Vertical Vibration Response Research Articles

Experimental study on flow-induced vibration under laminar flow and turbulent flow transition state in helical coiled tube

This study investigates the vibration characteristics induced by single-phase flow at low velocities within helical coiled tube, encompassing laminar and turbulent flow transition regimes. Modal experiments were conducted to ascertain the natural frequencies in the radial and vertical directions within the helical coiled tube. The influence of fluid mass in tube on vibration was considered, revealing the fluid mass has a greater influence on the vibration frequency in the vertical direction. When the coil was filled with water, the radial natural frequency decreased by 0.1 Hz, while the vertical natural frequency decreased by 0.8 Hz.By simplifying the spiral coil into a spring system, the intrinsic causes of the influence of mass on the natural frequency are studied and verified with the experimental data. The results show that the radial natural frequency is only related to the local mass change of the pipe, while the vertical natural frequency is related to the static deformation of the system under the influence of gravity.By conducting single-phase flow induced vibration experiments inside the pipeline, the radial and vertical vibration response characteristics were obtained, and the modal experimental results were analyzed. Findings indicated larger vibration displacements when laminar flow prevailed within the tube, with radial RMS (Root Mean Square) at 10.1 μm and vertical RMS at 14.5 μm. After the transition to turbulent flow, significant reductions in vibration displacements were observed, reducing the radial RMS to 2.3 μm and vertical RMS to 5.5 μm.Based on statistical and frequency-domain analysis methods, the influence mechanism of secondary flow on the vibration of helical coils at low flow rates was revealed, and the importance of friction coupling was clarified. Moreover, this study considered the impact of fluid viscosity on vibration response and experimentally validated the critical role of friction coupling in exciting secondary flows.

Vibration analysis of a rotor-bearing system using magneto-rheological elastomers

Magneto rheological materials are considered as a promising adaptive means of vibration control. This paper proposes a new configuration of smart bearings comprising magneto-rheological elastomer (MRE) layer inserted between the bearing pedestal and the foundation. This configuration provides a directional vibration controllability in both horizontal and vertical directions of a rotor-bearing system. The effect of using MRE layer on the vibration response and the resonant speeds of a rotor-bearing system is investigated. The finite element method is used to derive a dynamic model for the rotor-bearing system using shaft elements based on the Rayleigh beam theory and accounting for the gyroscopic effect and internal damping of the shaft. Simulation results reveal that the use of MRE materials in passive mode leads to downshifting of the first two resonant speeds and the attenuation of the steady state vibration response of the rotor bearing system in the horizontal and vertical directions at the resonance frequencies. When the MRE layer is subjected to a magnetic field generated by an electric current produced in the magnetic coil, the horizontal and vertical vibration responses are increased at the resonant speeds but decreased at other rotational speed ranges. Furthermore, the first two resonant speeds in the horizontal and vertical directions decrease further with the increase of the electric current.

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.

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.

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.

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.

Model-assisted clustering for automated operational modal analysis of partially continuous multi-span bridges

Long multi-span bridges represent a broad section of the civil roadway infrastructure. Despite being so common, their condition-based maintenance through vibration-based Structural Health Monitoring (SHM) has been scarcely investigated in the literature. The dynamic identification of such structures through Operational Modal Analysis (OMA) is especially challenging due to of their quasi-periodic nature and the common existence of weak inter-span coupling. Even when designed following an isostatic scheme, there always exists a certain degree of coupling between spans due to the continuity of the deck, the pavement and imperfect expansion joints. Hence, the modal poles of the spans typically appear as dense clusters with closely spaced frequencies and mode shapes with similar wavelengths, which significantly hinders the identification of physical poles through stabilization diagrams. In this light, this paper proposes a model-based machine learning approach to conduct and interpret the OMA results of partially continuous multi-span bridges. The proposed method is a hierarchical clustering approach that leverages on the analytical solution of the vertical free vibration response of multi-span girders with weak inter-span rotational coupling, allowing the estimation of the modal features of any bridge configuration ranging from simply supported to perfectly continuous conditions. Detailed parametric analyses and discussions are presented to appraise the correlation between the inter-span rotational coupling and the clustering of the modal poles of multi-span bridges, as well as the influence of damage conditions of varying severity and extension. On this basis, a model-based cut-off distance threshold for hierarchical clustering of stable poles is proposed to assist the automation of the global OMA of multi-span bridges. The developed formulation is tested in a real-world in-operation seven-spans reinforced concrete girder bridge, the Trigno V Bridge in Italy.

Vibration response analysis of footbridge based on pedestrian perception

This article aims to study the influence of random crowd loading on the perceived vibration response of pedestrians. Firstly, a vertical vibration response analysis method considering pedestrian perception was established based on the random crowd walking model. Secondly, change rules of maximum vibration response of pedestrians, occurrence time and position interval under different random walk models were compared and analyzed. Finally, the vibration response reduction factor was defined by studying the correlation between the maximum vibration response of pedestrians and the peak acceleration of the structure, and the approximate calculation method of the maximum vibration response of pedestrians was proposed. The results show that the maximum acceleration perceived by pedestrians obeys the normal distribution under the four crowd walking models, the response distribution of ordered arrangement model (OAM) is larger than that of the other three models; The location and occurrence time of the maximum response depend on the distribution of pedestrian locations on the footbridge, and there is no significant change with the increase of population density. In addition, the distribution of OAM and stochastic arrival model (SAM) are consistent, which is concentrated in the middle of the total time-history. In contrast, the distribution of stochastic distribution model (SDM) and dynamic equilibrium model (DEM) are relatively uniform. The maximum error between the calculated acceleration maximum value and the actual acceleration value felt by the pedestrian is less than 5%. These results can provide reference for quantitative evaluation of pedestrian-induced vibration comfort.

Analytical Formulae and Applications of Vertical Dynamic Responses for Railway Vehicles

To effectively improve the estimated level of railway vehicles’ vertical dynamic responses and provide a more suitable reference for the selection of its secondary suspension damping parameter, this paper has derived the root mean square values analytical formulae of the car body vertical acceleration, the secondary suspension vertical stroke, and the axle box vertical action force for railway vehicles under the random excitation of the track closer to the actual track characteristics. The correctness of the analytical formulae is verified by testing a real vehicle. Then, according to the analytical formulae derived, an analytical design method of the optimal damping ratio for the secondary suspension system is constructed based on the multi-objective programming and single-objective interval constraint analysis, which can be used to find the best trade-off for conflicting performance indices, such as ride comfort, running smoothness, and running safety, and the influences of the system parameters on the optimal damping ratio are analysed. This research can effectively characterize the vertical vibration response of railway vehicles and provide an effective reference for the initial design of the railway vehicle secondary suspension damping parameter.

In-situ experiment research on environmental vibration transmission characteristics of air-rail combined airport

The rail transit and civil aviation are the important components of the comprehensive transportation system. The development of the air-rail combined transport is an important effective way for China to become a country with strong transportation network. The transportation intersection form of railway under-passing airport transportation hub gradually becomes popular, thus the environmental vibration due to the under-passing railway cannot be ignored. In this paper, a large-scale integrated transportation hub construction project was taken as an example to analyze the transmission rule of environmental vibration due to the high-speed railway at the speed of 350 km/h under-passing airport in terms of the time domain and frequency domain by means of the on-site in-situ wheel-drop test. The research results show that the vertical vibration response of the ground surface along the normal direction of the railway is greater than those of the other two directions within 40 m from the centerline of the track. A vibration amplification zone appears within 5-40 m. The longitudinal vibration response of the ground surface is greater than those of the other two directions within 40-70 m. The local vibration amplification zones appear within 5-20 m and 30-60 m. The lateral vibration level of the ground surface along the normal direction of the railway increase gradually, but attenuates at the distance of 40 m and 10 m with the maximum attenuation rate of 0.67. The vertical vibration level amplifies at the distance of 60 m. The longitudinal vibration level attenuates at the distance of 20 m with the maximum attenuation rate of 0.3, but amplifies at the distance of 40 m with the maximum amplification rate of 1.8.

Random vibration analysis of an uncertain vehicle-track coupled system based on a polynomial dimensional decomposition

ABSTRACT In this paper, the uncertainty propagation of an uncertain vehicle-track coupled system (VTCS) subjected to track irregularity is quantified using a polynomial-dimensional decomposition (PDD). Firstly, the conditional power spectral density (PSD) of response related to uncertain parameters is derived using the pseudo-excitation method. Secondly, the PDD surrogate model that can describe the probabilistic characters of the uncertainty propagation is established by conducting the dimensional decomposition to the conditional PSD with component functions and performing the Fourier expansion to the component functions. Finally, the dimensional reduction integration and Gauss integration are introduced to overcome the difficulty of high-dimensional integration when calculating the expansion coefficients. In numerical example, the proposed method is applied to the uncertainty quantification of vertical vibration response of an uncertain VTCS, the accuracy and efficiency of the proposed method are verified by comparing the results of the PDD method with that of Monte-Carlo simulation.

Influence of inter-panel connections on vibration response of CLT floors due to pedestrian-induced loading

Long-span cross-laminated timber (CLT) floors are typically an assembly of prefabricated CLT panels connected together on the site. The actual connections are commonly neglected in design calculations. Hence, a CLT floor is modelled either as a monolith slab or more frequently as a set of CLT panels with no connections at all. This paper presents a numerical study designed to examine the influence of two most common inter-panel connections, i.e. single surface spline and half-lapped joint, on vibration modes and vibration responses of a range of different CLT floors due to pedestrian-induced loading. Although the inter-panel connections are relatively complex in reality, they are modelled here as an equivalent 2D elastic strip between the CLT panels. This relatively simple yet robust model can be used with ease in design practice, regardless finite element (FE) software used to extract vibration modes of a CLT floor. The corresponding monolith floors and floors without inter-panel connections are studied for the comparison of the results. Vertical vibration responses are simulated for low-frequency and high-frequency floors using the corresponding walking force models given in a popular design guideline for footfall induced vibrations of civil engineering structures. Vibration responses were calculated for single pedestrian occupants and their walking paths parallel and perpendicular to the line of connection. The results showed that including the inter-panel connections in a FE model resulted in up to 2.5 higher RMS acceleration levels. Hence, the common practice of modelling CLT floors as monolith slabs or as a set of panels without connections should be left behind.

Investigation on two-phase flow-induced vibrations of a piping structure with an elbow

The dynamic behaviors of a horizontal piping structure with an elbow due to the two-phase flow excitation are experimentally investigated. The effects of flow patterns and superficial velocities on the pressure pulsations and vibration responses are evaluated in detail. A strong partition coupling algorithm is used to calculate the flow-induced vibration (FIV) responses of the pipe, and the theoretical values agree well with the experimental results. It is found that the lateral and axial vibration responses of the bend pipe are related to the momentum flux of the two-phase flow, and the vibration amplitudes of the pipe increase with an increase in the liquid mass flux. The vertical vibration responses are strongly affected by the flow pattern, and the maximum response occurs in the transition region from the slug flow to the bubbly flow. Moreover, the standard deviation (STD) amplitudes of the pipe vibration in three directions increase with an increase in the gas flux for both the slug and bubbly flows. The blockage of liquid slugs at the elbow section is found to strengthen the vibration amplitude of the bend pipe, and the water-blocking phenomenon disappears as the superficial gas velocity increases.

Sensitivity Analysis for Pedestrian-Induced Vibration in Footbridges

This paper aims to provide a novel insight into the influence of uncertainties in system- and pedestrian-induced load parameters on the vibration response of footbridges. The study begins with a sensitivity analysis for the vertical vibration response of a representative footbridge to two loading cases: a single pedestrian and a crowd. Two methods are utilized: the Sobol’-based global sensitivity analysis method and the local sensitivity analysis method. Uncertainties in all model parameters (which include bridge and human body dynamics in a walking posture, as well as dynamic force generated by humans) are considered in stochastic response estimation. Parametric analysis is then performed to investigate the influence of the variation of the mean values of the bridge modal mass, damping ratio, and natural frequency on the results of global and local sensitivity analysis. Systematic comparison of the results of global and local sensitivity analysis is performed to identify their similarities and differences. It has been found that the sensitive parameters and their importance ranking strongly depend on bridge modal properties and loading scenarios (i.e., a single pedestrian or a crowd crossing). The damping ratio and natural frequency of the human body are found to be the only two insensitive parameters. Therefore, they could be treated as deterministic parameters in the stochastic estimation of human-induced vibration. Global sensitivity analysis is recommended as a choice for the sensitivity analysis of pedestrian-induced vibration of footbridges as it leads to more reliable results, owing to the advantage of characterizing model sensitivity over the entire input spaces.

Research on Acoustic Characteristics of Low-noise Modular Hydraulic Power Unit

As the power source of a hydraulic system, hydraulic power unit also act as the main vibration and noise source. In this paper, systematic noise source characteristic and vibration performance of the low-noise modular hydraulic power unit are analysed, and specific measures to reduce vibration noise in the design process are studied. Firstly, through dry and wet mode analysis of the system, it is proved that the optimization of the pipeline and the oil tank separator plates should be emphasized in the system design. Based on that, by identifying the exciting forces of the motor and applying them to the analysis model, the vertical acceleration vibration response of 16 measuring points could be calculated. The results show that the attenuation of shaft frequency vibration noise should be focused in the acoustic design of the system. Above all, this paper provides a way in low-noise modular hydraulic power unit design.

Research on the Vibration Isolation Characteristics of Floor Vibration Isolation Slab System under Train Operation

This study takes the vibration isolation measures of building floor vibrations induced by trains as the starting point and carries out both theoretical derivation and numerical simulation. A four‐degree‐of‐freedom (DOF) multi‐dimensional vibration isolation platform (VIP) dynamics model is established based on the theoretical research of single‐level, single‐degree‐of‐freedom vibration isolation systems. Under multi‐point excitation, the model can deduce the horizontal and vertical vibration responses of the VIP system. A comprehensive analysis of the vibration isolation performance of the VIP system on the floor and how the variation of the parameters influences the performance of the vibration isolation systems are presented. Several variables, such as the thickness, stiffness, damping ratio, and the number of isolators of the VIP system, are theoretically found to have a significant impact on the vibration isolation effect of the floor VIP system. Empirical results show that the VIP system significantly affects the vibration isolation of the building floor induced by a train and has the best vibration isolation effect on the acceleration response and the worst vibration isolation effect on the displacement response.

Vertical Vibration Response of Footbridges with Fundamental Natural Frequency up to 10 Hz under Dynamic Loading by Single Pedestrian

Abstract A design spectrum of characteristic acceleration response to pedestrian-induced dynamic loading has been developed for footbridge structures. The novelty of the proposed spectrum over the ...

Debonding Analysis and Identification of the Interface Between Sleeper and Track Slab for Twin-Block Slab Tracks

For China Railway Track System (CRTS) I twin-block slab tracks, the interface between the sleeper and track slab is susceptible to damage under the coupled effect of long-term train load and external environment factors. In order to analyze the damage behavior and identify the type of debonding at the interface, this paper established a three-dimensional finite element model and introduced the cohesion zone model and concrete damaged plasticity model to simulate the interface damage and the inner-layer damage of the track slab, respectively. The interface debonding induced by the temperature effect was analyzed, and the debonding types were identified based on the obtained vertical vibration responses of the sleeper surface under the train load. The results reveal that the damage mainly occurs on the bottom and lateral sides at the interface under the temperature load. The track model can be refined further to obtain higher analysis accuracy with acceptable calculation time using the sequential loading method. The 26 damage features derived from the time domain, frequency domain, and time–frequency domain are in good representativeness in reflecting the damage information hidden in the vibration signals. Among them, the peak values (maximum vertical acceleration of the sleeper) are 55.0, 56.7, 60.3, and 61.6[Formula: see text]m/s2 for no debonding, debonding on the lateral side, debonding at the bottom, and debonding on the longitudinal side of the interface under train load, respectively. Moreover, the identification accuracy of the debonding type can reach 93.75% combining the particle swarm algorithm and support vector machine. It indicates that the proposed identification method is effective and reliable to provide theoretical guidance for developing scientific maintenance and repair strategies for twin-block slab tracks.

Active Airframe Vibration Control Simulations of Lift-offset Compound Helicopters in High-Speed Flights

This paper studies the simulations of active airframe vibration controls for the Sikorsky X2 helicopter with a lift-offset coaxial rotor. The 4P hub vibratory loads of the X2TD rotor are obtained from the previous work using a rotorcraft comprehensive analysis code, CAMRAD II. The finite element analysis software, MSC.NASTRAN, is used to model the structural dynamics of the X2TD airframe and to analyze the 4P vibration responses of the airframe. A simulation study using Active Vibration Control System(AVCS) with Fx-LMS algorithm to reduce the airframe vibrations is conducted. The present AVCS is modeled using MATLAB Simulink. When AVCS is applied to the X2TD airframe at 250 knots, the 4P longitudinal and vertical vibration responses at the specified airframe positions, such as the pilot seat, co-pilot seat, engine deck, and prop gearbox, are reduced by 30.65 ~ 94.12 %.

Effect of Lift-offset Rotor Hub Vibratory Load Components on Airframe Vibration Responses of High-Speed Compound Unmanned Rotorcrafts

This paper investigates numerically the effect of rotor hub vibratory load components on the airframe vibration responses of high-speed compound unmanned rotorcraft (HCUR) using a lift-offset coaxial rotor, wings, and two propellers. The rotor hub vibratory loads are predicted using a rotorcraft comprehensive analysis code, CAMRAD II, and the airframe vibration responses are calculated by a finite element analysis software, MSC.NASTRAN. It is shown that the vibratory hub pitch moment of a lift-offset coaxial rotor is the most dominant component for both the longitudinal and vertical vibration responses at four specified locations of the airframe. Keywords: HCUR, Lift-offset ë™ì¶•ë°˜ì „ 로터, 로터 진동 하중, 기체 진동 응답 Keywords: High-speed Compound Unmanned Rotorcraft, Lift-offset Coaxial Rotor, Rotor Hub Vibratory Loads, Airframe Vibration Responses