Nonlinear Contact Research Articles

Nonlinear Vibration of Bolted Rotor Bearing System Accounting for the Bending Stiffness Characteristics of the Connection Interface

This paper considers the discontinuous characteristics of a real aero-engine rotor system, that is, the existence of bolted connection characteristics, and establishes a new bolted connection rotor system model. Taking into account the bending stiffness and the nonlinear Hertzian contact force of the rolling bearing, the Newmark-[Formula: see text] numerical method is used to solve the system response, and the influence of the bending stiffness on the system is studied. Moreover, the effects of bending stiffness and eccentricity on the system dynamics are analyzed. The results show that the nonlinear phenomena of the system are more abundant and the critical speed of the system is higher when the bending stiffness is involved. With the increase of bending stiffness, the critical speed of the system increases, and the frequency component of the system becomes more complex. Then, the influence of eccentricity on the system is studied based on the bending stiffness. It is found that the greater the eccentricity, the greater the critical speed of the rotor and the greater the amplitude of the main frequency. In the case of the same eccentricity, the main frequency increases as the rotational speed increases, and the frequency doubling component appears in the 2-period motion. This paper provides a basis for predicting the nonlinear response of bolted rotor-bearing system.

Hydro-mechanical modelling of interaction between monopiles and cross-anisotropic sandy seabed subjected to wave loadings

ABSTRACT Cross-anisotropy is a typical feature of marine sediments. To explore the monopile-seabed interaction in cross-anisotropic sandy seabed subjected to wave loadings, a hydro-mechanical model is established and the nonlinear monopile-soil contact behaviours such as slip and separation are considered. It is shown that, when the seabed properties in the horizontal plane were kept constant, the increase of seabed anisotropy results in three effects: A) the decrease of vertical coefficient of permeability k V, B) the increase in vertical elastic modulus E V and shear modulus G V, and C) the decrease of Poisson’s ratio µ HV. Effect A will lead to a reduction of excess pore water pressure and an aggravation of momentary liquefaction around the monopiles. Effect B is conducive to the decrease of lateral displacement and bending moment of the monopiles. Besides, wave-induced settlement of the monopiles is observed and is found to be alleviated by effect B.

A new general class of systems of elliptic quasi-variational–hemivariational inequalities

In this paper we study a general class of systems of strongly coupled quasi-variational–hemivariational inequalities with implicit constraints in reflexive Banach spaces. Each inequality contains a convex potential, a locally Lipschitz superpotential, and a implicit obstacle set. The solvability of the system is established based on a fixed point approach, monotonicity arguments, and nonsmooth analysis. The result generalizes several theorems on various particular cases on variational, variational–hemivariational, and quasi-variational inequalities. We illustrate the applicability of the abstract theory by a nonlinear static thermoelastic frictional contact problem with implicit obstacles for which we provide existence and regularity results.

Influence analysis of overlying soil layer to seismic behavior of inclined liquefiable soil and pile interaction system

The statistical data of earthquake hazard indicate that the liquefaction and large lateral flow deformation of ground is one of the main reasons of pile foundation failure. It is significant to focus on the seismic dynamic behavior of pile foundation in inclined liquefiable soil. Based on the Opensees finite element platform, an integrated finite numerical model of inclined liquefiable soil-pile group-structure interaction is established in this study, according to the shaking table model test of inclined liquefiable soil. The nonlinearity of pile-soil contact and the shear localization of soil layer are considered in the numerical simulation. The comparison of the numerical simulation result with the shaking table test results are verified. In order to discuss the influence of different overlying soil layer on the seismic behavior of soil and pile system, a typical inclined liquefiable soil-pile group-structure interaction finite element model is established by the proposed numerical simulation method. The results show that the overlying soil layer has an obvious influence on the seismic dynamic behavior of the pore pressure, the horizontal displacement of soil and pile. The increase of the thickness of overlying soil can reduce the liquefaction degree of sand and improve the mechanical performance of pile foundation.

Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems

Abstract This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for interface problems in nonlinear elasticity. It concerns 𝑝-Laplacian-type Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality.

Monitoring of breathing cracks of RC beams based on nonlinear vibro-acoustic modulation technique

ABSTRACT For challenges of early microcrack monitoring of reinforced concrete (RC) structures, a nonlinear vibro-acoustic modulation (VAM) based study was carried out, aiming at investigating the influence law between the excitation signal form and the nonlinear effect of sensing signals through both finite element analysis (FEA) and experimental validation. The mechanism of the nonlinearity in sensing signals coming from microcrack surface vibration collisions due to the breathing effect was found which is the theoretical basis of the VAM-based damage detection. The results show that the nonlinear modulation effect is the highest at the resonant frequency of the structure. The side frequency (SF) amplitude of VAM-based sensing signal in the RC beams with microcracks (damage degree between 0% and 70%) is obvious, but when the cracks continue developing, the effective contact area decreases sharply during the crack opening and closing process due to the nonlinear contact between interfacial crack surfaces. As the width of microcrack is altered from 0 nm to 100 nm, the normalised nonlinear coefficient β is reduced from 0.4 to 0.06 in the approximate form of power function, which can be used to characterise the damage development of the early cracks in RC structures.

A fully nonlinear three-dimensional dynamic frictional contact analysis method under large deformation with the area regularization

A fully nonlinear three-dimensional dynamic frictional contact analysis method under large deformation with the area regularization

Detection and Identification of Nonlinear Contact Dynamics at Workpiece Clamping Positions

1. HESSE S., KRAHN H., EH D., 2012, Betriebsmittel Vorrichtung - Grundlagen und kommentierte Beispiele, Carl Hanser Verlag, München. Google Scholar

Investigation of Lateral Stability of UHPC Beams Supported by Bearing Pads Considering the Nonlinear Lift-Off Effect

Ultrahigh-performance concrete (UHPC) is an advanced cement-based material with a compressive strength greater than 150 MPa. The application of UHPC on prestressed girders allows the design of very long spans with thin sections. However, the increased slenderness, low lateral flexural stiffness, flexible supports, and beam imperfections make lateral instability critical. Therefore, this paper presents an analytical prediction of precast beams’ behaviors considering the nonlinear contact interaction with the bearing pads. The nonlinear geometric theory for the slender element is coupled with the nonlinear contact mechanism developed between the beam and pad through the energy approach. The proposed solutions are compared with the equations available in the literature that consider the linear stiffness contact interaction. Changes in the limit load of up to 84% were a result of the lift-off effect (contact interaction). From the results, the UHPC is highly sensitive to lateral instability, giving a maximum load/dead weight ratio of up to 1.08 where the common technical recommendation is greater than four.

Fusing Expert Knowledge with Monitoring Data for Condition Assessment of Railway Welds.

Monitoring information can facilitate the condition assessment of railway infrastructure, via delivery of data that is informative on condition. A primary instance of such data is found in Axle Box Accelerations (ABAs), which track the dynamic vehicle/track interaction. Such sensors have been installed on specialized monitoring trains, as well as on in-service On-Board Monitoring (OBM) vehicles across Europe, enabling a continuous assessment of railway track condition. However, ABA measurements come with uncertainties that stem from noise corrupt data and the non-linear rail-wheel contact dynamics, as well as variations in environmental and operational conditions. These uncertainties pose a challenge for the condition assessment of rail welds through existing assessment tools. In this work, we use expert feedback as a complementary information source, which allows the narrowing down of these uncertainties, and, ultimately, refines assessment. Over the past year, with the support of the Swiss Federal Railways (SBB), we have assembled a database of expert evaluations on the condition of rail weld samples that have been diagnosed as critical via ABA monitoring. In this work, we fuse features derived from the ABA data with expert feedback, in order to refine defection of faulty (defect) welds. Three models are employed to this end; Binary Classification and Random Forest (RF) models, as well as a Bayesian Logistic Regression (BLR) scheme. The RF and BLR models proved superior to the Binary Classification model, while the BLR model further delivered a probability of prediction, quantifying the confidence we might attribute to the assigned labels. We explain that the classification task necessarily suffers high uncertainty, which is a result of faulty ground truth labels, and explain the value of continuously tracking the weld condition.

Dynamic Analysis of the High Speed Train–Track Spatial Nonlinear Coupling System Under Track Irregularity Excitation

Track irregularity is the main factor that affects the safety and comfort of high-speed railway. It is important to study the influence of the track irregularity on the safety service of high speed train–track coupling system. In this paper, a vehicle–track spatial nonlinear coupled system dynamics model is developed with FEM. The model includes vehicle subsystem and track subsystem, which are coupled by wheel–rail interface. The vehicle subsystem is a 31-DOF spatial vehicle model, and the track subsystem is a three-dimensional slab track model composed of the rail, rail pad and track slab. Considering wheel tread profile and rail head profile, the wheel–rail spatial contact geometry relationship is established, and the “Trace method” and the “Minimum distance method” are used to search for wheel–rail contact points. Considering the nonlinear contact between the wheel and the rail, a numerical approach is presented, where the “Trace method” is embedded into the algorithm for solving the vehicle–track nonlinear coupling dynamics equation by cross iteration, realizing searching the wheel–rail contact points and solving the vehicle–track nonlinear coupling equation simultaneously, which greatly improves the efficiency of numerical analysis. As application examples, the dynamic responses of a high speed train–track spatial nonlinear coupled system excited by the track V-shaped local profile irregularity and the track torsional irregularity are analyzed. The results show that the algorithm is effective in solving the vehicle–track spatial nonlinear coupled system dynamics problem, and the track irregularity has significant influence on the dynamic response of vehicle and track structure.

A new approach to model a system with both friction and geometric nonlinearity

This paper presents a new reduced-order model that can capture the nonlinear dynamics of a structure containing both friction and geometric nonlinearity, and proposes a procedure to derive the parameters of the model from quasi-static simulations. The Single-mode Implicit Condensation and Expansion (SICE) method was recently shown to be capable of capturing the resonant behavior of a geometrically nonlinear structure, and the modal Iwan model has proven effective at capturing the hysteretic behavior of a mode that exhibits nonlinearity due to friction. This paper combines the two into a new model, referred to here as the Iwan model with Geometric Nonlinearity (or the IGNL model). It consists of an Iwan model with an additional spring-slider unit, where the slider has infinite strength and the spring consists of polynomial terms that define the SICE-ROM. A procedure is also proposed to use Quasi-Static Modal Analysis (QSMA) to estimate the parameters of the IGNL model from a set of nonlinear force–displacement curves. Existing literature shows how QSMA can be used to characterize the force–displacement behavior of a nonlinear mode where the nonlinearity is due to friction or bending–stretching coupling, but not both simultaneously. This paper proposes certain adjustments to the QSMA procedure so that the two forms of nonlinearity can be isolated. Two case studies are presented to test the efficacy of the IGNL model, one consisting of a simple spring–mass model and the second, a finite element model containing both contact and geometric nonlinearity. The proposed method is shown to be significantly faster than performing dynamic simulations to estimate the amplitude-dependent frequency and damping behavior.

Damage detection in composite laminates using nonlinear guided wave mixing

This paper presents a delamination damage detection technique based on the nonlinear response of Lamb waves in composite laminates. In the approach, a network of transducers is employed to sequentially scan the structure by actuating and receiving dual guided waves. Using combined frequency waves originated due to contact nonlinearity when the incident dual frequency wave interacts with the damage, a damage localization imaging algorithm is proposed to locate the damage and determine the damage location. The proposed damage localization imaging algorithm is based on analysing the cross-correlation of the signal envelope at combined frequency wave with the excitation pulse envelope at incident waves for each transducer pair, the damage localization image is constructed. A numerical study using an experimentally validated finite element model is used to verify the proposed damage detection technique. The results of the numerical study show that, despite the small amplitude of the nonlinear components, the proposed method can effectively predict the damage location, and it does not require baseline measurements, which makes it potential to be a baseline-free damage detection technique.

Effect of asymmetric shroud gap and shroud friction coefficient on vibration response of shrouded blades

Based on the problem of shroud gap and shroud friction having impact on the blade collision vibration, a three-blade dynamic analysis model considering shroud friction and asymmetric gap is established in the present work. In order to study the effect of asymmetric gap and shroud friction coefficient on the vibration of the twisted shrouded blade in practice. The differential equations of shroud oblique collision between the twisted shrouded blade and adjacent blades were established, and a nonlinear Hertz contact force and an exponentially decaying friction model were used to describe the shroud contact collision force and friction, respectively. Numerical simulation and experiment are used to verify the vibration response of the blade under different gaps. The results show that the shroud movement under the asymmetric gap is more complicated than symmetric gap. The presence of shroud friction causes the passive blades to enter a cyclic motion. And shroud friction coefficient increases will decrease the amplitude of the blade.

Nonlinear Torsional Stiffness Analysis of Harmonic Drives Using Flexible Multibody Dynamics Simulation

Predicting the nonlinear torsional stiffness of harmonic drives is important not only for system control but also for the further development of the drive. However, it is difficult to predict the torsional stiffness because of the elastic deformation of the flexspline and the many contacts involved. Furthermore, nonlinear dynamic contact simulations between the elastic components of the harmonic drive are disadvantaged by high computational burden and convergence problems. To address these challenges, we establish a flexible multibody modeling process using augmented formulations of a floating reference frame to simulate the operation of the harmonic drive. The elastic deformation of the flexspline and the dynamic contacts between the main components are considered in the reproduction of the contact mechanism of the drive. Coordinate reduction techniques are used to properly replicate an elastic shaft, enabling the effective simulation of flexible multibody dynamics, including nonlinear elastic tooth contact analysis. The performance of the proposed modeling process is evaluated using catalog and experimental data on two types of standard harmonic drives (SHG-25-100-UH and SHG-40-100-UH). The hysteresis curve is predicted through flexible multibody dynamics simulation and the accuracy of parameters of torsional stiffness is approximately 91.7% on average. The proposed modeling method can be improved to predict other measures of performance and it remains a potential research topic.

Experimental research on the contact force of the bi-directional pig in oil and gas pipeline

The migration process of the pig in oil and gas pipeline is a complex dynamic problem. During the pigging operation, the variation of friction force caused by the nonlinear contact between the sealing disc and the pipe wall is the key factor affecting the dynamic characteristics of the pig motion. At present, the existed pigging models for predicting pigging behavior regard friction as an invariant constant. Experimental research indicates that the friction force of the pig varies with the contact force and the lubrication conditions. Therefore, the assumption that the friction force is constant cannot reflect the friction dynamic characteristics of the pig during pigging, and will also affect the accuracy of the pigging model. Exploring the variation of friction force of pig under different conditions is the basis of establishing the transient dynamic model of a pig. As a result, in this paper, a method of direct measurement of contact force between the pig and the pipeline is presented, the contact force, the friction force, as well as the friction coefficient of the pig are obtained from the experiment. Research results in this paper can help to establish a more accurate dynamic model of pig.

Finite Element Analysis of a Semi-Rigid Endplate Beam-to-Column Joint with Stiffeners

This article examines the mechanical behavior of steel endplate beam-to-column joints with different stiffeners under bending moment. This type of connection is commonly used in steel frameworks to transmit loads from beams to columns. In frame design procedures, engineers tend to consider beam-to-column joints either ideally pinned or fully rigid. The present study aims to show their semi-rigid behavior by analyzing the characteristics of the relation between the bending moment and the rotation of the studied connection. The analysis is based on the development of a finite element model considering the material, geometrical and contact nonlinearities between the components. Three types of stiffeners are introduced in different positions to investigate their effect on the global behavior of the joints. The moment rotation curve is defined together with the procedure of determination of the initial rotational stiffness, the elastic and plastic moments of the connection. The numerical model is validated by comparing the moment rotation curves with those of similar studies available in the literature and also with the design approach proposed by Eurocode 3. The obtained results have showed that the use of stiffeners in the column web or on the endplate increases significantly the rigidity of the studied connection. The failure modes have been discussed in detail for each configuration with respect to the rotation capacity and the initial stiffness. Finally, the model has been used to show the influence of three bolts classes on the ultimate load of the joints and the deformation of the endplate and bolts at failure.

An elastic-plastic kinking layer model for parallel-to-grain wood embedment behavior considering wood drilling damage

This paper presents the results of the experimental and numerical studies on the influence of drilling damage of wood on the wood embedment behavior. Wood drilling tests were conducted to quantify the distribution of wood residual strain by use of digital image correlation technique. Parallel to wood grain repetitive compression tests were also conducted to determine the mechanical properties of wood within the kinking zone. Wood half-hole bolt embedment tests were conducted, and a wood kinking layer model was proposed and incorporated into a FEM model for the wood embedment behavior simulation. The model predictions were compared with the embedment test results and results from FEM models with different consideration of the weakened wood around the bolt holes. It was found that drilling can develop significant parallel and perpendicular to grain and shear residual strain in the surrounding wood. The distribution and magnitude of the residual strains were correlated with the hole diameter and drilling speed, and the thickness of a kinking layer can be taken as 1/13 and 1/7 of the hole diameter under the low and high drilling speeds considered in this study, respectively. It was observed from the repetitive tests of wood that during the steady-state kinking process, wood exhibited nearly constant peak stress and reloading modulus of elasticity. The FEM model with the proposed kinking layer model achieved a better agreement with the test results than FEM models based on wood foundation theory or a nonlinear contact model regarding the embedment elastic modulus, the maximum load, and the distribution of the strain in the embedment zone.

Dynamic characteristic of thrust-vectoring nozzle adjusting mechanism considering clearance of motion joint

An essential device for managing the vectoring nozzle’s thrust direction is the thrust-vectoring nozzle adjusting mechanism. The attitude of an aircraft’s flight may be changed by adjusting the vectoring nozzle’s airflow, which affects the direction of thrust. The adjusting mechanism’s motion precision and operational stability are crucial in this procedure. In this paper, the influence of the clearance of the motion joint on the dynamic characteristics of the thrust-vectoring nozzle adjusting mechanism under different flight conditions are studied. First, a dynamic model of the thrust-vectoring nozzle adjusting mechanism that takes into account the clearance and friction properties of the motion joint is constructed by combining the Lagrange equation of the first sort with the mixed contact force model and the LuGre friction model. Second, the variation law of nonlinear contact stiffness is explored, and the precision of the dynamic model is confirmed by contrasting the results of the numerical simulation with those of the Simulink simulation. Finally, the simulation results reveal that while the motion joint’s clearance causes the adjusting blade’s velocity and acceleration to vibrate violently and momentarily during early operation, this clearance has minimal effect on the precision of blade motion throughout the stable phase.

Can transient simulation efficiently reproduce well known nonlinear effects of jointed structures?

Although joints are omnipresent in engineering structures, their proper consideration in simulations is still a challenging area of research. This is because joints introduce local nonlinearities which lead to load and preload-dependent resonance frequencies and damping, mode coupling, high variability of contact area and contact pressures. The knowledge about those phenomena has been gathered via systematic experimental testing. A meaningful digital or virtual replication of such tests would require a transient numerical time integration, where besides all dynamic effects, the local and fine discretized nonlinear contact and friction forces in the joint also need to be considered. The Finite Element Method can only provide this theoretically since the necessary computation times make practical use almost impossible. Newer methods, where the joint deformation is represented via so-called contact modes instead of nodal degrees of freedom, offer a perspective for transient virtual tribomechadynamics. This paper is devoted to the following question: Is it possible for the first time to numerically reproduce real experiments with low computing times so that the previously mentioned nonlinear effects can be observed? In this work the transient numerical response of a jointed structure due to different loads (sine sweep, sine, step and impulse) is evaluated and related to measurements. The application of the Hilbert Transform to the time data, as known from measurements, reveals load and preload dependent eigenfrequency and damping. Other measured phenomena like mode coupling, a high variability in the contact area and resulting contact force can also be observed numerically. The results are in good qualitative agreement with the experiments. This work proves the principal capability of virtual tribomechadynamics as an efficient complement to real testing for gaining deeper insight. All the powerful measurement methods can directly be applied to simulated data.