The quantitative analysis of the effect of low-frequency vibrations on the sitting comfort has been a pivotal focus in the field of transportation engineering. In this study, the transmission of vibration through the human-seat system with different excitation conditions is predicted and analyzed using the finite element modeling. Individual finite element models for the human body and the seat, along with their respective contact properties, are constructed and integrated into an overall finite element model of the human-seat system. The model parameters are validated utilizing experimental data from static body pressure distribution at cushion and backrest locations, as well as the measured seat transmissibility obtained with the vertical excitation. The results indicate the finite element model, validated through the calibration, demonstrates a good fit with experimental data for the seat transmissibility under the fore-and-aft excitation. However, there is a deviation in the amplitude at the resonance frequency. Additionally, the model predicts that the resonance frequency of the seat transmissibility decreases with an increase in the excitation amplitude, and this trend aligns well with experimental results, particularly under the vertical excitation. The constructed model accurately reflects the dynamic response of the human-seat system with different conditions. It serves as a valuable reference for the seat design.

The command‑FxLMS algorithm for multi‑order noise modulation has unnecessarily high output gain when there is a phase error between the command signal and the disturbance signal. Aiming at this problem, a multi‑order active sound profiling system based on the modified differential phase scheduled command filtered‑x least mean square (DPSC‑FxLMS) algorithm is constructed. By adjusting the phase of the command signal to keep it in phase with the disturbance signal, the output level of the control signal is reduced while keeping the same control performance. Simulation analysis and comparison of engine steady‑state multi‑order noise modulation using the above algorithms are carried out, and the control effect of the algorithms is verified. For the in‑phase case, two algorithms share the identical performance and control effect, while for the out‑of‑phase case, the DPSC‑FxLMS algorithm requires less control effort than the command‑FxLMS to achieve the same control performance. The multi‑order noise modulation simulation of the above algorithm is carried out using the multi‑order noise signal collected from a real vehicle. The simulation results validate the feasibility of the proposed algorithm for practical in‑vehicle applications.

A method of product sound quality classification and limit value evaluation based on satisfaction is proposed for the quantitative evaluation of product noise level by product manufacturers, product quality evaluation institutions, consumers and other stakeholders. Through subjective evaluation experiment and questionnaire survey, the relationship between product noise quality index and satisfaction degree was obtained. After comprehensive consideration of the current production level of the industry, affordability and consumer interests and other factors, the sound quality classification and limit assessment were carried out. The method is applied to household appliances and ships, and the product noise quality classification and limit evaluation are carried out to verify the effectiveness and applicability of the proposed method. The characteristics and problems needing attention when the method is applied to different fields and scenarios are discussed.

As a component widely used in various industries, the noise problem of fans has always attracted people’s attention. In equipment with relatively low noise energy levels, abnormal noise, such as whistling, or rattlesing, from fans are key factors that lead to user complaints. Taking laptop fans with various abnormal noises as an example, the correlation between the severity of fan abnormal noise and the main psychoacoustic parameters of sound quality was studied, and a linear regression model between the subjective score of abnormal noise and the objective parameters was established. The results show that loudness, sharpness, prominence ratio, and the frequency corresponding to the maximum value of pitch affect the subjective feeling of abnormal noise. The multivariate linear model including loudness and sharpness can better evaluate the subjective score of the severity of abnormal sound.

To ameliorate the low-frequency sound absorption performance of bulk porous materials, a theoretical model for predicting the sound absorption of the composite structure incorporating flexible ultra-thin and bulk porous materials is derived. The model integrates Johnson-Champoux-Allard (JCA) model and acoustic impedance model for flexible ultra-thin materials, employing non-woven fabric and melamine cotton as illustrative instances. The accuracy of this model is validated through experimental verification, and particle swarm optimization (PSO) is employed to optimize the parameters of the composite structure. The analysis results indicate that the addition of a layer of non-woven fabric on the surface of traditional bulk porous materials significantly enhances the low-frequency sound absorption performance. This paper provides a theoretical foundation for the determination, analysis and optimization of the sound absorption performance of the composite sound-absorbing structure composed of flexible ultra-thin and bulk porous materials, Additionally, it presents an effective method for improving the low frequency sound absorption performance without changing the thickness of the original sound absorber.

In order to explore the correlation between seated body pressure distribution and biomechanical loading, a setup scheme for the human-chair contact surface for human biomechanical modelling is proposed using body pressure information as a guide. The contact between the human body and the seat is simulated by a certain number of contact points, and based on the experimental body pressure distribution data, the relative contact strength is set as the relative magnitude of the average pressure in each partition of the body pressure cloud map. Through comparison, it is discovered that the average contact strength is set between 200~600, which can improve the solution accuracy and take into account the real muscle activation effect. At the same time, the scheme of different numbers of contact points was discussed, and it is more reasonable to choose to set 8 contact points in a comprehensive view. After comparing with the experimental data in the literature, it is shown that the contact scheme based on the body pressure distribution of the human chair biomechanical model can accurately reflect the muscle activation, joint force and other biomechanical indicators. Muscle activation and joint forces under hardwood planks and foam cushions were compared based on a contact scenario setup, explaining the reasons for more comfortable foam seating from a biomechanical point of view.

Artificial neural network modelling has been preliminarily employed to investigate effects on the biodynamic responses. In order to evaluate the vibration transmission characteristics of the seat‑occupant system, further quantitative research is needed. Drawing from a low frequency experimental investigation into whole body vibration, this study is aimed to develop an ANN model with the response surface method optimization. The age, stature, sitting height, knee height, buttock‑to‑knee, weight, gender, BMI, cushion thickness and frequency are used as network input to explore that these how to predict transmissibility from the seat base to the seat pan. Based on the interaction between hyperparameters, the mapping relationship between model hyperparameters and prediction performance indexes was established, and the optimal combination of hyperparameters was optimized and obtained. The results show that the resonance frequencies in the vertical inline and the fore‑and‑aft cross‑axis transmissibilities from seat base to seat pan decreased with increasing thickness of foam at the seat pan. BP‑ANN model has good performance in establishing the nonlinear relationship between the anthropometric, seat structure characteristics and vibration transmission characteristics of seat‑occupant system. Compared with BP‑ANN model, the error of RSM‑BP‑ANN model is reduced by 25% and 18% respectively in predicting vertical in‑line transmissibility and fore‑and‑aft cross‑axis transmissibility from seat base to seat pan. And this also provides an idea for adjusting the parameters of neural network models to improve the prediction accuracy of seat transmissibility.

The human body’s perception of one stimulus may change due to the occurrence of another stimulus, which leads to the possibility of a masking effect between vibrations that successively act on the human body. Whether the masking effect is significant or not is related to many factors. This study designed and carried out a seated human vibration experiment to explore the impact of time-domain masking effects on vibration comfort of the seated human body. Designed variables include： intensity of masking signals (3 levels）, vibration interval (4 levels）, and masking sequence (forward and backward）. The experimental results show that these factors do have an impact on the overall comfort when subjected to whole-body vibration； comparing the effects of forward masking tests and backward masking tests, the discomfort caused by backward masking tests is stronger； with the increase of vibration time interval and the decrease of the masking signal strength, the influence of the masking effect on human body discomfort gradually weakens. It can be found that in addition to frequency domain weighting, the time domain characteristics of vibration amplitude also have a non-negligible impact on the evaluation of human vibration discomfort. Comfort prediction based on objective responses should consider the influence of more factors.

Ride comfort evaluation of high‑speed trains has vital importance for continuously improving the structural design and passengers’ ride satisfaction. This paper tries to evaluate the long‑term and momentary ride comfort of high‑speed trains in China in the light of the European standard EN 12299：2009, and discuss the applicability of the standard. Objective vibration test and subjective comfort evaluation were carried out in a comprehensive inspection train. Average comfort index and discrete events comfort index recommended by the EN 12299：2009 standard were briefly introduced, and the two indexes were selected for long‑term comfort evaluation and momentary comfort evaluation respectively. For the three kinds of track sections with different subjective feelings, based on the measured vibration acceleration data, the long‑time and momentary comfort evaluation indexes were calculated respectively, the comfort of high‑speed train and track quality were analyzed. Combined with the subjective evaluation results, the applicability of the corresponding indexes was analyzed, and attempts were made to put forward suggestions for improvement. according to which the comfort of high‑speed rail ride and the quality of the track into the standard is analyzed. The applicability of these indices was analyzed by referring to the subjective evaluation, and certain suggestion was proposed to modify the indexes.

Vibration limit is one of the most essential contents in vibration serviceability research. Former studies showed that many factors, such as biological and environmental factors, significantly affected vibration limits deeply. As a reason of defects in traditional research, such as small scale data and unreal test environment, quantitative relationships between vibration limits and these factors stayed unknown. Based on data collected by crowd sensing in real environment, crest factor of vibration/ BMI/ human age/ floor of building were found key factors by using maximal information coefficient (MIC) in coefficient analysis. Functional relationship and 95% confidence intervals between vibration limits and key factors were proposed, respectively. Lilliefors test and normal probability plot show that residuals between fitted values of limits and measured ones follow a normal distribution. A novel approach of estimating vibration serviceability based on probability is proposed when key factors and vibration magnitude are known.

This paper proposes an accurate and efficient solution strategy for analyzing dynamic responses of flexible multibody systems. In the proposed strategy, flexible structures are modeled in the corotational frame, then the discrete mathematical model is solved by an optimized composite method. Due to the introduction of the corotational frame, some advanced linear elements can be directly employed, dramatically decreasing computational costs. For accurately calculating dynamic responses, an optimized three-sub-step composite method is developed wherein algorithmic parameters are optimized for minimizing local truncation errors. The optimized composite method achieves second-order accuracy, unconditional stability, and controllable stability. Some classical flexible dynamic systems are solved in this paper, and numerical results show that compared to the currently popular solution strategy based on the absolute nodal coordinate formulation and the Generalized-α method, under the same computational accuracy, our strategy has great superiorities in efficiency.

To study the influence of the vibration characteristics of ballastless track on bridge under the failed fasteners, this thesis adopts an existing scale model of ballastless track-box girder structure. Under the random loading, the influence of different invalid fasteners conditions on the vibration response change of the track-box girder structure is discussed. The results show that the peak value of acceleration admittance increases and the peak frequency of admittance moves forward when the fastener fails, it appears in each component of the mid-span section of track-box girder structure, especially appears in the rail and track plate. At the same time, it is found that when the distance between the failure fastener and the observed section is different, the vibration response effect of the rail-box girder components is also different. When the distance between the failure fastener and the observed section within one fastener spacing, the acceleration admittance of each component of the track-box girder increases significantly, with the peak value at the track plate increasing by 1.48 times. When the distance between the failure fastener and the observed section is more than three fastener spacings, the acceleration response increase of each component of the box beam is within 5%. In addition, it is found that the dynamic response of various components of the track-box girder structure is directly proportional to the number of failed fasteners. For example, the peak acceleration admittance of the three fasteners with continuous failure at the track plate is 1.9 times higher than that without failure of fasteners. The maximum increase of peak admittance at the top plate and wing plate is 131% and 82% respectively, while the increase of peak admittance at the web plate and bottom plate of the box girder is approximately less than 25%.

The control of vibration and acoustic radiation in rectangular confined spaces has been an important challenge in engineering. In this study, a solution is proposed with a sensor-actuator control system consisting of a loudspeaker, a base and a piezoelectric ceramic sensor. This design has the advantages of lightweight, low natural frequency and integrated sensing/actuator design. However, the strain-integra control scheme used for the integrated sensor-actuator suffers from stability problems. To overcome these problems, this paper utilizes a control strategy with a band-pass filter. The study tests the mechanical properties of this home-made inertial actuator, and determines the structural modes that have the greatest impact on the acoustic performance. A band-pass filter control strategy is used to selectively modulate these structural modes. The experimental results show that the homemade inertial actuator can effectively generate inertial forces, while the band-pass filter can effectively reduce the structural vibration, especially in controlling the first two acoustic cavity modes in the low-frequency band, which exhibits a significant effect. This approach is more flexible in controlling low-frequency noise in confined spaces and provides an efficient solution to the problem of structural noise in engineering environments.

In response to the problem of coupling vibration between equipment and coal rock during the anchoring drilling process of the comprehensive mining face in coal mines, considering the unevenness of the top and bottom plates of the working face, the mechanical characteristics of the anchoring drilling rig during the drilling process are mainly studied. Construct a dynamic model for synchronous anchoring operation of multi drilling rig anchoring drilling rig, and use numerical analysis methods to solve the vibration response characteristics of key components in the anchoring drilling rig. The results show that based on the time‑domain curve analysis, the maximum vibration radius of the drill pipe is 3.59 mm, and the minimum vibration radius of the drill frame is 1.51 mm； According to the frequency domain curve, it can be shown that the amplitude of the drill pipe reaches its maximum at around 11.94 Hz compared to other components of the drilling rig, with a maximum value of 392.6 mm； According to the vibration phase diagram, it can be shown that the overall stability of the power head, drilling frame, and crossbeam of the anchor drill is good during the vibration process. The vibration response characteristics of key components of the anchoring drilling rig during the drilling process were obtained through comparative experiments on the anchoring test prototype, which is basically consistent with the results of dynamic numerical simulation. This verifies the reliability of the theoretical analysis of drilling vibration characteristics of key components. The relevant theoretical results can provide a theoretical basis for the stability research of the anchoring drilling rig in the comprehensive excavation face.

The flexibility of gear teeth under cyclic varying loads can induce meshing impact and nonlinear vibration of gear pairs. Revealing the multi-state meshing characteristics and nonlinear dynamic characteristics of spur gear systems considering teeth flexibility lays the foundation for the safe and reliable operation of transmission systems. Based on the cantilever beam theory and gear meshing principles, the flexible deformation of meshing teeth is calculated, and the calculation method for flexible time-varying meshing parameters of gear pairs is derived； based on the contact states and loading conditions of the gear pairs, extract the characteristics of multi-state flexible meshing, and a nonlinear dynamic model of the spur gear system with multi-status flexible meshing is established； study the evolution laws of flexible time-varying meshing parameters and the distribution characteristics of flexible deformation of gear teeth under multi-parameters correlation, and uncover the global bifurcation and chaos characteristics of the system when the teeth flank clearance changes. The results indicate that the flexibility of the gear teeth reduces the double teeth meshing area, affects the meshing parameters and multi-status meshing characteristics of the gear system, and induces out-of-line meshing of the gear pair； the variation of teeth flank clearance causes the coexistence of periodic motions and chaotic motions, and incomplete bifurcation under multiple initial conditions is the fundamental cause for such dynamic behavior coexistence.

Mechanical metamaterials exhibit many counterintuitive mechanical properties by changing their internal geometry. We propose a mechanical metamaterial composed of gears as basic elements. The gear-based mechanical metamaterial proposed here is a multi-stable structure, which can be continuously converted between various stable states through the meshing of gear teeth. The continuous switching between states enables the mechanical metamaterial to exhibit in situ continuously tunable mechanical properties. The mechanical properties of the mechanical metamaterials were studied by using the finite element method. The results show that the gear-based mechanical metamaterials exhibited continuously adjustable stiffness, variable generalized shear stiffness, and adjustable acceleration transmissibility. These unique properties of mechanical metamaterials provide new ideas for creating programmable metamaterials with in situ continuously adjustable mechanical properties, and are expected to be applied in the fields of smart materials and engineering.

Aiming at the difficulties that the vibration response signal of the viscoelastic sandwich structure is strongly non-stationary and the change of vibration response signal caused by the change of aging state is weak, this paper proposes an intelligeat identification method for the aging state of the viscoelastic sandwich structure based on sparrow search algorithm (SSA) optimized variational mode decomposition (VMD) and adaptive neuro-fuzzy inference system (ANFIS）. The vibration response signals of different aging states of the viscoelastic sandwich structure are decomposed by the parameter-optimized VMD, and several intrinsic mode functions (IMFs) are obtained； The permutation entropy (PE) features of the obtained IMF components are computed, which are used to reflect the structural aging state change； The obtained permutation entropy features are constructed into feature vectors as inputs of ANFIS to realize the aging state intelligent iclentification of viscoelastic sandwich structure. The effectiveness of the method was verified through experiments, and compared with empirical mode decomposition (EMD) and ANFIS, parameter optimized VMD and radial basis function neural network (RBFNN) methods. The results show that the proposed method in this paper can more accurately identify the aging state of viscoelastic sandwich structure.

The intrinsic characteristics of all-composite honeycomb core sandwich panels (ACHCSP) were investigated using a combined approach of theory and experimentation. A theoretical model of the ACHCSP structure was established based on the high-order shear deformation theory and Gibson equivalent theory. The dynamic characteristics of this structure were determined using the Rayleigh-Ritz method and orthogonal polynomial approach. A relevant experimental platform was constructed to conduct tests on ACHCSP as the research subject, thereby confirming the accuracy of the theoretical model. The results indicate that this theoretical model can accurately predict the natural frequencies of ACHCSP plates. Based on the established model, the influence of fiber layer thickness, honeycomb cell wall thickness, and wall length on the natural frequencies of ACHCSP structures is discussed.

Analysis of the instantaneous angular speed (IAS) has been proven to effectively detect bearing faults. To investigate the generation mechanism of IAS signal double-impulses phenomenon in ball bearings, a dynamic model is proposed in this paper based on the coupling characteristics between the normal, tangential forces and the time-varying impact excitation, in which the influences of the rolling resistance and the sharp edges of local defect on the dynamic behavior are considered. In this model, the elastic quarter-space method is adopted to calculate the additional deformation induced by the local spalled edges and its corresponding time-varying displacement excitation model is deduced. Additional contact forces and time-varying displacement excitations are considered when steel ball enter into and exit from the defect. The disturbances of normal and tangential forces in the bearing under sharp-edge excitations of local fault are studied, and the time-varying tangential force excitation model is also deduced. The nonlinear dynamic equation sets are solved using the Runge-Kutta numerical integration method. Comparisons between the simulation results and the actual measured results of outer race local fault bearings show the established dynamic model can effectively reveal the mechanism of double-impulses phenomenon based on IAS signals.

To address the issue of unclear and challenging identification of non-contact rotating seal fault signals, this study established an experimental platform and acoustic emission testing system. It involved monitoring acoustic emission signals during various operational conditions, including normal operation and six typical fault scenarios of non-contact rotating seals. A total of 14000 feature samples were effectively collected. By applying the Bayesian optimization algorithm and incorporating continuous wavelet transform, an adaptive convolutional neural network classification model was constructed. Subsequently, the diagnostic performance of the fault recognition model was analyzed using confusion matrices and t-distributed stochastic neighbor embedding. The research results demonstrate that this model successfully classifies and identifies seven different operational conditions of non-contact rotating seals, including normal operation, dry friction, mixed lubrication, spring failure, end-face pitting, local spring failure, and end-face scratching, with an average recognition accuracy of 99.7023%. This achievement underscores the capability of effectively isolating and identifying seal fault sources from acoustic emission signals of non-contact rotating seals in non-stationary, complex, and overlapping environments, thereby establishing a solid theoretical foundation for practical engineering applications.

Blind source separation (BSS) can be used to extract modal coordinate vibrations from structural vibration signals. Complexity pursuit (CP) is one of the classical methods for solving the BSS problem. To improve the computational efficiency of the CP algorithm, this paper proposes two enhancements： it uses the negative log function of a Gaussian distribution as a nonlinear function to estimate signal complexity and derives formulas for rapidly computing signal complexity and its gradient； it employs a subspace search-based gradient descent algorithm to calculate the optimal mixing vector in the reduced subspace. The new formulas only require the covariance matrix of mixed signals and the covariance matrix of time delays when computing complexity and its gradient, without using all signal data. Numerical examples and structural vibration data are employed to evaluate the proposed method. The results demonstrate that the fast complexity pursuit algorithm outperforms traditional methods in terms of computational efficiency and accurately separates structural modal coordinate vibrations.

To overcome the shortcomings of traditional base isolation technology, such as non-adjustable isolation parameters, limited low-frequency isolation effect, and inability to achieve vertical isolation, magnetic levitation technology is introduced to design a magnetic levitation vibration isolation bearing. The relationships between the levitation force of the electromagnet and the coil current and levitation gap are analyzed. The nonlinear model of the magnetic levitation vibration isolation bearing is established. Combining the advantages of terminal sliding mode and super-twisting algorithm and introducing an adaptive law to adjust the coefficients in the super-twisting algorithm, an adaptive super-twisting terminal sliding mode control strategy is proposed. Through experimental verification, the proposed control scheme can suppress the chattering phenomenon in the traditional sliding mode control, with high control accuracy and good steady-state and dynamic performance. The magnetic levitation vibration isolation bearing has excellent stability and disturbance-resisting performance.

Flexible cable supported photovoltaic are prone to be significant wind induced vibrations, which can lead to various structural safety and usability issues. Currently, the law of wind induced vibrations is not clear, and there are no corresponding vibration suppression measures. This study conducted wind tunnel tests on the full aeroelastic model of flexible cable supported photovoltaic. It synchronously measured the displacement and cable force of single-layer flexible cable supported photovoltaic, analyzed the effects of wind speed, inclination angle, and wind direction angle on displacement and cable force, proposed corresponding vibration suppression measures, and verified their vibration suppression effect through experiments. The results show that the flexible cable supported photovoltaic undergoes vertical and torsional coupled vibration under strong wind. The maximum displacement response occurs at wind suction and the maximum of cable force occurs under wind pressure. Therefore, wind suction is an unfavorable working condition for designing the joints. Meanwhile, wind pressure is an unfavorable working condition for designing columns and bases. The anchor cable has a significant mitigation effect on the vertical and torsional displacement at wind suction. The larger of the tilt angle is, the better mitigation effects. For the cable end force, the anchor cable can effectively reduce the fluctuation of cable force. The larger the tilt angle is, the more effective the cable force reduction.

In order to obtain the main influencing factors of buffeting response calculation of Π‑shaped main girder cable‑stayed bridge, taking Qingzhou Minjiang River Bridge as the engineering background, the buffeting response characteristics of main girder displacement were analyzed by using three‑dimensional multi‑modal coupling buffeting calculation method on the basis of wind tunnel test. The significance of nine factors in buffeting response was tested by uniform experimental design and regression analysis method. The results show that the aerodynamic admittance, fluctuating wind correlation coefficient, vertical wind spectrum, average wind profile index, surface roughness height and air density have significant influence on the buffeting response of cable‑stayed bridge in the common range of values. The influence of structural mass and damping ratio is not significant, and its value deviation can be ignored in buffeting calculation. The horizontal wind spectrum only has a significant effect on the lateral buffeting response.

Seismic experience has shown that underground shaft structures are subjected to seismic threats and severe examples of damage have occurred. In order to obtain the seismic response of the shaft, the ‘beam-spring’ model was used to establish a system analysis model for the dynamic interaction between the large-diameter shaft and the soil based on the Pasternak foundation and the Timoshenko beam theory. On the basis of considering the normal earth pressure of site soil layer and shaft structure, the tangential shear force of site soil layer and shaft structure is further considered. The analytical solution of seismic response of large diameter shaft under horizontal earthquake was studied. The peak seismic response of the shaft along the depth direction is analyzed from the aspects of the ratio of the length to diameter of the shaft, the ratio of the inner and outer diameters, the ratio of the elastic modulus of the shaft to the site and the boundary conditions at the bottom of the shaft. The results show that the decrease of the ratio of the length to diameter of the shaft will lead to the increase of the peak response of the internal force of the shaft along the depth direction. The increase of the inner and outer diameter ratio of the shaft will reduce the peak internal force response of the shaft along the depth direction. With the increase of the ratio of the elastic modulus of the shaft to the site, the peak response of the internal force of the shaft along the depth direction will gradually increase. The displacement response of the shaft under the elastic soil foundation is larger than that of the rock-socketed foundation. The shear response under the rock-socketed foundation along the depth direction of the shaft is significantly larger than that of the elastic soil foundation, and the bending moment peak response of the rock-socketed shaft at the bottom position is larger.

The uncertainty of the combined incidence angle of seismic waves often has a significant effect on the dynamic response of faced rockfill DAMS. In this paper, the motion field of surface control points is decomposed by the principle of wave field superposition, and the time history of incident P and SV waves is obtained by two‑dimensional inversion. The angle of incident P wave and SV wave in the wave input model are randomly selected by the method of number theory. The influence of the uncertainty of combined incident angle on the seismic response of asphalt concrete faced rockfill dam is studied by the dynamic calculation of different combined incident angles. Taking a practical project as an example, by analyzing the mean value, coefficient of variation, 95% confidence interval limit and extreme value difference of the horizontal peak acceleration of foundation surface, panel stress and acceleration, dam body horizontal peak acceleration and permanent deformation, and other statistical laws and distribution type tests, and compared with the vertical incidence of seismic waves, The influence of random combination incidence Angle and input ground motion intensity on random response dispersion degree and obedience probability distribution is analyzed. The results show that considering the uncertainty of the combined incidence angle, the seismic response dispersion of the foundation surface of the dam will increase. The maximum principal tensile stress of the panel increases by at least 40% compared with the calculated result of vertical incidence. The influence of the horizontal peak acceleration on the dam crest and the panel crest is greater than that on the permanent deformation. Compared with the results of vertical incidence, the permanent deformation of the three groups of seismic waves has a transcendental probability of more than 70%. The statistical results of seismic response of dam body may not accord with normal distribution. The dispersion of seismic response results of overlay layer is greater than that of dam body.

Based on the basic concept of the generalized response displacement method, a dynamic sub-structure analysis method suitable for the longitudinal seismic response of a shield tunnel crossing longitudinally uneven sites is proposed. An explicit parallel calculation model of the longitudinal uneven free field and a three-dimensional (3D) refined explicit parallel calculation model of the surrounding rock-shield tunnel system are established by using the newly proposed sub-structure analysis method. The real-time transmission of dynamic deformation between the two models on the boundary is achieved through the sub-structure method. The free-field seismic wave at the buried depth of the tunnel is transformed into the equivalent earthquake action of the surrounding rock-shield tunnel sub-structure model. Compared with the traditional beam-spring model, the model method in this paper can achieve the 3D refined simulation of the surrounding rock-tunnel system and the longitudinal non-uniform ground motion input along the tunnel caused by the site seismic effect. The reliability of the model method in this paper is verified by comparing it with the calculation results of the 3D refined analysis model of the shield tunnel. The results show that the model method in this paper has a clear concept, simple modeling, low calculation cost and small differences in results, which can fully reflect the longitudinal seismic response of shield tunnel crossing longitudinal uneven sites. It provides a more efficient analysis method for the longitudinal seismic design of shield tunnels crossing longitudinal uneven sites with soft-hard connected media.

The non-uniform input of ground motion has a significant effect on the dynamic response of a concrete cut-off wall in deep overburden. In order to explore the response characteristics of the cut-off wall under non-uniform ground motion input at the overburden site, this study establishes the input method of P-wave three-dimensional oblique incident wave motion under any incident angle in space based on the wave field decomposition method and the viscoelastic artificial boundary method, and validates the input method. Nine non-uniform input conditions were designed to investigate the influence of different azimuthal and oblique incidence angles on the dynamic response of the cut-off wall under a combination of incidence. The results show that the maximum acceleration in the down-river direction of the cut-off wall at α=60° and γ=0° incidence is 3.89 times that of vertical incidence, and the maximum acceleration in the axial direction of the dam at α=60° and γ=90° incidence is 8.93 times that of vertical incidence. Non-uniform input causes a significant increase in the transverse riverward tensile stresses in the impermeable wall, up to 3.53 times that of the vertical incidence, with a significant change in the peak distribution region, and the vertical compressive stresses are significantly reduced at an oblique incidence angle of 90° incidence compared to the vertical incidence. The traditional vertical incidence method can ignore the expansion area of tensile stress of the cutoff wall under non-uniform input, so the non-uniformity of ground motion should be considered when analyzing the dynamic response of the cutoff wall in a deep overburden layer.