International Journal of Non-Linear Mechanics最新文献

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.

Drag plays a dominant role in the interfacial momentum exchange in mixture mass flows. In this study, we examine a general two-phase mass flow model formulated by Pudasaini [1], which incorporates drag. This model describes the mass flow comprising a mixture of solid particles and viscous fluid moving downhill under the influence of gravity. We construct explicit, analytical, and numerical solutions to the model using the Lie symmetry method. These new solutions disclose the role of generalized drag in the dynamics of both solid particles and viscous fluid. The solutions show that solid and fluid phases undergo nonlinear evolution in a coupled manner. Additionally, the solutions demonstrate that increased drag results in a tighter binding between solid and fluid components. We also analyze the role of pressure gradients. The solutions reveal that when solid pressure dominates fluid pressure, solid velocity increases faster than fluid velocity. These findings align with our expectations, emphasizing the importance of analytical solution techniques in understanding the complex process of mixture mass transport in mountain slopes and valleys, thereby enhancing our understanding.

Electrical connectors are crucial electro-mechanical components, with insertion, withdrawal, and electrical contact characteristics serving as key indicators of their reliability. Studying the electro-mechanical characteristics and regression models of electrical connectors is vital to enhance their reliability. This work focuses on the M2-type electrical connector, investigating its electro-mechanical characteristics and developing a regression model. A withdrawal force calculation model is established using cantilever beam theory. Simulation and analysis provide data on insertion force, contact pressure, and contact resistance. Experiments on insertion, withdrawal, and electrical contact are conducted using an insertion force tester and a DC low-resistance instrument, comparing experimental results with simulations. The study reveals the fitting relationship between contact pressure and contact resistance for the M2-type connector. Key findings include a stable fluctuation in contact pressure with a relative error of 1.72% between simulated and tested values, an average discrepancy of 3.81% for insertion force, and 2.38% for withdrawal force, with insertion force slightly higher than withdrawal force. Contact resistance shows a U-shaped trend with pin displacement, with an average experimental error 3.70% and 1.16% lower than theoretical values (4.86%). The new regression model (quadratic polynomial fitting) demonstrates mean absolute percentage errors of 0.1458% for simulation values and 0.2219% for experimental values, significantly lower than those obtained using theoretical formulas (0.7046% and 0.3451%). These results provide theoretical guidance for studying electro-mechanical characteristics and designing experiments for electrical connectors, offering valuable insights for designing and ensuring the reliability of new types of electrical connectors.

Background

Vibration response analysis serves as a critical tool in investigating the behavior of micro/nanoscale structures operating in dynamic environments, offering valuable insights into their performance and ultimately refining the design of devices. Particularly, when these structures are deliberately engineered to function near or within the postbuckling regime, understanding their vibratory behavior in this state becomes essential. This study focuses on exploring the postbuckling behavior and nonlinear frequencies of simply supported buckled porous functionally graded (PFG) size-dependent tubes. Internal resonances are not considered in this analysis.

Method

The nonlocal strain and velocity gradient theory, within the framework of the Euler-Bernoulli beam hypothesis, is employed to derive the nonlinear partial differential equations of motion. It is assumed that the material properties are gradually graded in the radial direction. Additionally, two different porosity distribution patterns are used in the radial direction. The method of multiple scales is used to solve the system of nonlinear ordinary differential equations obtained by applying the Galerkin method.

Results

The closed expression for the i-th nonlinear frequency of buckled porous functionally graded size-dependent tubes is determined based on the amplitude of the vibration modes involved. The findings indicate that porous M/NTs exhibit a loss of static stability at lower compressive axial loads compared to their nonporous counterparts. Furthermore, the softening effects resulting from a uniform porosity distribution are more pronounced than those from an uneven porosity distribution. Interestingly, nonporous M/NTs display the lowest nonlinear postbuckling frequency among the studied configurations. Moreover, it is observed that the nonlinear frequency tends to increase with a rise in the compressive axial load, while it decreases with an increase in the excitation amplitude.

This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system.