Dynamics, Volume 4, Issue 4 (December 2024) – 9 articles

In this paper, an analytical technique is proposed to obtain the forced response of a cantilevered tube conveying fluid. By considering the pipe subjected to an arbitrary harmonic force, either distributed or concentrated, an analytical solution is found using Green’s function method. The closed-form solution obtained satisfies the differential equations governing the vibrating tube conveying fluid. The proposed method, which provides exact solutions, is more accurate than the classical eigenfunction expansion or Galerkin’s method and eliminates the need for eigenfunctions, eigenvalues, or infinite series. Full article

In this paper, a brief review regarding the hydrodynamic circulation of the Mediterranean gulfs is presented. Studies concerning the hydrodynamics of the Mediterranean gulfs with significant environmental and commercial importance were gathered as an initial insight of studies in the Mediterranean microtidal environment. Numerical models, field measurements, and satellite images are the methods used by the investigators for the description and prediction of the circulation in the gulfs. The basic hydrodynamic characteristics of the gulfs are mainly defined by the wind action and less by tide and baroclinicity. Most of the gulfs are characterized by a cyclonic wind-driven circulation, since the tidal effect remains weak in the Mediterranean basin. However, tidal resonance and strong currents are evident in the shallow coastal areas as well as in the wider area of straits. Basic gulfs’ characteristics are summarized in a table that gives an overview of the main Mediterranean gulfs, which can be especially useful for young researchers or new hydroenvironmental studies in the Mediterranean marine and coastal environment. Full article

The specifics of a shock wave propagation down a positive column of a DC discharge in molecular chemically inert gases has been investigated. It was shown that axial gradients caused by the imbalance in the charged particle momentum transfer to the gas molecules can be a reason for the shock velocity dependence on the electric field direction. In pure nitrogen gas, the calculated shock velocity difference of up to 13.5% is in good agreement with the 12% value obtained in the experiment. A returning gas flow organizing in the discharge as a possible mechanism for an extended shock structure and a number of kinetical factors capable of affecting the shock motion are discussed. Full article

We propose a Ramsey-theory-based approach for the analysis of the behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero. The mechanical system is described by a Ramsey-theory-based, bi-colored, complete graph. Vectors of momenta of the particles ${\overrightarrow{p}}_i$ serve as the vertices of the graph. We start from the graph representing the system in the frame of the center of masses, where the momenta of the particles in this system are ${\overrightarrow{p}}_{cmi}.$ If ${(\overrightarrow{p}}_{cmi}(t)·{\overrightarrow{p}}_{cmj}(t))\ge 0$ is true, the vectors of momenta of the particles numbered i and j are connected with a red link; if ${(\overrightarrow{p}}_{cmi}(t)·{\overrightarrow{p}}_{cmj}(t))<0$ takes place, the vectors of momenta are connected with a green link. Thus, the complete, bi-colored graph emerges. Considering an isolated system built of six interacting particles, according to the Ramsey theorem, the graph inevitably comprises at least one monochromatic triangle. The coloring procedure is invariant relative to the rotations/translations of frames; thus, the graph representing the system contains at least one monochromatic triangle in any of the frames emerging from the rotation/translation of the original frame. This gives rise to a novel kind of mechanical invariant. Similar coloring is introduced for the angular momenta of the particles. However, the coloring procedure is sensitive to Galilean/Lorenz transformations. Extensions of the suggested approach are discussed. Full article

Wind–solar power generating and hybrid battery-supercapacitor energy storage complex is used for autonomous power supply of consumers in remote areas. This work uses passivity-based control (PBC) for this complex in accordance with the accepted energy management strategy (EMS). Structural and parametric synthesis of the overall PBC system was carried out, which was accompanied by a significant amount of research. In order to simplify this synthesis, a structural decomposition of the overall dynamic system of the object presented in the form of a port-Hamiltonian system, which was described by a system of differential equations of the seventh order, into three subsystems was applied. These subsystems are a wind turbine, a PV plant, and a hybrid battery-supercapacitor system. For each of the subsystems, it is quite simple to synthesize the control influence formers according to the interconnections and damping assignment (IDA) method of PBC, which locally performs the tasks set by the EMS. The results obtained by computer simulation of the overall and decomposed systems demonstrate the effectiveness of this approach in simplifying synthesis and debugging procedures of complex multi-physical systems. Full article

Regular damped oscillatory structures from the “effective” electromagnetic form factors of the hadrons $h={\pi }^{\pm },K^{\pm },K^0,p,n$ were investigated. The “effective” electromagnetic form factor behaviors were calculated from the experimental data on the total cross-sections ${\sigma }_{tot}(e^{+}{e}^{-}\to h\overline{h})$ with errors. The apparent oscillations were observed for the first time for the proton, and we show, also taking other hadrons into consideration, that they are an arbitrary artifact resulting from a very simplistic theoretical description based on an elementary three-parameter model. If the data are described by a more appropriate and physically well-founded Unitary and Analytic model, then the oscillations disappear. In spite of this, if the three-parameter model is used to describe the “effective” electromagnetic form factor data, an interesting phenomenon is observed. The oscillations are opposite for particles which form an isospin doublet. By using the physically well-founded Unitary and Analytic model, it is demonstrated that this feature originates from the special transformation properties of the electromagnetic current of the corresponding particles in the isotopic space. Full article

Structural Health Monitoring (SHM) plays a vital role in ensuring the health status of a wide range of structures, such as bridges, buildings, and large infrastructure in general. The advantages of this process can be further enhanced by incorporating more numerical and statistical approaches into traditional methods, such as finite element analysis and Machine Learning. In this study, a truss bridge structure is examined, and neural networks are trained with data derived from finite element analyses under static loads and dynamic excitations. The contributions of this work are based on comparing neural networks trained with static and dynamic analyses, as well as deriving important insights into the key parameters that impact their performance in SHM. Initially, a binary classification problem is addressed, where numerically trained classifiers are tasked with identifying whether the structure is in a healthy state or not. This category is further divided into two subcategories, depending on the extent of the damage present in the structure. Subsequently, a multi-class classification problem is defined, where three different damage classes of the same extent are considered, and the trained network is required to distinguish between them. Although the training of all neural networks was highly satisfactory, the prediction results varied, with success rates ranging from 55% to 90%. Finally, conclusions are drawn from the results of the study regarding the model error influence, the impact of the damage size, and the types of neural networks and training data used. Full article

Marine propeller design requirements have risen in quantity and quality in recent decades. Reduced propeller cavitation is targeted to ensure that comfort requirements and environmental regulations are met. This paper presents the development of a mesh refinement process for the numerical prediction of tip vortex cavitation (TVC) using the commercial CFD package STAR-CCM+. Given the strong dependence on the mesh resolution within the areas of interest, mesh refinement and the use of field functions for adaptive meshing were demonstrated. The developed numerical model was substantiated against relevant published test data. Subsequently, the validated mesh refinement process was extended to scaled-up models representing medium- and full-scale propellers. The results showed that this process can be applied to CFD simulations to capture the minimum pressure within a tip vortex core. This process is also applicable to different types of hydrodynamic propulsors at both model scale and full scale. Additionally, the cavitation inception scaling law was evaluated for all small-scale and full-scale models, and it was found that the scaling parameter obtained using the developed refinement process was somewhat close to that obtained using existing methods. It is expected that the mesh refinement process developed in this study can be used to investigate the effect of scaling on tip vortex cavitation inception. Full article

In this study, a novel non-cooperative two-player game for minimizing static (Player 1) and dynamic (Player 2) compliances is introduced, implemented, and demonstrated using a multi-scale topology optimization framework for triply periodic minimal surface (TPMS)-based lattice structures. Player 1 determines the optimal macro-layout by minimizing the static compliance based on a micro-layout provided by Player 2. Conversely, player 2 identifies the optimal micro-layout (grading of the TPMS-based lattice structure) by minimizing the dynamic compliance given a macro-layout from Player 1. The multi-scale topology optimization formulations are derived using two density variables in each finite element. The first variable is the standard density, which dictates whether the finite element is void or contains the graded lattice structure and is governed by the rational approximation of material properties (RAMP) model. The second density variable represents the local relative density of the TPMS-based lattice structure, determining the effective orthotropic elastic properties of the finite element. The multi-scale game is implemented for three-dimensional problems, and solved using a Gauss–Seidel algorithm with sequential linear programming. It is numerically demonstrated for several benchmarks that the proposed multi-scale game generates equilibrium designs with strong performance for both static and harmonic load cases, effectively avoiding resonance at harmonic load frequencies. Validation is achieved through modal analyses of finite element models of the optimal designs. Full article