Dynamics

This paper uses the flexural vibration of cantilever beams as a benchmark problem to test mesh-free and finite element methods in structural dynamics. First, a symbolic analysis of the “kernel collocation” type mesh-free method is carried out, in which the collocation function satisfies the boundary conditions. This enables both Finite Element (FE) and mesh-free results to be compared with exact analytical ones. Thereafter, the natural frequencies and Frequency Response Function (FRF), in terms of the beam parameters, are determined and compared with the analytical results, that exist in the literature. It is shown that by adjusting the parameters of the kernel function, we can find identical peaks to those of the analytical method. The finite element method is also employed to solve this problem, and the first three natural frequencies were computed in terms of the beam parameters. When comparing the two methods, we see that by increasing the number of elements in the FEM we can always achieve better accuracy, but we will obtain twice the number of modal frequencies. However, the mesh-free method with the same number of nodes does not provide these extra frequencies. From this benchmark problem, it is concluded that the accuracy of the mesh-free methods always depends on the adjustment of the kernel function. However, the FEM is advantageous because it does not require such adjustments. Full article

One concern in the field of Horizontal Axis Wind Turbines (HAWTs) is what control strategies are needed to handle gust pulses in the wind to prevent extreme oscillations of the blades to reduce fatigue stress, prevent blade rupture, and extend the turbine’s operational life. In order to design innovative control strategies to modify the blade’s oscillatory response, it is crucial to establish the fundamental vibrational behavior of the blades when excited by gust pulses of different frequencies and amplitudes present in the fluctuating wind inflow. In a series of previous works, the authors presented a novel Reduced-Order Characterization (ROC) technique that provided an energy-based characterization of the fundamental modes of oscillation of wind turbine rotors when excited by combinations of wind gust pulses of different frequencies and amplitudes. The main focus of the present work is to extend these original notions of energy-based ROC to a universal technique expressed in terms of non-dimensional quantities that could be applied to turbines of any size, operating in any set of wind conditions, as long as they share geometrical and material similarity. The ROC technique provides a simple formula that is capable of predicting the dominant vibrational modes of a blade with sufficient precision to be useful in the determination of a control decision that can be computed in real time, an aspect of fundamental importance in dealing with rapid fluctuations in wind conditions. Full article

The Ramsey approach is applied to analyses of the kinematics of systems built of non-relativistic, motile point masses/particles. This approach is based on colored graph theory. Point masses/particles serve as the vertices of the graph. The time dependence of the distance between the particles determines the coloring of the links. The vertices/particles are connected with orange links when particles move away from each other or remain at the same distance. The vertices/particles are linked with violet edges when particles converge. The sign of the time derivative of the distance between the particles dictates the color of the edge. Thus, a complete, bi-colored Ramsey temporal graph emerges. The suggested coloring procedure is not transitive. The coloring of the links is time-dependent. The proposed coloring procedure is frame-independent and insensitive to Galilean transformations. At least one monochromatic triangle will inevitably appear in the graph emerging from the motion of six particles due to the fact that the Ramsey number $R\left(\mathrm{3,3}\right)=6.$ This approach is extended to the analysis of systems containing an infinite number of moving point masses. An infinite monochromatic (violet or orange) clique will necessarily appear in the graph. Applications of the introduced approach are discussed. The suggested Ramsey approach may be useful for the analysis of turbulence seen within the Lagrangian paradigm. Full article

In recent years, inulin enzymatic hydrolysis has become a very promising alternative for producing fructose on a large scale. Genetically modified chicory was used to extract inulin of industrial quality. By using an adequate kinetic model from the literature, this study aimed to determine the optimal operating alternatives of a batch (BR) or fed-batch (FBR) reactor used for the hydrolysis of inulin to fructose. The operation of the FBR with a constant or variable/dynamic feeding was compared to that of the BR to determine which best maximizes reactor production while minimizing enzyme consumption. Multi-objective optimal solutions were also investigated by using the Pareto-optimal front technique. Our in-silico analysis reveals that, for this enzymatic process, the best alternative is the FBR operated with a constant control variable but using the set-point given by the (breakpoint) of the Pareto optimal front under the imposed technological constraints. This set point reported the best performances, regarding all the considered opposite economic objectives. Also, the FBR with a constant, but NLP optimal feeding, reported fairly good performances. Full article

Solving nonlinear oscillations is challenging, as solutions to the corresponding differential equations do not exist in most cases. Therefore, numerical methods are usually employed to calculate the precise oscillation frequency. In addition, many interesting mathematical approaches leading to approximate solutions have also been developed. This paper focuses on a classic case of a nonlinear oscillator: the oscillator with an odd-power polynomial restoring force. This case encompasses nearly all scenarios of undamped nonlinear oscillations. The idea is to combine two well-known strategies from the literature: He’s approximation, which is simple to apply and valid for small amplitudes, and the analytical solutions for oscillations with power-law restoring forces. It is shown that by combining these approaches, a universal equation accurate for any amplitude is derived. Many tests of the proposed method’s accuracy are presented using polynomials of various degrees and classic examples, such as the rotating pendulum, cubic–quintic Duffing oscillators, and oscillators with cubic and harmonic restoring forces. In addition, a novel ‘electrical analogue’ of the oscillation with a polynomial-type restoring force is introduced to demonstrate that the methods presented in this paper can be applied in real industrial applications. Full article

Global climate change has renewed interest in wind energy adoption and integration for on-grid and off-grid applications. Savonius wind turbines offer substantial advantages for small-scale energy generation in low-wind speed conditions, like urban environments, but suffer from low efficiency. This study focused on the numerical characterization of a novel compact three-blade Savonius rotor design with modified pointed deflectors to promote better flow attachment and enhance airflow guidance directionality. Computational Fluid Dynamics (CFD) was employed to identify the flow characteristics and optimal tip speed ratios for maximum power and torque coefficients under two different uniform low-wind-speed conditions. A Finite Element Analysis-Computational Fluid Dynamics (FEA-CFD) coupled analysis method was also utilized to determine the aerodynamic and structural characteristics of the design in ABS plastic. Flow visualization and FEA-CFD coupled analysis highlighted the novel tip deflectors’ exceptional performance in directing wind flow and pressure toward the concave side of the approaching blades, enhancing drag differential and rotor efficiency. Modest power and low torque coefficients and the optimal TSR values under different uniform low-wind-speed conditions were also identified. The work provided valuable insights on the turbine performance of the novel design and guidance on potential future improvements. Full article

In this paper, we introduce waveguide Quantum Electrodynamics (wQED) for the description of tryptophans in microtubules representing data qubits for information storage and, possibly, information processing. We propose a Hamiltonian in wQED and derive Heisenberg equations for qubits and photons. Using the Heisenberg equations, we derive time-evolution equations for the probability of qubits and the distribution of photons both at zero and finite temperature. We then demonstrate the resultant sub-radiance with small decay rates, which is required to achieve robust data qubits for information storage by coupling tryptophan residues containing data qubits with water molecules as Josephson quantum filters (JQFs). We also describe an oscillation processes of qubits in a tubulin dimer through the propagation of excitations with changing decay rates of JQFs. Data qubits are found to retain initial values by adopting sub-radiant states involving entanglement with water degrees of freedom. Full article

A novel method to measure dynamic flow stress and corresponding strain rates obtained from Taylor tests using profiled samples with a reduced cylindrical head part was applied to study the dynamic characteristics of similar commercial 7075 and V95T1 aluminum alloys. The measured dynamic flow stress is verified using a classical Taylor’s approach with uniform cylinders and compared with the literature data. Our study shows that the dynamic flow stress of 7075 alloy, which is 786 MPa at strain rates of (4–8) × 10³ s⁻¹, exceeds the value of 624 MPa for V95T1 alloy at strain rates of (2–6) × 10³ s⁻¹ by 25%. The threshold impact velocity resulting in fracture of the 4 mm head part of the profiled samples is 116–130 m/s for 7075 alloy and only 108 m/s for V95T1 alloy. The fracture pattern is also different between the alloys with characteristic shear-induced cracks oriented at 45° to the impact direction in the case of V95T1 alloy and perpendicular to the breaking off head part in the case of 7075 alloy. On the other hand, the compressive fracture strain of V95T1 alloy, which is 0.29–0.36, exceeds that of 7075 alloy, which is 0.27–0.33, by approximately 8%. Thus, V95T1 aluminum alloy exhibits less strength but is more ductile, while 7075 aluminum alloy exhibits more strength but is simultaneously more brittle. Full article

The Split-Hopkinson pressure bar (SHPB) test is a commonly accepted experiment to investigate the material behavior under high strain rates. Due to the low impedance of soft materials, here, the test has to be performed with plastic bars instead of metal bars. Such plastic bars have a certain viscosity and require a correction of the measured signals to account for the attenuation and dispersion of the transmitted waves. This paper presents a signal correction method based on a spectral decomposition of the strain-wave signals using Fast Fourier Transform and additional applied strain gauges in the experimental setup. The concept can be used to adapt the pulses and to concurrently validate the measurement method, which supports the evaluation of the experiment. Our investigation is carried out with a Split-Hopkinson pressure bar setup of PMMA bars and silicon-like specimens produced by the 3D printing process of digital light processing. Full article

In this study, we present an exact solution to the Lindblad master equation describing the interaction of two quantized electromagnetic fields in a decaying cavity coupled to a thermal reservoir at a finite temperature. The solution is obtained using the superoperator technique, leveraging commutation relations to factorize the exponential of the Lindblad superoperators into a product of exponentials. To demonstrate the applicability of this approach, we analyze the dynamics of the system both analytically and numerically for two initial conditions: nonentangled and entangled coherent states, exploring their temporal evolution. Additionally, we employ entropy and quantum discord analysis to characterize quantum correlations and analyze the behavior of entanglement (or lack thereof) during the evolution. This comprehensive analysis provides valuable insights into the behavior of open quantum systems and their interaction with the environment. Full article

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss). Full article

This study investigates mixed convection flow over a vertical thin needle with variable surface heat, mass, and microbial flux, incorporating the influence of gyrotactic microorganisms. The governing partial differential equations are transformed into ordinary differential equations using appropriate similarity transformations and then solved numerically by employing MATLAB’s Bvp4c solver. The primary focus lies in examining the influence of various dimensionless parameters, including the mixed convection parameter, power-law index, buoyancy parameters, bioconvection parameters, and needle size parameters, on the velocity, temperature, concentration, and microbe profiles. The results indicate that these parameters significantly affect the surface (wall) temperature, fluid concentration, and motile microbe concentration, as well as the corresponding velocity, temperature, concentration, and microorganism profiles. The findings provide insights into the intricate dynamics of mixed convection flow with bioconvection and have potential applications in diverse fields such as biomedicine and engineering. Full article

A static pressure probe is a crucial tool for measuring static pressure fluctuations, and its internal cavity structure can significantly affect the accuracy of the data obtained. This study investigates the impact of the static pressure probe cavity on the frequency response characteristics of fluctuating pressure using both experimental and numerical simulations. The results are validated by comparing them with the behavior of a second-order system. Our findings indicate that the internal cavity of the static pressure probe acts as a second-order underdamped system. This system amplifies fluctuating pressure signals at frequencies below the characteristic frequency while attenuating those above it. The frequency response characteristics of the probe’s cavity are similar to those of a Helmholtz resonator. Among various factors, the diameter of the pressure tap within the cavity has the most significant effect on the system’s characteristic frequency and amplification ratio. By optimizing the design of the static pressure probe’s cavity dimensions, the precision of fluctuating pressure data below the system’s characteristic frequency can be improved. In the research, based on the Helmholtz resonance equation, we provide a semi-empirical formula for predicting the characteristic frequency of fluctuating pressure in a static pressure probe. Furthermore, by leveraging the mechanism of the static pressure probe’s cavity as a second-order underdamped system, we propose a method for rapid and accurate calibration of the static pressure probe’s fluctuating pressure measurements. Full article

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