Article
Computer Science, Artificial Intelligence
Kemal Ucak
Summary: This paper introduces a new adaptive controller based on RK integration, adjusting adaptive parameters by treating control law as an ODE and using LM technique. Performance evaluation on VdV system shows reasonable results for the introduced adaptation mechanism.
Article
Engineering, Mechanical
Amaroju Kartheek, Kiran Vijayan, Xiaodong Sun, Steffen Marburg
Summary: Rotating shaft instability causing high amplitude vibration is a significant issue in various industrial applications. This study focuses on a conceptual model of a flexible shaft supported on hydrodynamic bearings (HDBs) to identify response statistics and propose design strategies to mitigate the vibration. The critical speeds that result in high responses are identified through a Campbell diagram analysis. The effects of whirling modes on the response are investigated considering the uncertainty introduced by manufacturing processes and operating conditions. Control strategies are designed to reduce the excitation of the first mode by altering the relative position of unbalance masses. Stochastic analysis is conducted to verify the effectiveness of the strategy.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Engineering, Mechanical
Gaute Fotland, Bjorn Haugen
Summary: In this study, the stability, efficiency, and accuracy of the Absolute Nodal Coordinate Formulation (ANCF) in the Arbitrary Lagrangian-Eulerian (ALE) formulation for cable simulation were examined. The Runge-Kutta method RK4 and the Generalized-������ method were compared in different frequency domains. The results showed that the Generalized-������ method is stable and accurate for low frequency simulations with large time-steps, while the RK4 method is more efficient for high frequency simulations. Different constraint techniques can be used to connect ALE-ANCF cable elements without affecting their ability to exhibit large deformations.
MECHANISM AND MACHINE THEORY
(2022)
Article
Computer Science, Software Engineering
Daniel R. Reynolds, David J. Gardner, Carol S. Woodward, Rujeko Chinomona
Summary: We introduce the ARKODE library, which contains one-step time integration methods for ordinary differential equation initial-value problems. It not only includes standard explicit and diagonally implicit Runge-Kutta methods, but also supports one-step methods for additive splittings of the IVP, such as implicit-explicit additive Runge-Kutta methods and multirate infinitesimal methods.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2023)
Article
Thermodynamics
S. Noor Arshika, P. G. Siddheshwar, Sameena Tarannum
Summary: The paper discusses two Rayleigh-Benard magnetoconvection problems with asymmetric boundaries, one involving a mono-nanofluid (H2O-Cu) and the other involving a hybrid nanofluid (H2O-Cu-Al2O3). A minimal Fourier-Galerkin expansion is used to obtain the generalized Lorenz model (GLM), which is then simplified to an analytically solvable Ginzburg-Landau equation using the multiscale method. The study reveals the impact of asymmetric boundaries on the dynamics and characteristics of the convection.
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY
(2023)
Article
Engineering, Multidisciplinary
Rainald Lohner, Harbir Antil
Summary: Deep neural network (DNN) architectures act as explicit Runge-Kutta schemes for numerical time integration without the need for training. The DNN approximation of the right-hand side is the only task left for physics-based integrators, allowing for clear estimation of approximation errors. An example of the architecture required for integrating a mass-damper-stiffness case is provided.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Takeru Matsuda, Yuto Miyatake
Summary: This study calculates the gradient of a function of numerical solutions of ODEs with respect to the initial condition, approximating it using the adjoint method. It is shown that when solving the initial value problem with a Runge-Kutta method, the gradient can be exactly computed, and a generalized numerical method for the adjoint system is proposed for partitioned RK methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Engineering, Mechanical
Shuaijun Ma, Yanjing Yin, Ben Chao, Ke Yan, Bin Fang, Jun Hong
Summary: This study proposes a dynamic model of a bearing-rotor system by introducing a semi-flexible body element (SFBE) to consider the flexibility of the rotor. By defining the deflection/force relationship between neighboring SFBEs, the same differential equations of motion as those for bearing assemblies were established, achieving real-time coupling and simultaneous solutions of the bearing and rotor models. The dynamic response of the system was determined by solving these equations. The good agreement between the experimental data and simulation results proves the validity of the proposed model. Additionally, the effect of eccentric excitation on the dynamic behavior of the bearing-rotor system was investigated.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2023)
Article
Mathematics, Applied
B. E. N. S. Southworth, Oliver Krzysik, Will Pazner
Summary: This paper presents a theoretical and algorithmic framework for solving the nonlinear equations arising from IRK methods, offering new linearizations and demonstrating their effectiveness and stability. By applying these methods to challenging fluid flow problems, the high accuracy and efficiency of high-order IRK methods are showcased.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Software Engineering
Patrick E. Farrell, Robert C. Kirby, Jorge Marchena-Menendez
Summary: Although implicit Runge-Kutta methods are accurate and stable, the implementation difficulties and high cost of solving the algebraic systems at each time step can be obstacles. Irksome is a high-level library that manipulates UM expressions to obtain UFL expressions for the coupled Runge-Kutta stage equations. It works with Firedrake package to efficiently solve the resulting algebraic systems, and numerical examples confirm its efficacy for various problems.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2021)
Article
Automation & Control Systems
Mahboubeh Asadi Varnusfaderani, Mostafa Irannejad Parizi, Masoud Hemmatian, Abdolreza Ohadi
Summary: Magnetorheological fluid is an effective smart fluid used for vibration control. In this study, analytical tools and algorithms are presented for identifying the parameters of flexible rotor systems equipped with MR squeeze-film dampers. The developed algorithm and finite element model are shown to accurately identify the system parameters.
Article
Mathematics, Interdisciplinary Applications
Abdelaziz Beljadid, Youssef Joundy, Hamza Rouah, Ahmed Taik
Summary: In this paper, the transition from thermal convection to chaos in a five-dimensional model in a porous medium with low Prandtl number is investigated. The numerical results reveal the transition mechanisms and characteristics from steady convection to chaotic convection.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Xiaole Yue, Yilin Xiang, Ying Zhang, Yong Xu
Summary: This paper studies the stochastic bifurcation of a shape memory alloy supporter system and identifies three kinds of bifurcation phenomena caused by collision between attractors and saddles. The study calculates transfer probability for escaping points within the basin of attraction, providing a quantitative explanation of the system's phase space structure with stochastic bifurcation. The extended composite cell coordinate system method is shown to be a powerful tool for revealing the mechanism of stochastic bifurcation.
Article
Computer Science, Interdisciplinary Applications
Razan Abu-Labdeh, Scott MacLachlan, Patrick E. Farrell
Summary: Most research on preconditioners for time-dependent PDEs has focused on implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid preconditioners for fully-implicit multi-stage Runge-Kutta (RK) time integration methods. These relaxation schemes lead to robust and scalable monolithic multigrid methods for a challenging range of incompressible fluid-flow models.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Acoustics
Guofang Nan, Yujie Zhu, Yang Zhang, Wei Guo
Summary: The study investigates the nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity and considers various factors such as unbalanced excitation and nonlinear stiffness. The research finds that the system exhibits complex nonlinear behaviors, and the nonlinear characteristics are significantly enhanced with increasing stiffness. The study contributes to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.
SHOCK AND VIBRATION
(2021)
