sample interpolation by combining the stochastic harmonic function. With the known of the target evolutionary power spectrum and target density function of non-Gaussian stochastic processes，the correlation function equations of non-Gaussian stochastic processes and underlying Gaussian stochastic processes are established through Mehler’s formula，and a fast calculation method for the evolutionary power spectrum of underlying Gaussian stochastic processes is proposed through interpolation method. Subsequently，a fast simulation method for non-stationary non-Gaussian stochastic processes is proposed by combining stochastic harmonic functions，The effectiveness of this method is verified by simulating single-point uniformly modulated non-Gaussian stochastic process and multi-point non-uniformly modulated non-Gaussian stochastic processes. The results show that，when calculating the evolutionary power spectrum of the underlying Gaussian random process under the condition of ensuring accuracy，the calculation time of interpolation solution is lower than that of Mehler’s formula solution，and as the number of excitations increases，the efficiency of interpolation solution in calculating the evolutionary power spectrum of the underlying Gaussian random process is more obvious. The proposed fast computational method of non-stationary non-Gaussian stochastic processes can effectively simulate the non-Gaussian stochastic processes with the target evolutionary power spectrum and the target density function.