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A novel multidimensional characteristics approach for inflow and outflow boundaries of compressible twodimensional flows is presented. The modified Riemann variables have been extracted from the Euler equations by considering the directions of waves reaching the inflow and outflow boundaries. By applying this model in a shortened computational domain, the boundaries can be located close to the nonlinear zone. The results of reduced and extended domains are in good agreement with each other. Using this model yields in a reduction of computational domain while keeping the solution accuracy and lowering the computation time.

It has recently been established that the tube formula and the Euler characteristic method give an identical and valid asymptotic expansion of the tail probability of the maximum of a Gaussian random field when the random field has finite Karhunen-Loève expansion and the index set has positive critical radius. We show that the positiveness of the critical radius is an essential condition. When the critical radius is zero, we prove that only the main term is valid and that other higher-order terms are generally not valid in the formal asymptotic expansion based on the tube formula. This is done by first establishing an exact tube formula and comparing the formal tube formula with the exact formula. Furthermore, we show that the equivalence of the formal tube formula and the Euler characteristic method no longer holds when the critical radius is zero. We conclude by applying our results to some specific examples.

Monitoring structural damage in terms of material degradation is extremely important for enhancing the residual life of civil infrastructure. For the past two decades vibration based techniques have gained importance in the field of structural engineering in damage detection. The changes in the dynamic characteristics are observed due to changes in the mass and stiffness of the structure/structural component. The present paper focuses on detection of damage through vibration analysis in simply supported beams and predicting the damage extent using machine learning technique. The numerical model is validated against the standard Euler-Bernoulli beam subjected to free vibration. The same finite element model is subjected to induced damage in terms of change in material properties. Modal characteristics of all the damage scenarios i.e. reduction in Young’s modulus by 10% -80% with increment of 10% at a time are captured and a machine learning algorithm (Support Vector Machine) is developed for the prediction of damage extent. It is concluded that the SVM algorithm is effective in the case of natural frequencies as input features rather than statistical parameters as input features in predicting the damage extent in the beams.

As a critical component of power systems, transmission lines increasingly traverse complex terrains and harsh environments with the continuous expansion of power grids. The growing incidence of ice-induced galloping failures necessitates a thorough investigation into the galloping characteristics of ice-coated conductors. This study focuses on low wind pressure conductors, a novel structural type with superior aerodynamic characteristics. To examine their ice galloping behavior, we developed a numerical model of ice-accreted low wind pressure conductors to calculate aerodynamic force data. From the perspective of energy conservation, a three-degree-of-freedom galloping equation was established based on Lagrangian equations. The governing equations were discretized using the Galerkin method and subsequently solved through the Runge-Kutta algorithm to obtain time-history displacement responses. Comparative analysis with conventional conductors under varying wind speeds demonstrates the distinctive galloping characteristics of low wind pressure conductors, providing crucial data support for their anti-galloping applications in transmission lines.

In this paper we study the smooth solutions of the hydrostatic Euler equations. By a careful construction we establish an analytical lemma; in this lemma, we find the explicit formula in a specific class of functions that maximizes the L 2 integral. Basing on a classical invariant transformation we simplify the problem. As a result, for a more general class of initial data we obtain the finite time blowup of the smooth solutions of the hydrostatic Euler equations in a strip domain by this lemma and repeatedly apply the method of characteristics.

In the present study a mathematical model of the equatorial water waves propagating mainly in one direction with the effect of Earth’s rotation is derived by the formal asymptotic procedures in the equatorial zone. Such a model equation is analogous to the Camassa–Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solution corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated. Our refined analysis is approached by applying the method of characteristics and conserved quantities to the Riccati-type differential inequality.

In this article, the behavior and the efficiency of a nonlinear passive vibration isolator based on a bar and an Euler beam are investigated analytically. The proposed isolator is specifically for isolating vehicle seat from unwanted disturbances in the low frequency range, thereby making the seat comfortable for the driver. The static characteristics of the negative stiffness as well as the nonlinear mathematical model are presented, and its dynamic characteristics are investigated using the harmonic balance method. In addition, the effect of the initial geometric imperfection of the Euler beam is included in the study. The study shows that the performance of the negative isolator has a large isolation frequency range than that of the linear isolator. The configuration parameter choice for the seat base will be vital for the suitable application of this isolator.

The pore-scale morphological description of two-phase flow is fundamental to the understanding of relative permeability. In this effort, we visualize multiphase flow during core flooding experiments using X-ray microcomputed tomography. Resulting phase morphologies are quantified using Minkowski Functionals and relative permeability is measured using an image-based method where lattice Boltzmann simulations are conducted on connected phases from pore-scale images. A capillary drainage transform is also employed on the imaged rock structure, which provides reasonable results for image-based relative permeability measurements even though it provides pore-scale morphologies for the wetting phase that are not comparable to the experimental data. For the experimental data, there is a strong correlation between non-wetting phase Euler characteristic and relative permeability, whereas there is a weak correlation for the wetting phase topology. The relative permeability of some rock types is found to be more sensitive to topological changes than others, demonstrating the influence that phase connectivity has on two-phase flow. We demonstrate the influence that phase morphology has on relative permeability and provide insight into phase topological changes that occur during multiphase flow.

To study the dynamic characteristics of remotely operated vehicle (ROV) underwater motion, a transformation matrix between the carrier coordinate system and the inertial coordinate system was established, and the rigid body dynamics model of the ROV was derived by using the Newton-Euler equation. According to the results of the ROV experimental prototype in this article, the dynamic model is simplified based on the force, motion characteristics, and structural characteristics. In the pool experiment, based on the propeller dynamic model, the least squares method was used to identify the parameters of the heading and vertical dynamic models, and through the experimental results under step control signals of different amplitudes, they were compared with the models under the same control signal. The output is subjected to error analysis. The experimental results show that the error between the theoretical value and the experimental value is small, verifying the accuracy of the ROV dynamics model established in this article.

Understanding and optimizing the dynamic characteristics of machine tools are essential for improving the efficiency and precision of manufacturing processes. An effective method for dynamic characteristic prediction and analysis of various tools is receptance coupling substructure analysis. Precision receptance coupling substructure analysis requires a frequency response function for the rotational degrees of freedom. Although computing the full receptance matrix, which includes rotational degrees of freedom, is possible through mathematical methods or finite element method, it is time-intensive and impractical for industrial applications due to the need for additional sensor attachments or other attachments on machinery. This study proposes a new approach for the receptance coupling substructure analysis of cutting tools and holders, aiming to efficiently predict and couple the full receptance matrix of cutting tools under free-free condition. The proposed methodology divides the cutting tool into several substructures and employs receptance coupling based on Euler–Bernoulli beam theory, thereby estimating the full receptance matrix of the subassembly. This approach also enables the prediction of dynamic characteristics of the system through inverse receptance coupling with a holder. We validated the accuracy of the methodology using the finite element method and experimental methods. The full receptance matrix of the machine tool and the estimated cutting tools were coupled and experimentally verified. In addition, the applicability of the proposed methodology is ensured by performing receptance coupling for various tool overhang lengths. This study is expected to contribute significantly to the quality improvement, design, and performance enhancement of machining equipment in the manufacturing industry. Further research is required to validate the robustness of this methodology across tools with diverse geometries and shapes.