查看更多>>摘要：In this paper, three implementations of B-differentiable Newton method (BDNM) for solving 3D elastoplastic frictional contact problems are presented. In the first two methods, a nested strategy is employed. The contact equations, which are solely associated with the contact conditions in the normal and tangential directions due to the introduction of the contact flexibility matrix, are expressed as B-differentiable equations. They are solved in the external iteration, or regarded as a sub-step nested within the solution of nonlinear equilibrium equations, leading to the decoupling of the calculations for nonlinear equilibrium equations and contact forces. In the third method, both the nonlinear equilibrium equations and contact conditions are expressed as B-differentiable equations simultaneously. Both nodal displacement and contact force are treated as independent variables, solved using BDNM to ensure the global convergence, with a variant of a Jacobian matrix associated with unknowns derived. In the numerical examples, the accuracy of the proposed methods is demonstrated by comparing with the results obtained from ANSYS. The convergence and computational efficiency are investigated through a series of models with varying degrees of freedom (DOFs) and contact node pairs (CNPs). The robustness of the proposed methods is presented by applying them to the analysis of an arch dam with seven transverse joints.
Manias, Dimitris M.Goldman, Ronald N.Goussis, Dimitris A.
1.1-1.15页
查看更多>>摘要：There are many applications governed by nonlinear dynamical systems in which the model introduced in a standard (natural) basis of a vector space, but it is more natural to analyze this model using a different set of basis vectors, which is more suitable for the acquisition the relevant physical insights. Here the case of multiscale dynamical systems is considered, which the appropriate alternative set of basis vectors is the one resolving the tangent space. Simple algorithmic tools are introduced that identify the fast and slow variables, thus facilitating (i) the construction of reduced models and (ii) the design of novel pathways for controlling complex multiscale systems across diverse scientific disciplines. The usefulness of these tools is demonstrated in two well-known multiscale models: the Michaelis-Menten and the Lorenz models.
查看更多>>摘要：Most studies on vibration control of a nonlinear energy sink (NES) for thin plates focus on singlefrequency or integral-multiple multi-frequency excitation. However, it is important to note that in practical scenarios, most plates are often subjected to arbitrary multi-frequency excitation. In this paper, a mathematical model is established for a rectangular plate with four-point support and a NES. To ensure the completeness of the solution for nonlinear vibration response under arbitrary multi-frequency excitation, a multi-frequency harmonic balance (MFHBM) method is proposed. The proposed method involves discretizing the excitation frequency equivalently and deriving an approximate solution in the form of harmonic superposition using trigonometric functions. The proposed method's validity and high computational precision have been validated through a comparison with numerical results. In addition, to demonstrate the excellent vibration damping effect of NES in multi-frequency vibration environments, parameter analysis is conducted using dual-frequency and tri-frequency excitation as illustrative examples. It revealsthat under specific NES parameters and different frequency parameters, the vibration damping effect at the center of the rectangular plate can exceed 37 % when resonance occurs. Furthermore, a comprehensive discussion on the parameter influence of NES showcases its remarkable versatility in multifrequency vibration environments. This study will serve a valuable reference for effectively mitigating arbitrary multi-frequency vibration in plates.
查看更多>>摘要：This study introduces a novel theorem focusing on predefined-time stability within fractional-order systems and applies it to the domain of predefined-time synchronization in fractional-order memristive delayed bidirectional associative memory neural networks. Leveraging the inherent characteristics of fractional-order calculus and the fractional-order comparison principle, this theorem is showcased. Unlike existing predefined-time stability theorems that rely on integer-order counterparts, our theorem adopts the fractional-order framework. By utilizing this theorem as a foundation, efficient controllers are developed to achieve predefined-time synchronization. The theoretical outcomes are verified through the examination of two numerical examples, affirming the robustness and applicability of our approach.
查看更多>>摘要：This paper addresses the issue of observer-based resilient scaled group consensus control for uncertain nonlinear multiagent systems subject to delays and disturbances. First, a distributed observer is introduced for each uncertain agent, enabling precise estimation of both the state and disturbance, while tolerating variations in observer gain. Next, a resilient proportional-derivative-like scaled group consensus protocol is formulated, accounting for both the observer and communication delays. Notably, this protocol achieves scaled group consensus while enhancing performance. A new delay-product type Lyapunov-Krasovskii functional is then developed, incorporating terms for triple integrals and Bessel-Legendre vectors, unlike the traditional quadratic form. By applying the Bessel-Legendre inequality and the extended reciprocally convex matrix inequality, new sufficient conditions for scaled group consensus are derived, yielding reduced conservatism. Finally, numerical examples are provided to validate the theoretical findings.
查看更多>>摘要：The two-dimensional anisotropic phase field crystal (APFC) model is a sixth-order nonlinear parabolic equation that can be used to simulate various phenomena such as epitaxial growth, material hardness, and phase transition. The scalar auxiliary variable method (SAV) is a common method to solve various nonlinear dissipative systems, and the improved SAV (iSAV) method is not only completely linear, but also strictly guarantees the original dissipation law. In this paper, we construct several efficient, accurate linear and original energy-stable numerical schemes of the APFC model based on the iSAV method. Firstly, a first-order iSAV scheme is considered to keep the original energy stability for the APFC model. Secondly, we propose a new stabilized iSAV scheme and give its rigorous energy stability analysis to keep its original dissipation law. Finally, several interesting numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed methods.
查看更多>>摘要：Interval-valued data have attracted attention across various applications, prompting an increase in research on spatial models for interval-valued data. The study of the nonlinear characteristics of spatial interval-valued data over time has become essential; however, existing models demonstrate significant limitations in adequately characterizing these dynamics. This paper presents a spatial panel interval-valued model with time-varying coefficient and individual fixed effects, utilizing the parametric method. The local linear generalized method of moments is employed for parameter estimation, and its consistency and asymptotic properties are discussed. Monte Carlo simulations are employed to validate the fitting and predictive performance of the proposed model across various scenarios. Furthermore, the model is used to real-world air quality datasets for forecasting purposes, highlighting the practical utility of the proposed model.
查看更多>>摘要：This paper aims to study the multi-physics coupling interaction mechanism between thermal, lubrication and dynamics of bearings. Firstly, considering the influence of clearance, the load distribution integral is introduced to evaluate the non-uniform load characteristics of the bearing. On this basis, the bearing point contact lubrication model was established based on elastohydrodynamic lubrication theory. Secondly, the heat transfer mesh model of the bearing was established based on the heat transfer theory to solve the thermal expansion of the bearing assembly. Furthermore, the lubrication model, heat transfer mesh model and existing mechanics model are coupled through the clearance factor, the bearing dynamics model considering the TLM (thermal-lubrication-mechanics) coupling characteristics was established, and the step-by-step correlation solution method was proposed which can effectively solve the coupled model. Finally, by comparing with the existing mechanical models, the effect mechanism of load parameters, bearing parameters and lubricating oil parameters on the dynamic response of the TLM model was analyzed. The research content supplements and optimizes the existing bearing dynamics models and analysis methods, and provides theoretical guidance for designers to effectively evaluate the impact of more comprehensive engineering factors on the bearing dynamic.
查看更多>>摘要：Based on a continuous model of memristors, memristive neural networks with interval delays are described in the flux-voltage-time domain. Considering memristors as uncertain parameters, the systems are reduced to neural networks with parameter uncertainties. Then, nonzero quasi-equilibrium points and the quasi-stability are first proposed for memristive neural networks with interval delays, which provide a new approach to study the boundedness of solutions. Quasi-stability criteria are derived by poly-topic uncertainty method and norm-bounded uncertainty method, respectively. Finally, an example is given to show the effectiveness of our theorems.
查看更多>>摘要：The response of the spiral wave chimera on the feedback signal from a measuring location is investigated in the three-component reaction-diffusion system with two spatial dimensions. When the feedback gain is small, the feedback forces the incoherent core to follow a circular orbit with finger-shaped bulges, and the circular path exhibits more complex structures with an increases of the time delay. For a large feedback gain, the excitation in front of the wave front causes the disappearance of the spiral arm except for some residual segments, which will be developed into the wave structures with multiple incoherent cores, where one of the cores is located at the measuring point. Four types of dynamical behaviors are identified for an intermediate feedback gain, depending on the time delay, and these behaviors cannot be observed in the local feedback control of normal spiral waves. For the first three types, the spiral chimera will eventually disappear, but through three different processes, including the formation of transient incoherent arcs, the drift of the incoherent core to the boundary along a spiral, and the complex drift with a transient closed path. The fourth type appears for a large time delay, where the incoherent core drifts to the measuring point along a spiral. These results relate to the control of the spiral chimera, where the spiral chimera can be eliminated by the feedback exhibiting the first three dynamical behaviors, and its core can be controlled to the designated location by the feedback exhibiting the fourth dynamical behavior.
NETL
NSTL
Elsevier