International Journal of Non-Linear Mechanics最新文献

The rotational and torsional oscillations of a rod in a fluid has relevance to several applications. Stokes recognized that the rotational oscillations in a Navier–Stokes fluid allows one to obtain an exact solution. This seminal work has been extended by Casarella and Laura to find an exact solution to both the rotational and torsional oscillations in a Navier–Stokes fluid. This work has been generalized to the case of several non-Newtonian fluids by subsequent authors. In this study we analyze the solution that corresponds to two classes of non-Newtonian fluids, the constitutive relation put forth by Carreau and Yasuda, and a relatively new constitutive relation due to Garimella et al. that mimics viscoplastic flow exhibited by many materials.

Under electric loading produced by compliant electrodes, a dielectric elastomer is prone to material instabilities which, in a microstructural level, may connect to single polymer chain instability. To reveal if such connection exists, we aim to use an electroelastic energy model for single polymer chain to study the chain instability. We approximate curvature shape of the chain under the electric loading by using trigonometry series in a spatial coordinate. The Rayleigh–Ritz method is then applied to solve the energy equation formed by the trigonometry series. We demonstrate in the numerical examples that the instability of the chain may occur at the value of electric field with corresponding configuration of the chain close to its full length.

For an autonomous nonlinear system, the Hopf bifurcation point along the equilibrium path is a critical feature that indicates whether the values of the parameters change from exhibiting fixed-point behavior to having a periodic orbit. To solve these problems, we developed a method of transforming an eigenvalue problem based on the Jacobian matrix at equilibrium into a minimization problem, enabling the rapid identification of a solution. Specifically, this generalized eigenvalue problem is solved by identifying the vector variable after reducing the number of eigenequations by one in the nonhomogeneous linear system. This can be achieved by normalizing the value of a selected nonzero component of the eigenvector and then moving the column containing this component to the other side of the equation. An appropriate merit function was established in terms of the Euclidean norm of the eigenequation, and this merit function was minimized using the golden section search algorithm to determine the eigenparameters of the bifurcation point. The accuracy of the method for identifying the parameter values and the corresponding imaginary eigenvalues at the Hopf bifurcation points was evaluated for numerous examples for both the continuous and discrete systems. The method was both fast and accurate. Moreover, its stability in the presence of noise was investigated, and the method was robust.

The aim of this comment is to point out three major errors in the paper Akolade et al. (2024).

The dynamic characteristics of the elastic plate are affected by changes in ambient temperature. In this study, tensile tests of rubber materials at different temperatures were conducted, revealing that rubber materials exhibit significant nonlinearity and sensitivity at low temperatures. Finite element models of Groove Elastic Plate (GEP) and New Mesh-Type Elastic Plate (NMTEP) were established, incorporating the corresponding rubber material parameters to simulate temperature effects. The stress, deformation, stiffness, and damping characteristics of the two types of elastic plates were analyzed under varying temperature conditions. Finite element calculations show that NMTEP maintains better structural stability, lower static/dynamic stiffness, and a higher damping ratio at low temperatures. Additionally, dynamic calculations indicate that temperature variations significantly impact the track system's dynamic performance. The vibration and wheel-rail forces for NMTEP are significantly lower than those for GEP under all temperature conditions, suggesting that NMTEP is more conducive to vehicle safety and stability at low temperatures.

This work focuses on the dynamics of a small network of three ring-coupled unidirectional Rayleigh-Duffing oscillators. The equations governing the Rayleigh-Duffing oscillator, containing a cubic term, make this study a more interesting and complex case to analyze. Coupling is achieved by perturbing the amplitude of each oscillator with a signal proportional to the amplitude of the other. The sixth-order self-driven nonlinear system obtained after coupling is analyzed, and presents up to twenty seven equilibrium points. Amongst these equilibrium points, we determined which can present the Hopf bifurcation. Also, the effects of the coupling coefficients and damping coefficients are analyzed. It is shown that varying these different coefficients leads to the appearance of extremely complex dynamic phenomena such as: instability and bifurcations (i.e coexistence of bifurcation branches), coexistence of up to fifteen attractors (heterogeneous multistability) and eight spiral chaotic attractor. The investigation of the coupled system is carried out by using to both analytical and numerical tools such as Hopf bifurcation theorem, the phase portraits, bifurcation diagrams, Lyapunov exponent diagram, frequency spectrum, to name but a few. The Routh-Hurwitz criterion is also used to analyze the stability of equilibrium points. We compute basins of attraction to highlight different zones corresponding to coexisting attractors. The implementation of an analog circuit of coupled Rayleigh-Duffing oscillators has enabled us to confirm the analytical and numerical results.

The little mass eccentricity of the workpiece is taken into account when we develop a single-degree-of-freedom regenerative turning chatter dynamic model. This study provides a numerical and analytical analysis of regenerative turning chatter, with a focus on the little mass eccentricity of the workpiece. By using a numerical approach, it is examined how a little mass eccentricity affects the turning chatter bifurcation features in various initial states. It primarily concentrates on applying the multiple scale method to analyze the impact of little mass eccentricity and workpiece angular velocity on the primary resonance of turning chatter. According to the research presented in this paper, mass eccentricity cannot be disregarded throughout the turning process.

The goal of this work is the development of a general nonlinear single-track model for the cases of curved flat or banked road paths and the identification of the fundamental “handling bricks” or vehicle “DNA”, extending an existing theory for flat road tracks. The handling bricks are related to specific design parameters of the vehicle. It is confirmed (both theoretically and numerically), that two structurally different vehicles, with the same handling bricks, exhibit very similar or identical handling behavior. The current nonlinear model accepts general steering input, and arbitrary axle characteristic functions and can be used for general (flat or banked) road tracks. If necessary, various types of constraints can be easily enforced, linking the dynamic parameters of the model. For example, given a complex steering input, the vehicle's (center of gravity) velocity and (or) the vehicle heading, can be related to the direction of the banked road path. On the other hand, the road path can be given independently of the steering data to check the deviation between the intended and the obtained road paths. An implicit nonlinear Crank-Nicolson time marching technique (with additional internal iterations at each time step), has been developed and implemented for the set of (nonlinear) ordinary differential equations (in a homemade VBA framework). The numerical results, using magic formula-based axle characteristic functions, confirm the robustness of the model formulation.

Construction of Riemann solutions for a hyperbolic system in conservative form arising from the one-dimensional mean-field games with the quadratic Hamiltonian and the logarithmic coupling term are provided in detail. Moreover, the delta shock formation is concretely analyzed from the limit of double-shock-solution as well as the emergence of vacuum state is also specifically discussed from the limit of double-rarefaction-solution when the coupling coefficient drops to zero. Accordingly, the remarkable cavitation and concentration phenomena can be closely observed and explored. Additionally, the numerical experiments are also presented in correspondence to authenticate the theoretical analysis results.

In the current study, the lattice Boltzmann method was used to explore the motion of an elongated microswimmer in a horizontal channel with finite fluid inertia. By employing an extended squirmer rod model, the swimming velocity, hydrodynamic efficiency, and interaction with the channel wall of the capsule-shaped squirmer rod were simulated. It was found that the aspect ratio α and the swimming Reynolds number Re_s of the squirmer rod significantly affect its swimming velocity and efficiency. Specifically, as the Reynolds number increases, the pusher rod's velocity increases, whereas the puller rod's velocity decreases. Moreover, compared with the puller rod, the pusher rod has a higher efficiency with the same power consumption. With the increase of the aspect ratio α, the velocity of the squirmer rod increases gradually, the power consumption of the pusher rod and the puller rod decreases gradually, and the efficiency increases gradually, showing the characteristics of lower energy consumption and higher efficiency. During the interaction of the squirmer rod with the wall, four distinct motion modes were identified, namely, steady linear motion, motion away from the wall, damped swinging motion, and wall-attraction oscillation. The emergence of these motion modes and their transitions could be associated with the pressure distribution formed between the squirmer rod and the wall. The results provide another perspective and theoretical basis for the design of bioinspired microswimming devices and microrobots, especially in medical applications such as precision drug delivery systems.