International Journal of Non-Linear Mechanics最新文献

Indentation of a very stiff membrane (like graphene) on an incompressible elastic material has been suggested as a method to measure the elastic modulus of the membrane, but so far the method is less explored than that based on indentation of a free-standing membrane clamped on the outer boundary, which relies on analytical solutions. However, we analyse the problem rigorously with an energy minimization in the Rayleigh sense with a one term approximation of the vertical displacement, and show that in the fully non-linear regime, the load $F$ has a single term solution increasing as the power 5/3 of the indentation $\Delta$. The solution is corrected only in the prefactor by extensive FEM investigation using a concentrated load resulting finally in $F=\frac{1.45\times 4\pi }{{\left(384\pi \right)}^{1/3}}{\mu }_s^{2/3}{E}_m^{1/3}{\Delta }^{5/3}{h}^{1/3}$, where ${\mu }_s$ is the substrate shear modulus, $h$ the membrane thickness, and $E_m$ its elastic modulus. We also find the effect of a finite membrane outer radius analytically, so that this method is also based entirely on analytical solutions. Comparison with experimental results seems very promising.

The linear stability analysis of a viscoelastic Navier-Stokes-Voigt fluid flow, or the Kelvin-Voigt fluid of zero order in a Brinkman porous medium, is investigated using both modal and non-modal analysis. The numerical solution is obtained using the Chebyshev collocation method. The combined effects of the medium's porosity, represented by the porous parameter, the fluid viscosity, represented by the ratio of effective viscosity to fluid viscosity, and the fluid elasticity, represented by the Kelvin-Voigt parameter are investigated using both modal and non-modal analysis. The modal analysis describes the long-term behavior of the system, obtained through plotting the eigenspectrum, eigenfunctions, growth rate curves, neutral stability curves, and streamline plots, along with accurate values of critical triplets. In non-modal analysis, the pseudospectrum of the Orr-Sommerfeld operator, transient energy growth curves, and regions of stability, instability, and potential instability are depicted. The results obtained from modal analysis indicate that the porous parameter, Kelvin-Voigt parameter, and the ratio of effective viscosity to fluid viscosity act as stabilizing agents. However, using non-modal analysis, it is observed that while the porous parameter and the ratio of effective viscosity to fluid viscosity act as stabilizing agents, the Kelvin-Voigt parameter acts as a destabilizing agent over shorter periods.

The dynamic characteristics of the cages of cylindrical roller bearings (CRBs) significantly impact the service life of the bearings. This paper considers the lubrication between the roller and cage and the effect of cage whirling and establishes an accurate CRBs nonlinear dynamic model. On this basis, the correlation between the stability of the cage centroid trajectory, cage sliding characteristics, and bearing operating parameters is elaborated on. In addition, the influence of structural parameters, such as the number of rollers and pocket clearance, on the dynamic characteristics of the bearing system is also investigated. The results indicate that in the design stage of CRBs, it is essential to ensure a reasonable number of rollers and a smaller cage clearance ratio to reduce the slippage rate and enhance the stability of the bearing cage. Furthermore, during the usage stage of CRBs, changes in load or rotational speed operating parameters can lead to cage whirling. However, the stability of the cage whirling under the former condition is higher than that under the latter. Therefore, it is necessary to fully consider the reasonable rotational speed and load conditions to prevent premature damage to the cage.

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.