Dynamics

The recently proposed conformable deformation of quantum mechanics by a fractional parameter $\alpha \in (0,1]$ has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at $\alpha =1$. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the $x^{\alpha }$-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the $\alpha =1$ limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator. Full article

We present an analytical framework for describing light propagation in infinite waveguide arrays, incorporating a generalized long-range coupling to achieve a more realistic model. We demonstrate that the resulting solution can be expressed in terms of generalized Bessel-like functions. Additionally, by applying the concept of eigenstates, we borrow from quantum mechanics a basis given in terms of phase states that allows the analysis of the transition from the discrete to the continuum limit, obtaining a relationship between the field amplitudes and the Fourier series coefficients of a given function. We apply our findings to different coupling functions, providing new insights into the propagation dynamics of these systems. Full article

Fractional modeling has emerged as an important resource for describing complex phenomena and systems exhibiting non-local behavior or memory effects, finding increasing application in several areas in physics and engineering. This study presents the analytical derivation of equations pertinent to the modeling of different systems, with a focus on heat conduction. Two specific boundary value problems are addressed: a Helmholtz equation modified with a fractional derivative term, and a fractional formulation of the Laplace equation applied to steady-state heat conduction in circular geometry. The methodology combines the separation of variables technique with fractional power series expansions, primarily utilizing the Caputo fractional derivative. An important aspect of this paper is its instructional emphasis, wherein the mathematical derivations are presented with detail and clarity. This didactic approach is intended to make the analytical methodology transparent and more understandable, thereby facilitating greater comprehension of the application of these established methods to non-integer-order systems. The final goal is not only to provide a different approach of solving these physical models analytically, but to provide a clear, guided pathway for those engaging in the treatment of fractional differential equations. Full article

This research explores how RC columns respond to blast-induced dynamic effects, with a novel focus on partially submerged scenarios, bridging a gap between air blast and underwater explosion (UNDEX) research. Using advanced finite element modeling in LS-DYNA, the study captures the unique behavior of RC columns under mixed-media conditions, where shockwaves propagate through water and air interfaces. Comprehensive parametric analyses explore the influence of charge size, blast stand-off, and depth of water, revealing distinct dampening mechanisms and structural responses. Key findings include a measurable reduction in peak displacement of partially submerged explosions compared to fully submerged explosions, attributed to the moderating effects of the water–air interface. A total of 60 simulation cases were conducted to systematically analyze partially submerged scenarios, providing robust insights into energy transmission and damage mechanisms. The numerical models, validated against published experimental data by others, demonstrate the accuracy of computational modeling in simulating damage profiles, displacement histories, and energy dissipation trends. This research offers practical implications for designing resilient RC structures in coastal and maritime environments. The results contribute significantly to the field of blast mechanics, advancing our understanding of mixed-media shockwave dynamics and their impact on critical infrastructure. Full article

The buoyancy of radially oscillating spark-generated bubbles is studied experimentally. Bubble sizes, defined as the maximum bubble radius, range from 26.6 to 52.1 mm, and the bubbles oscillate at a hydrostatic pressure of 127 kPa in a large expanse of liquid. We found that the position of these bubbles is relatively stable during the first two oscillations. They move upwards only in short time intervals when their size is, due to contraction, close to the minimum volume. The vertical movement, therefore, takes place in the form of steps. The relative heights of these steps, defined as the ratio of step heights to bubble size, increase with bubble size and range from 0.15 to 0.29. No significant deformations in the spherical shape of bubbles are observed during the first two oscillations. Full article

A variational formulation and variationally consistent boundary conditions were derived for a coupled system of two boron nitride nanotubes (BNNTs), with the piezoelectric and surface effects taken into account in the formulation. The coupling between the nanotubes was defined in terms of Winkler and Pasternak interlayers. The equations governing the vibrations of the coupled system were expressed as a system of four partial differential equations based on nonlocal elastic theory. After deriving the variational principle for the double BNNT system, Hamilton’s principle was expressed in terms of potential and kinetic energies. Next, the differential equations for the free vibration case were presented and the variational form for this case was derived. The Rayleigh quotient was formulated for the vibration frequency, which indicated that piezoelectric and surface effects led to higher vibration frequencies. Next, the variationally consistent boundary conditions were formulated in terms of moment and shear force expressions. It was observed that the presence of the Pasternak interlayer between the nanotubes led to coupled boundary conditions when a shear force and/or a moment was specified at the boundaries. Full article

To address grid variability caused by renewable energy integration and to maintain grid reliability and resilience, hydropower must quickly adjust its power generation over short time periods. This changing energy generation landscape requires advance technology integration and adaptive parameter optimization for hydropower systems via digital twin effort. However, this is difficult owing to the lack of characterization and modeling for the nonlinear nature of hydroturbines. To solve this issue, this paper first formulates a six-coefficient Kaplan hydroturbine model and then proposes a parametric optimization tuning framework based on the Nelder–Mead algorithm for adaptive dynamic learning of the six-coefficients so as to build models that describe the turbine. To assess the performance of the proposed optimal parametric tuning technique, operational data from a real-world Kaplan hydroturbine unit are collected and used to model the relationship between the gate opening and the generated power production. The findings show that the proposed technique can effectively and adaptively learn the unknown dynamics of the Kaplan hydroturbine while optimally tune the unknown coefficients to match the generated power output from the real hydroturbine unit with an inaccuracy of less than 5%. The method can be used to provides optimal tuning of parameters critical for controller design, operational optimization and daily maintenance for hydroturbines in general. Full article

This research work aims to design and develop a dynamic vibration absorber that effectively reduces the vibrations of a flexible structure subjected to external loads. The analysis presented in this paper initially focuses on identifying the resonance frequencies of a typical structural system, which serves as the case study, since these frequencies are critical to dampening due to their potential to cause excessively large vibration amplitudes. Following this, the optimal parameters of the vibration absorber, including the mass, stiffness, and damping characteristics of the proposed design, were determined. Additionally, this paper proposes and examines the use of viscous-type damping, which is achieved through piston–cylinder systems connected to the structural components of the analyzed frame structure. Thus, the main contributions of this work include the analytical dimensioning, the technical design, and the virtual prototyping of a dynamic absorber constructed using a guyed mast structure capable of significantly reducing mechanical vibrations. This design solution ultimately enhances the strength and durability of the frame structure represented in the case study under external excitation, particularly in the worst-case scenario of seismic action. Furthermore, a key aspect of this study is implementing a new numerical procedure for identifying the system equivalent stiffness coefficient based on its mass and modal parameters, which is particularly useful in engineering applications. The numerical experiments conducted in this work support the effectiveness of the proposed design solution, devised specifically for the dynamic vibration absorber developed in this paper. Full article

An analytical study of the nonlinear response of imperfect stiffened doubly curved shells made of functionally graded material (FGM) is presented. The formulation of the problem is based on the first-order shear deformation shell theory in conjunction with the von Kármán geometrical nonlinear strain–displacement relationships. The nonlinear equations of the motion of stiffened double-curved shells based on the extended Sanders’s theory were derived using Galerkin’s method. The material properties vary in the direction of thickness according to the linear rule of mixture. The effect of both longitudinal and transverse stiffeners was considered using Lekhnitsky’s technique. The fundamental frequencies of the stiffened shell are compared with the FE solutions obtained by using the ABAQUS 6.14 software. A stepwise approximation technique is applied to model the functionally graded shell. The resulting nonlinear ordinary differential equations were solved numerically by using the fourth-order Runge–Kutta method. Closed-form solutions for nonlinear frequency–amplitude responses were obtained using He’s energy method. The effect of power index, functionally graded stiffeners, geometrical parameters, and initial imperfection on the nonlinear response of the stiffened shell are considered and discussed. Full article

This paper presents a comprehensive review of tethered unmanned aerial vehicles (UAVs), focusing on their challenges and potential applications across various domains. We analyze the dynamic characteristics of tethered UAV systems and address the unique challenges they present, including complex tether dynamics, impulsive forces, and entanglement risks. Additionally, we explore application-specific challenges in areas such as payload transportation and ground-connected systems. The review also examines existing tethered UAV testbed designs, highlighting their strengths and limitations in both simulation and experimental settings. We discuss advancements in multi-UAV cooperation, ground–air collaboration through tethers, and the integration of retractable tether systems. Moreover, we identify critical future challenges in developing tethered UAV systems, emphasizing the need for robust control strategies and innovative solutions for dynamic and cluttered environments. Finally, the paper provides insights into the future potential of variable-length tethered UAV systems, exploring how these systems can enhance versatility, improve operational safety, and expand the range of feasible applications in industries such as logistics, emergency response, and environmental monitoring. Full article

In this work, we introduce an edge centrality measure for the Helmholtz equation on metric graphs, a particular flow network, based on spectral edge energy density. This measure identifies influential edges whose removal significantly changes the energy flow on the network, as indicated by statistically significant p-values from the two-sample Kolmogorov–Smirnov test comparing edge energy densities in the original network to those with a single edge removed. We compare the proposed measure with eight vertex centrality measures applied to a line graph representation of each metric graph, as well as with two edge centrality measures applied directly to each metric graph. Both methods are evaluated on two undirected and weighted metric graphs—a power grid network adapted from the IEEE 14-bus system and an approximation of Poland’s road network—both of which are multigraphs. Two experiments evaluate how each measure’s edge ranking impacts the energy flow on the network. The results demonstrate that the proposed measure effectively identifies influential edges in metric graphs that significantly change the energy distribution. Full article

Buffer stops have always been installed on blind tracks to mitigate the hazards associated with overruns due to insufficient or wrong braking. Conventional buffer stops fixed to the rails may absorb only limited energy while Energy-Absorbing Buffers Stops (EABS) dissipate higher energy hydraulically and/or by friction from sliding blocks clamped to the rail head. The assessment of EABS performances in terms of maximum stopping distance and maximum allowed deceleration is usually performed by using the common kinematic rules of motion and considering the overrunning train as a single mass hitting the buffer stop. This paper studies the dynamic characteristics of the collision of entire trains with a friction EABS applying a Longitudinal Train Dynamics (LTD) approach. Several realistic scenarios using the UIC approved TrainDy software were simulated considering various train compositions, with different types of vehicles (locomotives, freight wagons and passenger coaches) and different kinds of buffers. The results show that high dynamic loads are exerted on the vehicles within the train, while the average deceleration and the stopping distance are not greatly influenced when compared with a simpler Finite Element Method (FEM) approach that does not consider the train composition. The progressive application of the EABS braking force increases the stopping distance but can reduce the peak deceleration of about 50%. The results may be used to tune the design parameters of friction EABS according to the currently available specifications and standards for rolling stock structural assessment considering that no international standards for EABS exist currently. Full article

As high-speed train operations increase, the aerodynamic pressure generated by these trains can jeopardize the structural integrity of sound barriers, potentially compromising train safety and the stability of nearby facilities. This paper investigates the unique aerodynamic pressures and load distribution of various types of sound barriers. We analyze the aerodynamic pressure distribution on sound barriers in relation to high-speed trains by utilizing Computational Fluid Dynamics (CFDs) analysis. We explore the theoretical foundations, design of the computational domain, and settings for boundary conditions. The findings indicate that high-speed trains generate both overpressure from compression waves and under pressure from expansion waves. As the barriers become more open, peak aerodynamic pressure and fluctuations decrease. Notably, the highest pressure occurs at the entrance of the barriers. The accuracy of the model is validated with data from a CRH series train traveling at 350 km/h. This paper offers valuable insights to enhance our understanding and improve sound barrier design for a quieter future. Full article

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