International Journal of Non-Linear Mechanics最新文献

Flexible rolling technology is the current development trend of strip production industry. However, due to the simultaneous change of mechanical, process and strip specification parameters in the flexible rolling process, the motion state of the system is difficult to analyze and stability control is hard to achieve. In this paper, the active motion characteristics of rolls in flexible rolling technology are considered, and the dynamic rolling process model is established to reflect the influence mechanism of process and specification parameters on the dynamic rolling force. The dynamic model of a 4-high rolling mill was developed and the structure-process-strip coupling strategy was applied to couple the models. The Runge-Kutta method was applied to solve the dynamic equation to obtain the maximum Lyapunov exponential spectrum for a single parameter variation. It is noteworthy that the two-parameter dynamics method was adopted to solve the dynamics on the two-parameter plane considering the nature of simultaneous variation of the system parameters, which solves the limitations of the traditional analytical method and is suitable for the application of the flexible rolling system. The results suggest that the parameters influence the motion state in the form of coupling, the influence pattern of each parameter on the stability is clarified, the evolution of the stable domain under the effect of parameter coupling is revealed, and the parameter matching strategy is determined. The results will provide a solution for the system parameter setting of flexible rolling technology and a theoretical reference for enhancing the stability of the rolling mill.

In this paper, we investigate the co-dimension two bifurcations and complicated dynamics of an optoelectronic reservoir computing (RC) system with single delayed feedback loop. We focuses primarily on its underlying system’s Hopf-Hopf bifurcation. Firstly, we apply DDE-BIFTOOL built in Matlab to sketch the bifurcation diagrams with respect to two bifurcation parameters, namely feedback strength $\beta$ and time delay $\tau$, and find the existence of the Hopf-Hopf bifurcation points. Then, using the multiple scales method, we obtain their normal forms, and using the normal form method, we unfold and classify their local dynamics. Then numerical simulations are conducted to verify these results. We discover rich dynamical behaviors of the system in specific regions. Besides, other complicated dynamics, such as fast-slow phenomena, Period $n$ solutions, and chimera, are found in the system. All these rich dynamical phenomena can provide excellent performance potentially for this optoelectronic reservoir computing system with single delayed feedback loop.

The significance of Single Degree of Freedom (SDOF) systems lies in their ability to serve as foundational elements for modeling more complex dynamic problems. By capturing essential dynamic behavior with simplicity, SDOF models enable efficient analysis and comprehension of complex systems, justifying the investigation of these simplified models. In nonlinear scenarios, SDOF models result in time series data wherein vibration frequencies vary over time. Classically, time–frequency or Hilbert transforms applied to temporal responses are frequently used to identify the evolution of frequencies and damping ratio over time. These techniques provide results that reflect the spectrum composition achieved for the analyzed time window and present difficulties in precisely determining the magnitude and the exact instant of an effective frequency or damping ratio variation. In this sense, this work introduces a new methodology capable of accurately identifying the vibration frequency as a function of time, i.e., the instantaneous frequency, along with the instantaneous damping ratio. At this initial stage, the focus is on validating the methodology by comparing its performance with the classical approach based on time–frequency transforms. The initial results obtained from synthetic free vibration decay responses of SDOF nonlinear models highlight the accuracy of our findings compared to those obtained from time–frequency transforms. The presented methodology holds promise for further advancement, with potential impacts including structural damage identification, modal identification and nonlinear dynamic analysis.

This paper conducts a nonlinear analysis of cable-beam model of cable-stayed bridges by using the exact mode superposition method (EMSM) and the cable-beam dragging method (CBDM), respectively, comparing and exploring their theoretical foundations and practical implications. The EMSM is based on the global mode function of the cable-beam structure for nonlinear analysis, yet it requires more computational resources. The CBDM is based on the cable-beam dragging equations for nonlinear analysis, which can quickly obtain the static equilibrium state and dynamic response of the cable-beam system, but it requires some simplifying assumptions on the cable-beam connection conditions. Research results demonstrate qualitative and quantitative differences between these two methods through parametric analysis on dynamic behaviors, which provide a significant methodological study and a reference for the design and dynamics of composite structures.

This paper proposes a comprehensive approach to the dynamic modelling of Cable-Driven Parallel Robots (CDPRs) by means of Differential-Algebraic Equations (DAEs). CDPRs are usually modelled through a minimal set of Ordinary Differential Equations (ODEs), often by making some simplification or just focusing on the unconstrained platform/end-effector dynamics. The alternative use of redundant DAEs provides several benefits since several non-ideal properties and peculiar operations of CDPRs can be easily and accurately modelled. To provide a comprehensive modelling frame, the typical components of a CDPR with rigid cables are here discussed and modelled by exploiting the concept of DAEs, which use redundant coordinates and embed kinematic constraints in the algebraic part of the equations. Through such advantageous features, it is possible to model swivelling guiding pulleys with non-negligible dimensions and mass. The use of rheonomous constraints is proposed as well, to represent in a simple way the effect of the movable exit-points, that are widely adopted in reconfigurable CDPRs. Finally, the use of Natural Coordinates is proposed for representing spatial end-effectors and modelling some challenging operations such as its overturning or the picking of heavy objects. Numerical simulations and the comparison with the results provided by a benchmark software are shown to demonstrate the accuracy and the computational efficiency of the proposed approach.

A transition from two-dimensional to three-dimensional liquid sloshing in a symmetric vessel under external periodic forcing is considered. The three-dimensional response is commonly associated with well-ordered swirling, although can exhibit also a chaotic behaviour. Such transition is well-known in the vicinity of the primary 1:1 resonance between the lowest eigenfrequency of the sloshing mass, and the frequency of the external force. The transition pattern, i.e., the dependence of the transition threshold on amplitude and frequency of the external forcing, demonstrates remarkable qualitative similarity for very different physical settings. This observation is illustrated by comparing the results of our own experiments concerning the sloshing in relatively soft cylindrical shell, to earlier results with rigid tanks of different geometry. The aforementioned similarity allows one to assume that this transition can be described by means of low-order phenomenological dynamical model with universal general structure. The parameters of such model should depend on the specific physical setting of the sloshing system. The suggested model comprises a two-dimensional damped nonlinear oscillator with unidirectional forcing. The transition to the swirling in the original sloshing system is associated with the loss of stability of the one-dimensional response in the reduced model. Analysis by means of a multiple-scale expansion allows mapping the transition threshold on the plane of parameters for given initial conditions. One reveals that in order to match the available numeric and experimental results; a polynomial model with combined softening and hardening is required. The results are verified by means of direct numeric simulations of the complete reduced-order model; additional response patterns are revealed.

This paper presents an improved path integration method for a soft-impact system under stochastic excitation, which focuses on the response of the system on the impact surface. The system involves complex impact processes, including contact, deformation, recovery, and disengagement. To address the technical challenges posed by the system discontinuity at the moment of impact, we establish a mapping relation between impact events to solve the system response. Considering that the non-smooth moment of such systems exists only at the moment of contact with the impact surface, we chose to select the impact surface as a Poincaré cross-section. Two independent mappings were established to describe the transition of the oscillator from leaving the obstacle to the next contact with the obstacle, and from contacting the obstacle to leaving the obstacle. These two consecutive mappings were integrated into the plane to form a unified mapping. This method was employed to investigate the response probability density function of the system for autonomous and non-autonomous systems, respectively. The effectiveness of the methodology was validated by the use of Monte Carlo simulations, in addition to the discovery of the stochastic P-bifurcation phenomenon.

Hyperelastic models are extensively employed in the simulation of biological tissues under large deformation. While classical hyperelastic models are incorporated into certain finite element packages, new hyperelastic models for both isotropic and anisotropic materials are emerging in recent years for various soft materials. Fortunately, most hyperelastic models are formulated based on strain invariants, which provides a feasible way to directly implement these newly developed models into the numerical simulation. In this paper, we present a general framework for employing strain-invariant-based hyperelastic models in finite element analysis. We derive the general formulation for the Cauchy stress and elasticity tensor of both isotropic and anisotropic materials. By substituting the strain–energy density into these general forms, we are able to directly implement various hyperelastic models, such as the Fung–Demiray model and the Lopez-Pamies model for isotropic materials, and the Gasser–Ogden–Holzapfel model, the Merodio-Ogden model, and the Horgan-Saccomandi model for anisotropic materials, within the ABAQUS user-defined material subroutine, offering a numerical approach to implement materials not available through the built-in material models. To demonstrate the feasibility of our approach, we utilize these subroutines to compute several classic examples related to both homogeneous and inhomogeneous problems. The good agreement between the obtained results and the analytical or experimental solutions confirms the validity of developing these models by the proposed framework. The general framework and results presented in this study are useful for fast implementing newly developed hyperelastic models and are helpful to the finite element simulation of biological tissues.

This study presents the development of an isothermal model for characterising the stress-strain behaviour of clay, in the framework of thermomechanical restrictions. Clay is assumed to be a decoupled material, where the accumulation of the Helmholtz free energy can be decoupled into two components, elastic and plastic, that result in the explicit definitions of the shift and dissipative stress tensors, respectively. An anisotropic yielding function fulfilling the first and second laws of thermodynamics is then derived from the rate of plastic dissipation, where the loading tensor and fractional plastic flow tensor are also obtained. A compression-and-shearing hardening mechanism is introduced by further evaluating the thermodynamic restrictions of the rate of Helmholtz free energy at critical state. The developed model contains seven constitutive parameters, where the identification methods are discussed. Finally, an application of the developed model to simulate the drained and undrained stress-strain responses of different clays are provided.

Generalized continuum theories can describe the mechanical behavior of microstructured materials more accurately than the classical Cauchy theory. In this manuscript, a micromorphic beam theory is developed for the efficient multiscale analysis of the linear and nonlinear deformation and vibration behavior of metamaterial beams. The proposed approach extends the conventional nonlinear Timoshenko beam theory by including three additional independent degrees of freedom, which allow to accurately capture four distinct microstrains for stretch, bending, and two types of shear behavior at the microscale level. The novel beam model is able to capture size effects and can accurately describe beams with only few unit cells through the thickness direction. However, consisting of 3 macro and 3 micro degrees of freedom, it is much more efficient than 2D or 3D micromorphic continuum models. It is demonstrated that the micromorphic material parameters can be identified from comparison studies with representative volume elements of the microstructure. For the numerical discretization of the governing equations for static deformations as well as vibrations, the differential quadrature method is employed here. The presented numerical examples show the accuracy of the method in obtaining deflections, linear eigenfrequencies, and nonlinear frequency responses for metamaterial beams with weakly separated macro and micro scales.