International Journal of Non-Linear Mechanics最新文献

The first-order phase transition from oscillation to steady state, known as explosive death (ED), is prevalent in various dynamical models. However, previous studies on ED have predominantly focused on interactions between pairs of elements. In this work, we investigate how death transitions occur when both pairwise and three-body interactions are present in an extended Van der Pol oscillator network with attractive–repulsive coupling. By examining both global and non-local interaction mechanisms, the impact of higher-order interactions on ED and the differences in the transition process are comprehensively analyzed. Firstly, we construct a diagram of the global dynamics in the context of higher-order and first-order coupling strengths, identifying that the higher-order interactions promote the onset of ED with a contribution comparable to that of first-order interactions. Specifically, for global coupling, the theoretical backward critical curves matching the numerical results are derived through linear stability analyses, showcasing a linear correlation with a slope of -1 between the higher-order and first-order coupling strengths. Under non-local coupling, fitting the numerically obtained backward critical curves likewise yields a consistent quantitative relationship. Additionally, during the transition process of ED, we discover intriguing coexisting states in the hysteresis area under non-local coupling, including the coexistence of chimera states with coherent or incoherent oscillation, and the coexistence of chimera states with oscillation death. This is attributed to symmetry breaking induced by non-local action. These findings enhance the understanding of higher-order interactions in complex systems and provide a fresh perspective for studying multi-stability behavior in biochemical and physical systems.

The accuracy of the vibration response in a defective bearing dynamics model depends on the precise representation of the lubrication friction state between the rolling element (RE) and the raceway within the model. In this study, a fault dynamic model for outer ring defect of deep groove ball bearings (DGBBs), considering the lubrication state transition in a thermal environment, is established. This model accounts for the asperity contact effect during the lubrication state transition and integrates the lubrication-friction model for temperature changes into the dynamic model when skidding occurs. The influence of lubrication state change on the fault frequency of outer ring of DGBB in thermal environment is studied. The experimental and simulation results indicate that the lubrication state of the bearing is gradually deteriorated from elastohydrodynamic lubrication to mixed lubrication with the increase of working temperature. The transformation of the lubrication state is shown to have a significant effect on friction, resulting in the fault frequency of the outer ring increasing with temperature, which exhibits substantial deviation in the thermal environment. In the temperature range of 30 °C–150 °C, the deviation of defect frequency reaches 15.5%, which affects the accuracy of bearing fault diagnosis. This study may offer recommendations for enhancing the condition monitoring of rolling bearings under extreme working conditions.

In this work, the nonlinear free vibration analysis of the imperfect cylindrical panels in contact with discontinuous unilateral elastic base are conducted, evaluating the influence of the type of contact, unilateral or bilateral, and the contact area of the elastic base on the natural frequencies and nonlinear frequency-amplitude relations. For that, the structural cylindrical panel model considers the Donnell's nonlinear shallow shell theory to obtain the partial differential equilibrium equation and the compatibility and continuity equation. To represent the unilateral capability of the elastic base, a signum function is inserted in the reaction force of the elastic base to describe its dependence of the transversal displacement field of the cylindrical panel. To apply the elastic base in certain subdomain of the cylindrical panel, a Heaviside-type function is also inserted into elastic base's reaction forces. The nonlinear equilibrium equation is discretized by the Galerkin method, using a consistent transversal displacement field that it was obtained from a perturbation technique. The discretized set of equilibrium equations is employed to obtain the natural frequencies and the nonlinear frequency-amplitude relations, evaluating the influence of the unilateral contact and the contact region of the elastic base on these results. Depending on the signal of the imperfection's magnitude and the type of contact of the elastic base, the imperfect cylindrical panel can display an initial gap between the cylindrical panel and the elastic base, and this possibility is also investigated in this work. From the numerical results, it is observed that the unilateral elastic base applies less structural stiffness than the bilateral elastic base, decreasing the natural frequencies for the same imperfect cylindrical panel. The localization of the elastic base in the cylindrical panel also affects the natural frequencies, increasing or decreasing them depending on the modifications on the structural stiffness. The frequency-amplitude relations are strongly influenced by both unilateral contact of elastic base and the type of the contact consideration between the cylindrical panel and elastic base, exhibiting an intricated nonlinear behavior.

In this study, a new hysteresis mechanical model of metal rubber was developed based on the magnetic flux change of metal rubber damper after cyclic loading and the subsequent static stiffness degradation This new model aims to overcome the shortcomings of the traditional high-order friction theory hysteresis model in explaining the stiffness fluctuation and temperature magnetic flux change of the shock absorber. Through the large load cyclic loading experiment of the metal rubber damper, the hysteresis characteristics of the metal rubber damper without fatigue fracture were ana-lyzed in depth. Based on the electromagnetic theory and the force and displacement constitutive relationship of the metal rubber, the Preisach mechanical hysteresis model was established. The experimental test outcomes were substituted into the model for parameter identification and the model was modified as necessary. Compared to the traditional dynamic hysteresis model based on power series and elliptic equation, the Preisach model showed higher accuracy in simulating the energy dissipation and damping ratio of the experimental data of the shock absorber. The error was controlled within 2 %. Especially in the abrupt region of the unloading curve, the nonlinear stiffness error of the Preisach model was determined to be only half of that of the traditional model. The Preisach mechanical hysteresis model deeply explores the microscopic electromagnetic characteristics of the metal rubber damper, thus revealing the internal mechanism of its hysteresis change. This model can not only accurately simulate the sudden change of the curve of the shock absorber during the unloading process, but also make the model prediction closer to the actual application scenario through the highly simulated simulation results.

Bearing misalignments are common defects in machinery. One of the most important types of that is the angular misalignment of the bearing rings. In this study, crookedness specific signature related to thrust ball bearing shaft washer is investigated. For this purpose, a vertical structural thrust ball bearing test rig was considered. In the following, effects of rotational shaft speed, crookedness value and axial external force on the shaft washer crookedness signature were studied at several relative positions of sensors. It is shown that crookedness of thrust ball bearing shaft washer has specific frequency and sensor phase difference pattern in the nonlinear vibration responses. Also, the experimental results are applied to validate results of a 4-dof nonlinear dynamical system related to the shaft washer crookedness of thrust ball bearing. In the next step, by comparing input and output amplitude and also existence of flip bifurcation, it is illustrated that this system is a nonlinear dynamical experimental system. It was shown that this nonlinearity makes crooked shaft washer pattern difficult to identify. Finally, by the phase portrait of the sensor response and the relative error value of crookedness signature frequencies, it is clear that the crookedness of shaft washer creates quasi-chaotic behavior supporting crookedness signature frequencies and phase pattern as a supplement property.

We study in this paper linear and weakly nonlinear waves within the framework of a Hall-magnetohydrodynamic model. An optimal ordering, which allows the Hall effect to be seen in the leading order equations, is used to discuss the propagation of such waves; an evolution equation is obtained where the nonlinearity and Hall effect enter through the parameters that influence the wave propagation significantly. The interplay between nonlinearity and Hall effect leads to the emergence of a dispersive shock wave, which appears as the solution to the initial value problem associated with the evolution equation. The present study reveals a number of interesting flow characteristics which are not seen in the theory of ideal magnetohydrodynamics.

This paper is devoted to constructing a dynamic numerical model for the firing dispersion caused by the autocannon dynamic characteristics. The buffer dynamics and projectile-barrel coupling are considered. First, the simulation of autocannon firing dispersion using commercial software usually leads to expensive computational costs. Second, autocannon dynamic design includes multiple subsystem models with nonlinearities. The conventional design method makes it difficult to describe the dynamic response of such complex systems with a unified model. To end these, a dynamic junction bond space method is proposed for analyzing muzzle vibration and firing dispersion under continuous firing loads, where the gene expression programming (GEP) method is adopted to construct the surrogate model for the buffer flow field. For the coupling analysis of the projectile and barrel, the projectile load is applied at a moving junction, which coincides with the flexible node of the barrel. By this, the dynamic numerical model for autocannon firing dispersion is established, and then the system state equation is obtained for each time step. Moreover, an autocannon standing target shooting example is presented to demonstrate the validity of the proposed method; the results show that the firing dispersion from the bond space model is consistent with the test.

This paper first detects hidden system from plastic deformation of metallic glasses by sparse identification. The extracted model simulates four types of stress-time curves and displays the prediction of serrated events. This interpretation effectively explains various experimental phenomena of repeated yielding. Further, in terms of parametric sensitivity analysis to the model, two parameters are taken as bifurcation parameter, and the analysis of codimension-one and codimension-two bifurcation are carried out to excavate the causes of dynamic transformation, including saddle–node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and cusp bifurcation. Different bifurcation points correspond different types of stress-time curves. The homologous phase diagrams including periodic orbit, unstable orbit and chaotic behavior are presented to show the dynamics diversity of the model. In addition to dynamic analysis, statistical analysis for plasticity values is also applied to excavate the crossover between periodic and chaotic plastic dynamic transitions. Our results provide a novel perspective on the deformation of metallic glasses from the viewpoint of dynamic model and are also important for evaluating the plastic deformation properties of metallic glasses in practical applications.

High-aspect-ratio (HAR) airplane wings have higher energy efficiency and present an economical alternative to standard airplane wings. HAR wings have a high span and a high lift-to-drag ratio, allowing the wing to require less thrust during flight. However, due to their length and construction, HAR wings exhibit low-frequency, high-amplitude vibrations in both vertical (yaw axis) and longitudinal (roll axis) directions. To combat these unwanted vibrations, a two-dimensional nonlinear vibration absorber (2D-NVA) is constructed and attached to a model HAR-wing airplane to verify its effectiveness at reducing vibrational motion. The 2D-NVA design, which was presented in a previous study, consists of two low-mass, rigid bodies namely the housing and the impactor. The housing consists of a ring-like rigid body in the shape of an ellipse, while the impactor is a solid cylindrical mass which resides inside the cavity of the housing. The 2D-NVA is designed such that the impactor can contact the inner surface of the housing under both impacts and constrained sliding motion. The present study focuses on the use of the 2D-NVA to mitigate multiple modes of vibration excited by impulsive loading of a model airplane with HAR wings in both vertical and longitudinal directions. The effectiveness of a single 2D-NVA is investigated computationally using a finite element model of the model airplane. These results are verified experimentally and the performance of two 2D-NVAs (one on each wing) is also investigated. The contributions of this work are that: 1) the 2D-NVA alters the global response of the model aircraft by mitigating all relevant modes in both directions simultaneously; 2) a single 2D-NVA is optimal for mitigating motion in the vertical direction, while two active 2D-NVAs are optimal for the longitudinal direction; and 3) the performance of the 2D-NVA is robust to changes in the frequency content of the parent structure.

The present study focuses on the finite amplitude analysis of Poiseuille flow in an anisotropic and inhomogeneous porous domain that underlies a fluid domain. The nonlinear interactions are studied by imposing finite amplitude disturbances to the Poiseuille flow. The former interactions in terms of modal amplitudes dictate the fundamental mode, the distorted mean flow, the second harmonic and the distorted fundamental mode. The harmonics are solved progressively in increasing order of the least stable mode obtained from the linear theory to ascertain the cubic Landau equation, which in turn helps to determine the bifurcation phenomena. The presented weakly nonlinear theory predicts the existence of subcritical transition to turbulence of Poiseuille flow in such superposed systems. In general, on moving away from the bifurcation point, it is found that a decrease in the value of inhomogeneity (in terms of $A_i$), Darcy number $\left(\delta \right)$ and an increase in the value of depth ratio ($\hat{d}$; the ratio of fluid domain thickness to that of porous domain) favours subcritical bifurcation. For the considered variation of parameters, the bifurcation, either subcritical or supercritical, remains the same irrespective of the value of media anisotropy ($\xi$) in the vicinity of the bifurcation point except for $\hat{d}=0.2,A_i=1$. In such a situation, subcritical (supercritical) bifurcation is witnessed for $\xi =0.001,0.01,0.1$ (1,3). Furthermore, in contrast to isotropic and homogeneous porous media, both subcritical and supercritical bifurcations are observed when moving away from the bifurcation point. A correspondence between the type of mode via linear theory and the type of bifurcation via nonlinear theory is witnessed, which is further affirmed by the secondary flow patterns. Finally, the presented theoretical results reveal an early onset of subcritical transition to turbulence in comparison with isotropic and homogeneous porous media.