Vertical Response Research Articles

Evaluation of the effect of the vertical component of an earthquake on the seismic response of container cranes using the shake table test

In this study, the effect of the vertical component of earthquakes on the seismic response of a container crane was investigated by using the shake table test on a 1/20 scale container crane. The effect was investigated by comparing the seismic response of the container crane when subjected to the horizontal component of earthquakes versus the horizontal and vertical components of earthquakes. The seismic responses of the container crane were compared based on acceleration responses, displacements, and internal forces. The main findings of this study are as follows: (1) Vertical acceleration response increased when the vertical and horizontal components of earthquakes were used simultaneously. A maximum increase of 79% was observed for the vertical acceleration response at the trolley-boom girder. The horizontal acceleration response either increased or decreased. The maximum difference was 24% when the container crane was subjected to horizontal component earthquakes versus horizontal and vertical component earthquakes. (2) The horizontal displacements of the container crane increased or decreased under the simultaneous action of the horizontal and vertical components of the earthquakes. The maximum difference was 278% with regard to the derailment of the seaside legs. (3) The internal forces at the top of the lower legs were affected by adding the vertical component of the earthquakes. The maximum difference in the axial force response was 100%, while that of the bending moment was 24%. Therefore, the seismic response of container cranes should be analyzed with and without the vertical component of earthquakes to determine the most extreme case of the seismic response.

Key trends in the response of suction bucket foundations to extreme axial cyclic loads

The offshore wind industry is currently expanding into emerging markets at a rapid pace. Some of these markets are located in areas characterized by frequent extreme events. From a geotechnical perspective, this results in new design challenges, as foundations must withstand severe loads repeatedly throughout their intended lifetimes. Jacket structures resting on suction buckets represent a new foundation concept that still requires research to become a potential optimal solution. The vertical cyclic response of bucket foundations constitutes the main topic of this article. The current study is based on observations of the behavior of a scaled model installed in dense sand. Both normal and extreme conditions were simulated by applying axial cyclic loads of varying amplitudes, means, and frequencies. High amplitude and low frequency cause significant stiffness degradation and permanent displacement. These scenarios occur due to build-up of excess pore pressure, with subsequent triggering of liquefaction. A criterion for liquefaction occurrence is identified and may be readily used for practical applications. Considerable levels of tensile loading lead to a high rate of heave, regardless of frequency. For one-way compressive forces, after an extreme loading sequence, stiffness returns to its initial level, as long as no liquefaction develops priorly. This bears essential implications in predicting the change of natural frequency of the system.

Experimental investigation on wind-induced vibration of photovoltaic modules supported by suspension cables

Under the background of the global energy crisis and excessive carbon emissions, solar power stations have increased rapidly in number and size in recent years. To satisfy the construction needs on complex or special sites (e.g. intertidal zone, mountainous area, fishponds, etc.), a suspension cable supported photovoltaic (PV) module was developed recently and quickly aroused market interest; however, such cable-supported flexible PV systems are susceptible to wind loading and associated aerodynamic effects thereon remain unclear. Therefore, both aeroelastic and rigid model wind tunnel tests were conducted to investigate the wind-induced vibration (WIV) characteristics of a typical cable-supported PV module. The effects of module tilt angle, cable pre-tension, and wind speed on the vertical displacement response and the aerodynamic damping were evaluated. Based on wind pressure tests and finite element simulation, the three-dimensional WIV behavior of PV modules could be investigated. The non-dimensional gust loading factor representing the load dynamic amplification was presented based on multi-target equivalent static wind loads. Results show that wind-induced vertical vibration of the PV modules increased with tilt angle but reduced with increasing cable pretension. The fluctuating displacement shows a quasi-linear increase with the square of the wind speed. Negative aerodynamic damping was found for a tilt angle of 10° under high wind speeds. Compared to vertical vibration, horizontal and torsional responses were insignificant for the tested PV modules. The estimated gust loading factor for the PV module with tilt angle of 10° was between 1.1 and 2.5.

Research on comfort analysis method and optimization design of pedestrian bridge

In this paper, the characteristics and modes of pedestrian load are summarized, and the norms of pedestrian load in different countries are compared. At the same time, the pedestrian excitation load is briefly introduced .Then, combining the three conditions of single, double and three-person pedestrian load with the above four common pedestrian load conditions, 12 groups of different load conditions are formed, and the case study is carried out, and the conclusion is drawn as follows: Under the condition of slow walking, the vertical peak acceleration response of the structure under inconsistent stride length slightly increases, but the impact on the pedestrian comfort of the bridge is not significant. When walking slowly and at the same pace, the vertical peak acceleration of the structure increases significantly, which has a significant impact on the pedestrian comfort of the bridge. The common vibration control measures are also introduced. Through the comparison of relevant regulations, combined with case studies and common vibration control measures, it is hoped that it will be helpful to improve the comfort of pedestrian Bridges in the future, and the relevant regulations in China will be revised.

In Situ Investigation of the Dynamic Response and Settlement in the Expressway Culvert–Subgrade Transition Section Using a Vibration Exciter

During the operational phase of the expressway, a significant challenge arises concerning substantial differential settlement in the transition zone connecting the culvert and the general subgrade, affecting its smoothness. In order to address the issue of abrupt stiffness variations within the transition section and to mitigate the occurrence of differential settlement, a gradient pile–reinforced-concrete slab composite foundation was implemented for the first time within an expressway culvert–subgrade transition section. At the same time, an in situ vibration test was conducted through the SBZ30 vibration exciter to comprehensively understand the vertical dynamic responses in the culvert–subgrade transition section under various axle loads and speed conditions. Furthermore, continuous monitoring was conducted to track the long-term settlement of the roadbed. The findings indicate that the utilization of gradient pile–reinforced-concrete slab composite foundations can significantly mitigate the amplitude of the dynamic response parameters. Moreover, dynamic parameters and attenuation coefficients exhibit a gradual reduction as the depth increases. Dynamic stresses, acceleration, and displacements on the roadbed surface exhibited positive correlations with both the axle weight and vehicle speed. However, at deeper depths, the load weight exerted a more pronounced influence. As the speed rose, acceleration decayed faster, affecting a shallower depth. Conversely, the increased load slowed the acceleration decay. The cumulative deformation of the roadbed and the number of excitations followed exponential function characteristics. Settlement values progressively increased while the settlement rate gradually diminished, eventually reaching a stable state, ultimately stabilizing within 4.7 mm. These research outcomes offer valuable guidance and serve as a reference for the implementation of gradient pile–reinforced-concrete slab composite foundations within the culvert–subgrade transition section.

An offshore non-ergodic ground motion model for subduction earthquakes in Japan Trench area

With the improvement of the world’s largest seafloor observation network (S-net) and the increase in the quantity and quality of records, the ergodic assumptions can be further relaxed in the modeling of offshore ground motion models (GMMs). This allows accounting for systematic and repeatable source, site, and path effects to further understand the characteristics of offshore ground motion in the Japan Trench region. We developed an offshore ergodic backbone GMM for subduction earthquakes and classified the sites into four categories using horizontal–vertical response spectral ratio to investigate site amplification. The offshore ergodic GMM is applicable for subduction earthquake scenarios with moment magnitudes ranging from 4.0 to 7.4 and rupture distances ranging from 10 to 300 km. Comparing offshore ergodic GMMs with onshore GMMs for subduction earthquakes, we found that offshore GMMs were significantly different from onshore GMMs, especially in the long-period and unburied states. Then a new offshore non-ergodic GMM was developed based on the offshore ergodic GMM. The systematic and repeatable source and site effects were captured by the spatially varying coefficients represented by Gaussian processes, while the systematic and repeatable path effects were captured by cell-specific anelastic attenuation proposed by Dawood and Rodriguez-Marek (2013), calculated with the Cohen-Sutherland computer graphics algorithm. The non-ergodic GMM revealed systematic and repeatable source, site, and path effects that were not captured by the ergodic GMM. Moreover, the non-ergodic GMM showed reduced aleatory variability and epistemic uncertainty on ground motion estimation compared to ergodic GMM. The reduction of aleatory variability and epistemic uncertainty had a significant impact on probabilistic seismic hazard analysis. Quantifications of these results are contributed to conduct reasonable seismic design and seismic risk assessment for marine engineering in offshore regions vulnerable to strong subduction earthquakes.

Vertical Monotonic and Cyclic Responses of a Bucket in Over-Consolidated Clay

Bucket foundations, especially multi-bucket foundations, have become an alternative for large offshore wind turbines. Vertical responses of a single bucket are critical for the serviceability design of tripod or tetrapod bucket foundations. Centrifuge tests are conducted to investigate the responses of a single bucket under monotonic and symmetric cyclic loading in over-consolidated clay. The strength of clay is obtained by cone penetration tests. The monotonic vertical capacity measured in the centrifuge tests are compared with the finite element results, with errors less than 6%. The effects of the ratio of cyclic loading amplitude to vertical capacity (ranging between 0.37 and 0.64) and the number of cycles on the accumulation of vertical displacement and evolution of stiffness are explored. Simplified functions are proposed to predict the evolutions of dimensional and dimensionless stiffness.

Spatiotemporal Variations of Ocean Upwelling and Downwelling Induced by Wind Wakes of Offshore Wind Farms

Offshore wind farms (OWFs) generate large-scale wind wakes, which might lead to upwelling/downwelling. Understanding the vertical marine response to the wake effects is crucial for assessing the ecological impacts of OWFs and optimizing their co-deployments with mariculture. In this study, we employ a high-resolution ocean model to investigate the spatiotemporal variations of upwelling and downwelling induced by the wind wakes of OWFs through idealized numerical experiments. We have two main findings. First, the wind-wake-induced upwelling and downwelling are not balanced in the north–south direction, resulting in a net effect of thermocline rising. Second, the thermocline depth changes caused by wind wakes develop nonlinearly over time. Specifically, when the elevated thermocline approaches the sea surface, the upwelling slows down significantly. The spatially asymmetric pattern of the upwelling is attributed to horizontal Ekman transport, while its temporal nonlinear evolution is caused by stratification changes. By utilizing the simulated change law of thermocline depth, we calculate the ocean response of OWF wakes in China’s adjacent waters. The results suggest that baroclinic theory overestimates the ocean response in the Bohai Sea, the Yellow Sea, and the nearshore waters of the East China Sea. However, in the open seas and the South China Shelf, the upwelling/downwelling is expected to be close to the theoretical calculations. This study provides a foundation for conducting regional simulations with high resolutions in areas where OWFs will be constructed.

Investigation on Gas-Liquid Two-Phase Flow-Induced Vibrations of a Horizontal Elastic Pipe

Abstract This paper is concerned with experimental analyses on the vibration behaviors of a horizontal pipe containing gas–liquid two-phase flow with different flow patterns. The effects of flow patterns and superficial velocities on pressure fluctuations and structural responses are evaluated in detail. Numerical simulations on the fluid–structure interactions within the pipe are carried out using the volume of fluid method and the finite element method. A strongly partitioned coupling method is adopted to ensure the compatibility and equilibrium interface conditions between the fluid and the elastic pipe. The accuracy of the numerical solutions is confirmed by comparing with experimental results. It is found that the fluctuation frequency of the pressure fluctuations of the two-phase flow ranges from 0 Hz to 5 Hz. The standard deviation (STD) value of the pressure fluctuation of the two-phase flow increases with an increase in the superficial liquid velocity, and the maximum magnitude appears in slug flows. The vibration responses of the pipe exhibit strong dependence on the momentum flux of the two-phase flow, which mainly excites the fundamental flexural vibration mode of the pipe. The magnitude of vertical vibration response of the pipe is equal to that of the lateral vibration response, and the vibration response measured at the middle of the pipe does not contain the second-order operating mode. Moreover, the STD value of the structural responses of the pipe increases proportionally with an increase in the gas flowrate, while the predominant vibration frequency of the pipe slightly increases.

Aerodynamic interference mechanism of vertical vortex-induced vibration of a ∏-shaped girder paralleled with a truss girder

In this study, the aerodynamic interference characteristics and mechanism of vertical vortex-induced vibration (VIV) of a ∏-shaped steel–concrete composite girder of a highway cable-stayed bridge and a steel truss girder of a railway cable-stayed bridge are investigated via experimental and numerical simulation methods, respectively. To this end, firstly, wind tunnel tests are conducted on section models with a geometry scale of 1:60, consisting of the ∏-shaped girder paralleled with truss girders to investigate their aerodynamic interference behaviors. Moreover, the fluid–structure interaction (FSI) approach based on dynamic mesh and user defined functions (UDF) is applied to study the wind-induced vibrations (WIV) of the single ∏-shaped girder and two parallel main decks for wind attack angle of 0°, respectively. Furthermore, the characteristics of vorticity, surface pressure, and vortex-induced force (VIF) distributions of the ∏-shaped girder and the truss girder are analyzed to investigate the aerodynamic interference mechanism. The results reveal that, the significant vertical vortex-induced vibrations (VIV) of the single ∏-shaped girder are observed, however, no obvious vertical VIV occurs for the single truss girder. Moreover, when the truss girder locates in the windward of the ∏-shaped girder, no obvious vertical VIV responses are observed. However, the ∏-shaped girder and the truss girder both exhibit significant vertical VIV responses for wind from the ∏-shaped girder side, and the maximum vertical VIV amplitude of the ∏-shaped girder is amplified by 32% compared with the single ∏-shaped girder. The vortices shed from the truss girder section disrupt the regular vortex shedding of the ∏-shaped girder section, thus suppressing the VIV of the ∏-shaped girder section. The WIV of the truss girder section is due to the forced vibration caused by the vortex impact of the dominant vortices shed from the ∏-shaped girder section. As the downstream flow field is blocked by the truss girder section, the scale and intensity of the dominant vortices is increased, leading to an amplification of the VIF and the VIV amplitude of the ∏-shaped girder section.

Impacts of the North Atlantic biases on the upper troposphere/lower stratosphere over the extratropical North Pacific

The winter upper troposphere/lower stratosphere temperature/vertical motion response over the extratropical North Pacific induced by North Atlantic changes is not well understood. Here, using robust diagnostic calculations conducted in a fully coupled high-resolution climate model, we correct the North Atlantic ocean circulation biases and show that during wintertime, the North Atlantic cold surface temperature biases lead to a warmer upper troposphere/lower stratosphere over the extratropical North Pacific. In the upper troposphere/lower stratosphere over the extratropical North Pacific, this winter warming temperature response is linked to the vertical motion response through a simple leading order thermodynamic relationship between changes in the horizontal advection and adiabatic heating. The upper troposphere/lower stratosphere vertical motion response, which is also associated with the North Atlantic induced Walker circulation response over the tropical North Pacific, can provide a rough estimation of the upper troposphere/lower stratosphere warming response over the extratropical North Pacific.

Monitoring and analysis of railway-induced vibration and structure-borne noise in a transit oriented development project

With the rapid development of modern cities, the construction of over-track buildings and buildings along the subway line are increasing gradually. In order to evaluate the influence of rail transit on these buildings, the railway-induced vibration and structure-borne noise of subway stations and buildings in a Transit Oriented Development (TOD) project are monitored and analyzed in this paper. The vibration monitoring data in the subway station shows that the vibration acceleration response of the measuring point in the station caused by the train entering and leaving the station is the largest in the vertical direction, followed by the along-track direction, and the vertical-track direction is the smallest. The corresponding predominant frequency of vibration is usually in the range of 100 Hz-200 Hz. The vibration monitoring data of the building foundation along the subway line shows that the railway-induced vibration of the building foundation along the track near the subway station decreases with the reduction of the distance from the subway station. The monitoring vibration results of the over-track building on the metro depot are different from the buildings near the main line. The predominant frequency of the vibration at the measuring point is in the range of 30 Hz-40 Hz. The small vertical vibration acceleration response of the measuring point corresponds to a high vibration level. In addition, the amplitude of railway-induced vibration in some building rooms near the metro depot is basically consistent with the amplitude of background vibration, but the monitoring value of the structure-borne noise is obviously higher than the background noise. The research results of this paper show the influence of railway-induced vibration on the over-track buildings and the buildings along the subway line, which has important reference value for the comprehensive development of rail transit.

Influence of Variable Height of Piers on the Dynamic Characteristics of High-Speed Train–Track–Bridge Coupled Systems in Mountainous Areas

With the increase in the occupancy ratio of bridges and the speed of trains, the probability of trains being located on bridges during earthquakes increases, and the risk of derailment increases. To investigate the influence of unequal-height piers on the dynamic response of high-speed railway train bridge systems, a seismic action model of high-speed train–track–bridge dynamic systems was established based on the in-house code using the finite element method and multi-body dynamics method. It is found that (1) compared to equal-height piers, the peak lateral dynamic response of unequal-height piers (with gradually increasing pier heights) decreases, while the peak vertical dynamic response increases; (2) the peak lateral dynamic response of unequal-height piers (with a steep increase in pier height) increases sharply, while the peak vertical dynamic response decreases; and (3) the safety indicators of equal-height piers are significantly superior to the two unequal-height pier operating conditions.

Core taxa drive microeukaryotic community stability of a deep subtropical reservoir after complete mixing.

Microeukaryotes are key for predicting the change of ecosystem processes in the face of a disturbance. However, their vertical responses to multiple interconnected factors caused by water mixing remain unknown. Here, we conducted a 12-month high-frequency study to compare the impacts of mixing disturbances on microeukaryotic community structure and stability over different depths in a stratified reservoir. We demonstrate that core and satellite microeukaryotic compositions and interactions in surface waters were not resistant to water mixing, but significantly recovered. This was because the water temperature rebounded to the pre-mixing level. Core microeukaryotes maintained community stability in surface waters with high recovery capacity after water mixing. In contrast, the changes in water temperature, chlorophyll-a, and nutrients resulted in steep and prolonged variations in the bottom core and satellite microeukaryotic compositions and interactions. Under low environmental fluctuation, the recovery of microbial communities did not affect nutrient cycling in surface waters. Under high environmental fluctuation, core and satellite microeukaryotic compositions in bottom waters were significantly correlated with the multi-nutrient cycling index. Our findings shed light on different mechanisms of plankton community resilience in reservoir ecosystems to a major disturbance over depths, highlighting the role of bottom microeukaryotes in nutrient cycling.

Towards a New Design Methodology for Vertical Traffic Calming Devices

With increasing emphasis on new soft mobility in urban areas, it becomes more and more important to provide effective speed control measures for vehicular traffic. Among those, the ones based on vehicle vertical deflection, namely vertical traffic calming measures, are historically the most widespread. However, since the basic operating principle of these devices is related to the vertical dynamic response due to the interaction between the moving vehicle and the road profile, different vehicles may exhibit different speed behaviors when traveling on a specific road profile shape. As a matter of fact, recent research provided evidence of this connection, and therefore it has been worth investigating the dynamics underlying the phenomenon in order to develop a new approach to the design of vertical traffic calming devices. In this paper, following an initial state-of-the-art review, an in-depth study on the dynamic interaction between vehicle and road profile has been presented by means of an ad hoc-developed mathematical model. The proposed simulation model has been used to evaluate the root mean square acceleration value associated with each vehicle/traffic calming device/crossing speed. Following the outcomes provided by numerical simulations, an experimental investigation has been designed and carried out on a vertical traffic calming device. Speed profiles of different vehicles have been acquired, and preliminary results seem to provide evidence of a different dynamic response for each vehicle type, yielding the basis to reconsider the design approach of such devices in order to control urban traffic speed.

Confinement mechanism of rectangular CFST components using double horizontally-corrugated steel plates

This paper presents experimental and analytical investigations on the confinement mechanism of a novel rectangular concrete-filled steel tube (CFST) component for use in composite shear walls. The CFST component consists of a steel tube made by welding double horizontally corrugated steel plates and double flat steel plates, and infilled with concrete. Tests of eight components and finite element analysis of twenty-three components under uniform compression were conducted to explore confinement mechanism of the novel tube to core concrete. The impacts of several factors such as steel plate thickness, nominal sectional aspect ratios, slenderness ratios, and the strength of the steel and concrete on the confinement mechanism were analyzed. The non-uniform confinement mechanism of horizontally corrugated steel plates was investigated based on their vertical and horizontal strain responses at the wave crests, middles, and troughs. The test results and numerical simulations demonstrate that the proposed CFST components exhibited desirable axial compressive behavior with ductile failure modes. The tested specimens with nominal sectional aspect ratios ranging from 1.2 to 2.39 had strength indexes greater than 1.17. Even with a width-thickness ratio of 325.33, the horizontally corrugated steel plates effectively confined the core concrete. Furthermore, this research proposed a design strength model that considered the confinement effects of corrugated plates. The model accurately predicted the experimental and numerical results.

On the Observed Wind-Driven Circulation Response in Small Semienclosed Bays

Abstract This study analyzes horizontal and vertical wind-driven circulation responses in small semienclosed bays, the associated offshore dynamic conditions, and the relative importance of each term in the momentum balance equations using a multiplatform observational system. The observational platform consists of three ADCPs and a land-based radar monitoring the velocity field within the bay and in the contiguous offshore area. The wind-driven patterns in the bay can switch from a barotropic cyclonic or anticyclonic circulation to a two-layer baroclinic mode response as a function of the wind regime (its direction and magnitude). For the baroclinic mode, the vertical location of the inflection point in the velocity profile can vary according to the proximity of the boundary current to the entrance of the bay. The influence of offshore combined meteorological and marine conditions on the inner-bay dynamics is evidenced under moderate to strong wind conditions and is almost nonexistent under negligible wind. The momentum balance analysis as well as the nondimensional numbers evidence the impact of wind stress, coastline shape, stratification, and the nonlinear advective terms. Advection can be at the same order of magnitude as pressure gradient, Coriolis, or wind stress terms and can be greater than the bottom stress terms. The nonlinear terms in the momentum equations are frequently neglected when analyzing wind-driven circulation by means of in situ data or analytical models.

Vertical Resonance Simulation of Superconducting Electrodynamic Suspension Train/Bridge Coupled System

The superconducting electrodynamic suspension (EDS) train, which speed over 600 km/h, has the advantages of a lightweight, large suspension gap (up to 100 mm), stable suspension, etc. Therefore, it is expected to become one main form of the next generation of high-speed and ultra-high-speed manned rail transit. The bridge will vibrate and deform when the train passes through the bridge. And the vibration and deformation of the bridge will affect the dynamic response of the train as well. Therefore, the train and the bridge will form an interaction system. And under a certain running speed, train/bridge coupled resonance will occur, directly affecting the train's safety and comfort. In this paper, the MLX01 superconducting EDS train is taken as the research object, established a 14-DOF dynamic model for vertical and pitching vibration analysis of a superconducting EDS train and established a single-span Euler-Bernoulli simply supported bridge. Nonlinear levitation forces connect the train and bridge subsystem to form a superconducting EDS train/bridge coupled vertical dynamic model. Simulation calculation explores the effects of train speed and bridge damping ratio on the superconducting EDS train/bridge coupled system's vertical resonance response. The results show that the train speed and the bridge's natural frequency are two main factors affecting the vertical resonance of the train/bridge. In train operation, the first resonance speed should be avoided. Increasing the damping ratio of the bridge cannot prevent the train/bridge resonance, but it can weaken the dynamic response of the bridge during resonance, and properly increasing the damping ratio of the bridge is conducive to the stability of train operation.

Dynamic Interaction Factor of Pipe Group Piles Considering the Scattering Effect of Passive Piles

Based on the plane–strain assumption, a calculation model of pile–soil–pile vertical coupling vibration response considering the scattering effect of passive piles is established in this paper. Using this model, the vertical displacement expressions of pile core soil and pile surrounding soil, soil displacement attenuation function, and longitudinal complex impedance are obtained. Then, based on the strict pile–soil coupling effect, the displacement of the active pile under vertical load and scattering effect, as well as the displacement of the passive pile under incident waves, are solved separately. A new type of dynamic interaction factor for pipe group piles is derived by introducing scattering effect factors. A numerical example shows that the degenerate solution in this paper is in good agreement with the existing solution, which verifies the rationality of the solution. Considering the scattering effect is helpful in improving the accuracy of vibration response analysis of pile groups. The variation in parameters such as slenderness ratio, pile spacing, and outer diameter has significant effects on the interaction factor, and compared with the solid pile, the influence of parameter change on the pipe pile is smaller.

Research on vibratory & oscillatory coexistence nonlinear dynamics based on drum-subgrade coupling model

In order to provide theoretical basis for subgrade continuous compaction monitoring technology and intelligent compaction technology, it is urgent to study the nonlinear coupling dynamics of drum and subgrade in the process of vibratory and oscillatory compaction. In this study, a nonlinear coupling dynamic model of 6-degree-of-freedom vibratory drum-subgrade is proposed, which considers the elastoplastic characteristics of the subgrade during compaction. According to the geometric and physical relationship between the drum and the subgrade in the contact area, the longitudinal dynamic contact force coefficient is derived, which establishes the coupling relationship between the drum-subgrade vertical vibration and longitudinal oscillation. Combined with the evolution law of material properties of subgrade in actual compaction operation, the nonlinear dynamic behavior of coupling system in the whole compaction period is analyzed. The results show that the chaotic compaction state in the vertical direction of the drum may occur during the full compaction cycle, which is related to the excitation parameters of the drum. Furthermore, the excitation parameters are more sensitive to the longitudinal one-cycle vibration response of the system than the vertical vibration response. Through the response characteristics of the drum and the subgrade and the bifurcation diagram of the drum, it is proved that the proposed model can effectively simulate the longitudinal-vertical nonlinear coupling characteristics of the drum and subgrade, and can provide a premise for theoretical exploration for the vibratory & oscillation compaction mode.