Nonlinear Contact Research Articles

Research on non-linear dynamic simulation model of feeding system

Abstract The automatic gun feeding system is an important mechanism for achieving continuous shooting, but due to its complex structure, there is a lot of contact during firing, and its reliability is lower. To improve the reliability of the feeding system and its dynamic characteristics, a multi rigid body dynamic simulation model of the feeding system considering contact nonlinearity was established based on nonlinear dynamics theory. The dynamic characteristics of the feeding system were analyzed for single and continuous firing. The research results indicate that the presence of contact nonlinearity increases the interaction forces between components and also increases the uncertainty of component motion.

The stick-slip bending behavior of the multilevel helical structures: A 3D thin rod model with frictional contact

The multilevel helical structures in various engineering and natural fields offer excellent deformation flexibility and load bearing capabilities. Understanding the interplay between the local frictional contact and the geometric characteristics of the helical structure under complex external loads has attracted considerable interest. In this work, the effect of local frictional contact behaviors on the bending in multilevel helical structures is investigated by using a combination of theoretical modeling, finite element (FE) simulations, and experiments. In the case of pure bending, the kinematic parameters of the bent multi-stage helix are derived concisely by the idea of the kinematic analogy. The bending stiffness of the multi-stage helix is further obtained. In the case of the combined tension/torsion and bending, the 3D thin rod model incorporating Coulomb’s friction is established to describe the mechanical responses. It is found that the relationship between equivalent bending stiffness and the laying angle exhibits nonlinearity. A comparison with the classical Papailiou model reveals that, for helical structures at large laying angles, the influence of friction is primarily determined by the internal force in the tangential direction, which is the core assumption of the Papailiou model. However, in the case of small laying angles, the helical twisting characteristics and the contribution of the internal forces and moments in the other two directions (normal and binormal directions) to the friction cannot be ignored. Subsequently, a multilevel frictional contact transmission formulation is proposed according to the force action–reaction principle. Based on the above formulation, the non-simplified thin rod equations with Coulomb’s friction are extended to describe the multilevel stick-slip bending behaviors of the second stage cable (3*3). The dissipation capacity of helical structures is evaluated quantitatively under the hysteretic bending. Finally, the theoretical model is verified by FE simulations and experimental results. This work provides insights for unveiling the intrinsic relationship between the nonlinear bending and local frictional contact behaviors in the multilevel helical structures.

Schistosomiasis mathematical model in a spatially heterogeneous environment

Schistosomiasis is classified by WHO as a neglected tropical disease. Recent research works have shown that large-scale development projects involving massive population displacement and water irrigation, such as the construction of dams, lakes, and the development of agricultural areas, favour the proliferation of bilharzia. These observations motivate us to propose a reaction–diffusion model to assess the role of the displacements of humans, snails, cercaria, miracidia in the transmission dynamics of Schistosomiasis. The model incorporates a general non-linear contact functions and density-dependent parameters. The aim is to better understanding the role of spatial interactions on the spread of Schistosomiasis, in order to propose appropriate recommendations for the control of that silent threat. We characterize the basic reproduction number R0 of the model. The uniform persistence theory, the maximum principle are used to conduct an in-depth analysis of both the homogeneous and heterogeneous models. Theoretical results are illustrated through numerical simulations.

Contact analysis of output mechanism of cycloidal pinwheel reducer

In order to study the effect of design parameters on the contact performance of cycloid reducer, a new contact collision force model applicable to various restitution coefficients is proposed. Firstly, based on the L-N nonlinear contact theory and improved Winkler model, a contact force model with contact depth index and damping was proposed. Secondly, Hertzian contact theory was used to clarify the contact area, precise position and relative contact speed between the output pin and the cycloidal wheel in the presence of a clearance. By using the improved contact force model and simulation analysis, the effects of structural design parameters and working condition parameters on contact force were discussed. Finally, with the goal of reducing the contact force and volume of the reducer, the NSGA-II multi-objective genetic algorithm was used to construct an optimization model for the structural parameters of the reducer. The results show that the optimized structural parameters can effectively reduce the contact force of the output mechanism.

A nose beam segmental construction process for large-span composite emergency bridges

The effectiveness of the incremental launching method with lightweight, flexible nose beam in the construction and erection of emergency bridges with large-span composite materials is investigated through a combined experimental and numerical study. A theoretical model is developed to characterize the additional bending movement induced during the flexible nose launching process and analyze stress fluctuations in structural components during critical launching stages, providing theoretical underpinning the for lightweight nose beam design. Results indicate that the stress attributable to the additional bending moment during critical launching stages constitutes approximately 9.6 %, significantly impacting lightweight nose beam design con-siderations. Additionally, it was shown that conventional static analyses are difficult to adequately capture the internal force changes during the launch of a flexible nose beam. Therefore, a finite element model accounting for geometric and contact non-linearity is proposed, exhibiting higher precision in predicting additional bending movement values compared to traditional finite element models. The accuracy of the finite element model is confirmed through scaled-down experiments.

An algorithm based on B-differentiable equations method for solving problems involving frictional contact coupled with concrete plastic damage

In this paper, an algorithm is proposed to solve the frictional contact problems while considering elasto-plastic material properties. The static and dynamic solution procedures are derived in incremental form, respectively. The proposed method employs a two-layer iteration strategy. In the outer iteration layer, the equilibrium equations are solved, with the stress and stiffness matrix updated at each iteration. Within the inner iteration layer, the contact force is calculated, where the contact equations, expressed as B-differentiable equations, incorporate only contact conditions in normal and tangential directions, and the contact flexibility matrix, obtained by applying unit force pair to all contact node pairs in turn, is introduced. Consequently, the solution for nonlinear equilibrium equations and contact equations is decoupled, requiring only one decomposition of the stiffness matrix for each calculation of the contact flexibility matrix, as it remains constant within the contact iteration layer. In addition, the constitutive model of concrete developed by Lee and Fenves is utilized. This model adopts two independent variables to describe tensile and compressive damage, together considering the strength recovery of the concrete. Numerical examples demonstrate the accuracy of the proposed method by comparing the results from Abaqus. Furthermore, the present algorithm is applied to static and dynamic analyses of a concrete arch dam with several transverse joints, where the effects of gravity, water level, the number of contact surfaces, and seismic load are considered, and some conclusions are obtained.

Developing a scalable analytical framework for predicting the contact behavior of elastic rings against rigid surfaces

An elastic ring interacting with rigid surfaces is a fundamental engineering challenge with vast practical implications in various disciplines. However, the exploration of closed-form solutions for this issue has been limited, and existing studies often present complex, numerically unstable solution methods influenced by specific boundary conditions. Furthermore, the lack of scalable design principles for the ring-in-contact scenario has hindered its broader application across different geometries and materials. This study introduces a streamlined analytical and numerical approach to predict the contact behavior of orthotropic rings against centrosymmetric rigid surfaces, encompassing both flat and curved surfaces. Our approach, which simplifies the closed-form solution for extensible Timoshenko curved beams coupled with a contact algorithm that prevents penetration, yields robust and accurate predictions of nonlinear contact behaviors in elastic rings, including deformation patterns, contact angles, stresses, and stiffness. Additionally, we present a design map that serves as a scalable guideline for engineering elastic rings in contact, facilitating the choice of geometry and materials, such as ring radius, thickness, and elastic moduli. This research enhances the theoretical underpinnings of elasticity concerning ring contact and expands the engineering viewpoint on designing elastic rings in various contact scenarios.

Study on the tribological performance at the interface between a steel wire rope and groove during a twisting process

In actual use, a steel wire rope is often stretched and twisted around a groove, increasing the risks of contact fatigue, friction and wear at the rope-groove interface under a long-term service condition. With the consideration of influence factors such as the nonlinear contact and wear between the rope and groove, the tribological performance at the rope-groove interface during a twisting process is analyzed in this study. A winding rope-groove model is first established in order to obtain the contact and sliding solutions at the interface between the rope and groove, which are then used as the load conditions of a simplified local model that is built for wear solution using a modified Archard's wear theory. Based on the finite element simulation software ABAQUS, the ALE adaptive mesh technology and UMESHMOTION subroutine secondary development are adopted to analyze the evolutions of wear topography and contact behavior between the rope and the groove. The results show that the twisting movement of the steel wire rope around the groove causes an interfacial wear between them. The wear scars occur on the outside wire of the steel wire rope and the bottom area of the groove, and the wear scar on the groove is smaller but deeper. A ring-shaped region of stress concentration happens near the edge of wear region. As the wear process proceeds, the depths and dimensions of the wear scars increase, while the contact pressure decreases. The contact performance and wear change dramatically at the beginning of wear process and tend to be stable subsequently. An increment of lay angle of the outside wire aggravates the wear and contact between the steel wire rope and the groove.

On fuzzy fractional differential inclusion driven by variational–hemivariational inequality in Banach spaces

The aim of this paper is to examine an evolution problem (FFDIVHVI) involving a fuzzy fractional differential inclusion and a variational–hemivariational inequality (VHVI) in Banach spaces. First, we show a uniqueness and existence theorem for VHVI under the theory of monotone operators and the surjectivity theorem. Then, by utilizing fixed point theorem for multivalued contraction mapping and fuzzy set theory, we establish the existence result for FFDIVHVI. In addition, it is proven that the collection of all mild trajectories of FFDIVHVI exhibits compactness. Finally, we illustrate the applicability of the abstract theory by a nonlinear quasistatic thermoelastic frictional contact problem for which we provide existence results.

Study on seismic response of liquefiable soil-pile group considering pile cap and soil contact

In this paper, based on the centrifuge test of liquefied soil-pile foundation system, a numerical model of liquefied soil-pile foundation-structure system is modelled by using OpenSees platform. In the simulation model, the friction effect between liquefied ground and low pile cap is considered, and the method of establishing virtual nodes is used to deal with the non-linear contact between liquefiable soil and low pile cap. The rationality and effectiveness of the numerical simulation method adopted in this paper has been verified and evaluated by comparing with the results of centrifuge experiments. A typical liquefaction soil-pile integrated finite element model is modelled using validated numerical simulation methods. The law of seismic response of the pile foundation system with different embedding depths of pile cap, different contact modes between the pile cap and saturated sand, and the thickness of the overlying saturated loose sand layer are discussed. The results show that the pile cap and pile foundation in the high pile cap system show higher seismic response characteristics than the other three low pile cap system conditions; Under the condition of different contact modes between the pile cap and the surrounding saturated sand, the peak bending moment and residual displacement of the pile foundation calculated by the bond contact are larger than calculated by the friction contact, and the deformation of pile is more significant. By comparing the working conditions of different thicknesses of overlying saturated loose sand layer, it is found that the degree of liquefaction in shallow soils is less affected by thickness of the saturated loose sand. As the thickness of saturated loose sand layer increases, the peak bending moment and residual displacement at the top of the pile also gradually increase. The change of peak bending moment at the soil interface is more obvious.

Prospects of silicide contacts for silicon quantum electronic devices

Metal contacts in semiconductor quantum electronic devices can offer advantages over doped contacts, primarily due to their reduced fabrication complexity and lower temperature requirements during processing. Some metals can also facilitate ambipolar device operation or form superconducting contacts. Furthermore, a sharp metal–semiconductor interface allows for contact placement in close proximity to the active device area avoiding damage caused by dopant implantation. However, in the case of gate-defined quantum dots in intrinsic silicon, the formation of a Schottky barrier at the silicon–metal interface can lead to large, nonlinear contact resistances at cryogenic temperatures. We investigate this issue by examining hole transport through metal oxide-semiconductor transistors with platinum silicide contacts on intrinsic silicon substrates. We extract the contact and channel resistances as a function of temperature and improve the cryogenic conductance of the device by more than an order of magnitude by implementing meander-shaped contacts. In addition, we observe signatures of enhanced transport through localized defect states, which we attribute to platinum clusters in the depletion region of the Schottky contacts that form during the silicidation process. These results showcase the prospects of silicide contacts in the context of cryogenic quantum devices and address associated challenges.

Damage characteristics and mechanical properties of CRTS III track structure in curved sections under longitudinal uneven subgrade settlement

This paper first presents a CRTS III track structure (TS) model specifically designed for curved sections, highlighting its adjustable superelevations feature that enhances adaptability to various high-speed railway curve profiles. The model considers the distribution of steel bars within the TS, concrete damaged plasticity, as well as contact nonlinearity. Afterward, the intricate impacts of longitudinal uneven subgrade settlement (LUSS) position (7 positions), amplitude (5–30 mm), wavelength (5–30 m), and TS superelevation (15–175 mm) on structural damage, stress, deformation, and interlayer gap are studied. The findings reveal that: 1) Under different LUSS positions, the concrete base (CB) experiences the most severe damage, particularly on its thick side. For the TS with 175 mm superelevation, in the wavelength range of 10–20 m, the maximum damage value of CB exceeds 0.9 when LUSS amplitude reaches 20 mm. With the movement of LUSS position, the main damage position of CB changes obviously. When the concrete stress reaches the tensile strength, the steel bars located in adjacent positions progressively assume the primary role in load-bearing. 2) The influence of LUSS on TS deformation and interlayer gap is inevitably associated with the distance between settlement center and expansion joints. Interlayer gaps vary among structural components, which are primarily distributed near settlement center, expansion joints, and settlement edges. 3) As the amplitude increases, both CB and self-compacting concrete layer (SCCL) damage are aggravated. Increasing wavelength initially causes damage to increase, then decrease, and 10–20 m is the most unfavorable wavelength range for most cases. 4) The effect of superelevation on TS damage is complex, varying with structural components and settlement characteristics. In most cases, as superelevation increases, the damage to CB increases, whereas the deformation decreases.

Dual flexible contact material removal model for robotic disk grinding

High-precision machining of flexible materials, such as rubber, presents a challenge in manual grinding. The implementation of robotic grinding has the potential to significantly enhance machining precision and efficiency. Normally, an accurate material removal model is needed for precise planning of the robotic grinding parameters. Existing models are mostly built for metal materials, and neglect the large deformation of flexible workpieces, resulting in deficiencies in accuracy and generalization. To this end, a nonlinear dual flexible contact force model is presented, considering the significant deformation of both the tool and the workpiece, to characterize the dual flexible contact mechanism. Then, the contact force model is combined with the Preston equation, yielding the material removal model. The effectiveness and superiority of our contact force model and material removal model are substantiated by force–displacement experiments and robotic grinding experiments, respectively. These experiments show a remarkable reduction of 68.17% in the root-mean-square error (RMSE) for the contact force model and a noteworthy 29.31% decrease in RMSE for the material removal model.

Establishing mechanisms for nonlinear collector tribodynamics of magnetization under ferroresonance regimes

The paper considers a parallel electromagnetic oscillating circuit with a nonlinear inductance under conditions of excitation of ferroresonances. Physical mechanisms of dynamic self-regulation of the system of spin magnetic moments of ferromagnetic and ferrimagnetic dielectrics in the surrounding magnetic field are established. It is shown that upon entering the magnetic saturation regime, the effect of dynamic antiferroresonance is observed, due to the cyclic reversal of magnetization in the internal magnetic field. This effect has a collector character and corresponds to the maximum potential energy of the magnetic moment in the field and the antiparallel orientation of the moment with respect to the field. Such regimes are realized in thermodynamically non-equilibrium conditions and are correlated with unstable equilibrium positions of the corresponding mechanical analogues. The resulting forms of oscillations correlate with the dynamics of an inverted pendulum and have a significantly non-harmonic character. Autosynchronization of frequencies and nonlinear mixing of such forms with quasi-static modes imitating the time form of external excitation of oscillations were revealed. It is shown that the nonlinearity of ferromagnetic elements self-limits the height of resonance maxima. And on the other hand, it contributes to the cascade transport of energy by the spectrum of disturbances, which can have negative consequences when exciting low-frequency ferroresonances in power grids. The effect of dynamic antiferroresonance has the opposite direction to the known quasi-static behavior of the system of spin magnetic moments in an external field and must be taken into account when calculating and operating electrical systems with nonlinear inductances. Examples of collector self-oscillating modes similar in their physical mechanisms in nonlinear contact tribodynamics systems are given

Seismic performance of shuttle-shaped double-restrained buckling-restrained brace: Experimental investigation and numerical analysis

To solve the problems of excessive cross-section size and self-weight and buckling instability of super-long buckling-restrained brace, a new lightweight shuttle-shaped double-restrained BRB (SDR-BRB) is proposed in this study. Firstly, cyclic loading experiments are conducted on three SDR-BRB specimens to investigate their failure mode and seismic performance. Then, a finite element model considering geometric, material, and contact nonlinearity is established and verified by experimental results. Finally, the effect of the restraining ratio on the hysteretic performance of SDR-BRB is studied by parameter analysis, and the restraining ratio requirement of the energy-dissipation type of SDR-BRB that meets the ductility requirements is obtained. The results show that SDR-BRB has stable and plump hysteretic curves, excellent energy-dissipation capacity, and low cycle fatigue performance, exhibiting obvious strain-strengthening characteristics. The restraining ratio is an important factor affecting the overall stability and failure mode of SDR-BRB, and it is recommended that the restraining ratio requirements of the SDR-BRB should be 2.25. The above research can provide a design reference for the practical engineering application of SDR-BRB.

Intelligent identification of differential subgrade settlement of ballastless track system based on vehicle dynamic responses and 1D-CNN approach

The millimeter-scale deformation control standards of high-speed railways make the monitoring and identification of subgrade settlement a key technology, especially for ballastless track systems. Addressing the uncoordinated deformation between track and subgrade caused by high track stiffness, this paper proposes an intelligent identification method for subgrade settlement based on vehicle vibration signals and deep-learning technology. Firstly, a high-speed vehicle-ballastless track-subgrade coupled dynamics model considering the track-subgrade nonlinear contact state is utilized, to obtain various vibration responses of the vehicle subsystem due to differential subgrade settlement. After data preprocessing, a multi-channel one-dimensional convolutional neural network (1D-CNN) is established to extract features from the vehicle vertical acceleration dataset and output subgrade settlement status automatically. Finally, the robustness of the model is verified using Gaussian white noise. The research indicates that the vertical accelerations of the car body and bogie frame contain dynamic characteristics caused by medium-long wavelength settlements, while the vertical acceleration of the wheelset is more sensitive to short-wavelength settlements. It is feasible to identify the degree of subgrade settlement using car body, bogie frame and wheelset vertical accelerations as parameterized multi-source input of the 1D-CNN network. The three-channel input model significantly improves the identification accuracy and demonstrates the robustness against noise interference compared to the single-input and dual-input models. This method can effectively enhance the identification capability of ‘concealed’ subgrade settlements in high-speed railways, offering a scientific methodology for status maintenance of ballastless track lines.

Bogdanov–Takens Bifurcation of Kermack–McKendrick Model with Nonlinear Contact Rates Caused by Multiple Exposures

In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes a Bogdanov-Takens bifurcation with codimension 2. During the bifurcation process, numerous lower codimension bifurcations may emerge simultaneously, such as saddle-node and Hopf bifurcations with codimension 1. Finally, employing the Matcont and Phase Plane software, we construct bifurcation diagrams and topological phase portraits. Additionally, we emphasize the role of symmetry in our analysis. By considering the inherent symmetries in the system, we provide a more comprehensive understanding of the dynamical behavior. Our findings suggest that if this occurrence rate is applied to the SIR model, it would yield different dynamical phenomena compared to those obtained by reducing a 3-dimensional dynamical model to a planar system by neglecting the disease mortality rate, which results in a stable nilpotent cusp singularity with codimension 2. We found that in SIR models with the same occurrence rate, both stable and unstable Bogdanov-Takens bifurcations occur, meaning both stable and unstable limit cycles appear in this system.

Unloading properties based elastoplastic continuous contact force model: Restitution and stiffness characterization

A nonlinear contact force model is developed for spherical elastoplastic impacts. The nonlinear contact force model is constructed based on an existing piecewise model and the other based on the force–displacement diagram. The energetic impact law of the coefficient of restitution is used to solve for the unloading restitution stiffness. An integration of the dynamic equation of motion and proper use of initial conditions is performed to solve for the maximum deformation. Furthermore, the contact force law from the force–displacement diagram is used at maximum deformation to obtain a physical expression of the final indentation in terms of the maximum deformation and compression and restitution stiffness. In addition, the principle of the unloading linear stiffness is used and two equivalent closed form solutions are derived for the unloading linear stiffness. Moreover, a closed form solution of the maximum force is derived based on the unloading stiffness closed form solutions. The final and unloading indentation properties of the new model are investigated by performing numerical simulations for all coefficient of restitution values ranging from elastic to plastic impacts.

Modal approach to the dynamics of string instruments over the audible range

The present theoretical analysis addresses the dynamics of the bow instruments in the whole audible range of frequencies. Several scenarios are considered for the string-bridge-soundbox system: natural vibrations and frequency spectrum, external periodic excitation on some bridge point, and vibration induced by the bow rubbing. The single parts of the musical artifact are conveniently modelled and the bridge interfacing between the strings and the top plate of the soundbox is studied considering two possible vibrating modes of the bridge: a translational mode along its symmetry axis and a rotational mode around the waist centre. The bridge mechanical model is thus definable from both the kinematical and the dynamical aspects, and the relations between the forces and displacements of the strings and the sound box are formulated.The coupled natural modes of vibration are obtained in non-dissipative conditions, finding that the whole frequency spectrum is roughly given by the union of the uncoupled spectra, of the strings and the harmonic box. Then, introducing some level of dissipation, the frequency response to a transverse harmonic excitation on an arbitrary bridge point and the admittance on another arbitrary point of the instrument are studied, obtaining a useful tool to identify or verify the mechanical characteristics of the system. At last, the response to the bow excitation is analysed introducing an appropriate model for the nonlinear stick-slip contact between the bow and the strings and solving the motion equations by modal decomposition.

Vibration characteristics and safety analysis of production string in high temperature, high pressure gas wells

During the production of high-temperature, high-pressure (HPHT) gas wells, the gas entering the production tubing column induces vibration, which in turn leads to changes in the mechanical properties and safety of the tubing column. A dynamic model of the production string in an HPHT gas well was established to study the dynamic characteristics of its production string. The additional axial force caused by the transient temperature change and the nonlinear contact collision between the production string and the casing were considered. The Newmark-β method was used to solve the problem by analyzing and comparing the flow-induced vibration characteristics of the production pipe string. In this study, a gas well in the southwest Sichuan Basin was used as the research object to study the effects of gas production, packer setting position, and string wall thickness on the dynamic characteristics of the string. The results show that in the gas production process, intense vibrations are generated in the transverse and longitudinal directions of the tubular column. After high-velocity gas flows through the production tubing column, the vibrations at the wellbore inclination and the top of the tubing column are more intense. With the rise of production and the downward movement of the packer setting position, the vibration displacement and frequency of the tubing column increase. In addition, as the column's wall thickness increases, the column's stiffness rises, which, in turn, reduces the vibration of the column. When the gas production increases from 60 × 104 m3/d to 150 × 104 m3/d, the maximum transverse vibration displacement of the production string will increase by 22.2%–39.3%, while the frequency will increase by 15.3%–54.3%. When the wall thickness of the pipe column reaches 9.53 mm and 10.92 mm, it can be employed to enhance the safety factor of the string and extend the fatigue life of the string. This study provides a theoretical framework for field string protection and production guidance.