International Journal of Non-Linear Mechanics最新文献

A modified generalized harmonic function perturbation method is proposed in this paper. Compared with the classical version of this method, the modified version can execute its procedures pure symbolically without the need to assign any system parameters even for some complicated nonlinear oscillators. This means that the relations between amplitude of limit cycles and system parameters can be derived analytically from the proposed method. Meanwhile, the analytical expression of characteristic quantity of limit cycles can be also obtained. Via these analytical expressions, the evolutional process of limit cycles can be studied quantitatively in amplitude domain. It demonstrates the entire live period of each limit cycle from its generation to bifurcation to destination. To show the feasibility of the proposed method, a complicated oscillator named generalized Duffing–Harmonic–Rayleigh–Liénard oscillator is investigated in this paper. First, the two analytical expressions mentioned above are derived and the global evolution of its limit cycles are analyzed quantitatively. Second, the critical value of homoclinic and heteroclinic bifurcation parameters are also predicted via this two analytical expressions. Moreover, the analytical approximate solutions of both limit cycles and homo-heteroclinic orbits are calculated. To prove the accuracy, all the above results obtained via the proposed methods are confirmed by the Runge–Kutta method, which show a good accordance. Therefore, the proposed method can be considered as an effective modification for a classical perturbation method. It provides another feasible and reliable analytical quantitative method for analyzing global dynamics of strongly nonlinear oscillators.

The abnormal development of embryos is closely linked to abnormal cell division and elongation, but the underlying mechanism remains to be elucidated. The embryonic development of C elegans embryo is different because it occurs without cell proliferation or cell rearrangement. Here, we focus on a spectacular 4-fold elongation that is achieved approximately 3 h before the egg shell hatches and results from active filament networks. The body shape is represented by an inhomogeneous cylinder, which allows us to assess the active stresses induced by the actomyosin network located in the cortex and the muscles in ventral position near the epidermis. By considering the specific embryo configuration, we can quantitatively obtain the contractile forces induced by actomyosin filaments and muscles for a bending torsion event with defined curvature. We find that the active stress induced by actomyosin molecular motors or muscles increases with elongation and bending curvature, while also varying with radius. Both elongation and torsional deformation contribute to increased moment magnitudes that explain the dynamics of the embryo in the egg. Our results highlight the complex interplay between biomechanical factors in modulating embryonic deformation.

A model for the macroscopic mechanical behavior of rank-1 laminates including two shape memory alloy (SMA) phases is presented. The model expresses the general behavior of the composite with phases undergoing rate-independent elastic and inelastic deformations. Homogenization techniques (including the rank-1 laminate model) are used to establish the effective behavior of the SMA laminated composite (SLC) based on the information about the mechanical response of the individual phases and their volume concentrations. A stress-control algorithm is put forward to implement the model. With the aid of the stress-control algorithm, an implicit expression for the effective tangent stiffness and an evolution equation for the effective inelastic strain are derived. Results are compared with the outcomes of an FE-based computational homogenization and a very good agreement is seen. By using a constitutive model with internal variables for the dense SMA, the overall response of the SLC under different mechanical loadings is evaluated. The effective response of the SLC for various volume concentrations of the phases is assessed and exclusive comparisons are illustrated. Furthermore, the influence of different temperatures on the effective superelastic behavior of the SLCs is studied. The findings have implications for the analysis and the design of more complex shape-memory-alloy laminated composites for high-end applications.

Following a lengthy tenure of service, suspension systems may exhibit inaccurate model parameters due to the presence of complex conditions, which can result in a deterioration of control and the potential for operational failures. It is therefore imperative to estimate the key parameters of suspension systems. This paper introduces two data-driven methods for addressing the inverse problem in suspension systems subjected to stochastic track excitations. By employing physics-informed neural networks (PINNs) and Monte Carlo (MC) simulation, we are able to address the resulting integro-differential equation that arises from stochastic jump processes, thus avoiding the necessity for mesh grids. In order to mitigate the numerical challenges that arise from the system parameters, a residual-based adaptive sampling method is proposed. These methods effectively infer unknown parameters, addressing scenarios where data is directly available as a probability density function (PDF) or only sparse trajectories are given. In the latter case, a novel loss function employing Kullback-Leibler divergence facilitates learning from stochastic trajectories. Both methods successfully obtain solutions to the forward Kolmogorov equation, as validated by numerical experiments testing their robustness against added noise. The results demonstrate accurate parameter estimation under varying noise intensities, highlighting the methods’ robustness.

Quasi-static and impact compression experiments were conducted on EA4T steel using a Gleeble-3800 thermal simulation machine. The study aimed to investigate the complex microstructural evolution and thermal deformation behavior of EA4T steel under various experimental conditions, including temperatures ranging from 970 °C to 1170 °C and strain rates ranging from 0.01s⁻¹ to 1s⁻¹. To precisely elucidate these phenomena, we meticulously constructed a unified visco-plastic constitutive model using the internal variable methodology. The model's parameterization was achieved through the effective application of genetic algorithm optimization techniques. Rigorous validation of the model was performed by meticulously comparing its outputs with experimental data, including key metrics such as average grain size, recrystallized fraction, and effective flow stress. In addition,a comparative analysis with the improved Arrhenius model highlights the superior performance of the unified visco-plastic constitutive equation in capturing the intricate microstructural evolution and thermal deformation behavior exhibited by EA4T steel.

The work is devoted to the research of an expansion into a vacuum of a ball, which is filled with a two-phase fluid. In assumptions that the dynamics passes in a regular mode, the velocities of the phases are linear functions by space coordinate and the first phase spreads into the void faster than the second phase there is obtained a solution of equations of two-phase fluid dynamics, which describes an expansion of a ball into a vacuum. This solution generalizes the known Sedov solution, which determines an expansion of a gas cloud into a vacuum, to the case of a ball filled with a gas suspension. In the last part of the work there are derived asymptotic formulas determining a relationship between the velocities of the phases and the radii of two balls.

This work calculates the collapse load and collapse mechanism of 2D frames with slender structural members and uniformly distributed loads. The search for the collapse mechanism and the collapse load is carried out using step by step method: the load factor is increased and at each step the balance and compatibility equations must be satisfied that the value of the plastic moment is not exceeded in any section. It is verified that the results are different in the cases of point loads and uniform distributed loads, both from a qualitative and quantitative point of view.

To achieve an ultralow-frequency vibration isolation platform for simulation of space environment, suspension method is always utilized. However, the natural frequency of the suspension system is inversely proportional to the length of the suspension cable. In order to further reduce the dynamic stiffness, compress the suspension area, and achieve vibration isolation for wide-amplitude excitations, we propose parallel-stack-assembly (PSA) design principle for Origamis to construct absolute zero-stiffness for required intervals. The dynamic model for wide-range amplitude and deformation, design criteria for required low-frequency large-amplitude isolation effectiveness, and analysis for nonlinear vibration isolation property are given. Finally, the prototype is carried out to validate the theoretical analysis and design principle. The PSA design principle of Origamis creates the large-amplitude and ultralow-frequency isolation property, and, the study expands the applicability of isolators for low-frequency excitation with large amplitude for the systems in aviation, marine etc.

A quasi-static approximation is studied of linearised nonhomogeneous anisotropic compressible thermoelasticity on a non-compact region. Differential inequalities are constructed which under appropriate conditions lead to algebraic spatial growth and decay estimates for various cross-sectional and volume measures of the temperature, displacement and their spatial gradients.

The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.