Dynamics

A fundamental aspect in the design of modern utility-scale wind turbines is predicting the vibrational response of their blades when excited by gust pulses of various amplitudes and frequencies in atmospheric flow. Improved designs based on accurate blade-response predictions can prevent extreme oscillations, reduce fatigue stress, and extend turbine’s operational life. In previously published works, the authors introduced and applied a novel technique that provided an energy-based Reduced-Order Characterization (ROC) for the oscillatory response of wind turbine rotors, when excited by wind gust pulses with different combinations of timespan and amplitude under various operational conditions. Those studies established the universal nature of the ROC by expressing the turbine aeroelastic response as a vibrational Stability Map, plotted in terms of non-dimensional quantities, which could be applied to turbines of any size that share a similar blade construction. In the present paper, the authors will expand the ROC technique beyond the scope of their previously published studies, to analyze the Multi-Modal Response observed in regions located at the external boundaries of the stable zones of the Stability Map. This will provide valuable information about rotor stability behavior in extreme turbine operational conditions which were previously unexplored. Full article

Variational principles and variationally consistent boundary conditions are presented for double-layer graphene nanoribbons undergoing time-dependent and free vibrations. The van der Waals forces acting in the core region are modelled as shear and tensile–compressive effects. The nonlocal constitutive formulation of the problem is based on the sandwich beam model in order to represent the graphene nanoribbon layers as faces and van der Waals forces acting in the core region. The constitutive equations which govern the vibrations of the nanoribbons are in the form of four coupled partial differential equations involving the in-plane and out-of-plane deflections. The first part of the study involves the derivation of the variational principle for the system undergoing time-dependent vibrations. Hamilton’s principle is formulated based on the kinetic and potential energies of the system. The next section involves the freely vibrating nanoribbon system and the formulation of the variational principle for this case is given. Based on this formulation, the expressions for the Rayleigh quotients are obtained for the longitudinal natural frequency and the transverse natural frequency. The last section involves the derivation of the variationally consistent boundary conditions and the expressions for the shear force and moment at the boundaries. Full article

Lift-plus-cruise electric vertical takeoff and landing (eVTOL) aircraft exhibit complex stability characteristics during transition flight, when rotor-borne and wing-borne regimes coexist. This work investigates the dynamic stability of a lift-plus-cruise eVTOL using a nonlinear six-degree-of-freedom model incorporating aerodynamic forces, tractor propulsion, and vertical lifter dynamics. Linearization about representative trimmed conditions enables longitudinal and lateral–directional modal analysis. The results identify a critical near-stall region where lift-curve slope reduction markedly decreases short-period damping. Residual lifter authority partially compensates for this degradation, improving stability in the transition regime. To ensure smooth control transfer, an airspeed-dependent blending strategy between hover and fixed-wing controllers is implemented. Comparative analyses show that a sigmoid blending law improves the minimum short-period damping ratio relative to a linear strategy while preserving similar overall damping variation. Closed-loop simulations of a complete mission profile demonstrate the effectiveness of the proposed approach and reveal an asymmetric dynamic response between hover-to-forward and forward-to-hover transitions. These findings provide a physically grounded explanation for stability degradation during transition and establish practical guidelines for control authority blending in lift-plus-cruise eVTOL aircraft. Full article

The effect of atom size on the shock-wave structure in a binary monatomic gas mixture with Rydberg atoms has been investigated. The problem was solved numerically using the system of hydrodynamic equations in argon gas for the atom-size ratios between 2 and 100, T = 1500 K, and the density between 10¹⁷ and 10²⁰ m⁻³. It was found that the presence of larger-sized atoms in the mixture results in shock front splitting that is on the order of the mean free path for this component. The results could be of interest in supersonic plasma dynamics and in astrophysics, studying shock waves in the environments where high-n Rydberg states are present. Full article

In high-rise firefighting scenarios, unmanned aerial vehicles (UAVs) equipped with water-spraying systems are subjected to high-intensity and rapidly time-varying reaction forces induced by high-speed water jets. These forces introduce mismatched uncertainties with unknown bounds and make stable flight control particularly challenging. To address this problem, this paper proposes an adaptive robust constraint-following control (ARCFC) strategy for vector–rotor UAVs (VRUAVs). The controller is developed directly for the strongly nonlinear dynamics of the VRUAV without resorting to model linearization. Within a constraint-following-based nonlinear regulation framework, water-jet effects are explicitly modeled as rapidly time-varying uncertainties with unknown bounds, and an adaptive law is introduced to estimate conservative uncertainty bounds online for robust compensation. Lyapunov-based analysis is conducted to establish the uniform boundedness and uniform ultimate boundedness of the closed-loop system, and simulation results are presented to verify the effectiveness of the proposed approach. Compared with representative conventional control methods, the proposed ARCFC strategy provides improved disturbance-rejection capability and enhanced flight stability under demanding firefighting conditions. Full article

A recent two-layer theory for long-runout turbidity currents explains sustained bypass by allowing a dense lower layer to exchange mass with a more dilute upper layer while avoiding rapid over-thickening. Here, a morphodynamic extension is developed that couples suspended load and bed exchange while treating the two-layer hydrodynamics as a prescribed background. A suspended-sediment balance with bed exchange and Exner’s equation are written on that background, the depositional state variable $B=E_s/\left(rC\right)$ is introduced, and an exact nonlinear evolution equation for B is derived within the prescribed-background setting. In the weak-exchange limit this equation reduces to an algebraic onset criterion, thereby identifying the regime in which the simpler threshold is valid. Applied to an Amazon-like local-normal-flow reconstruction, the model shows that finite exchange shifts depositional onset upstream relative to the weak-exchange estimate. Background-fidelity checks, grid-refinement tests and closure/inlet sensitivities are reported to delimit the quantitative use of the reduced application. The framework is therefore best interpreted as a coupled reduced theory for suspended load and bed exchange on a prescribed two-layer bypass background rather than a fully hydro-morphodynamic closure. Full article

Computational modeling and machine learning have impacted several different areas of science and accelerated advancements in multiple venues. Yet traditional machine learning models have many well-known drawbacks: besides demanding a significant amount of data, they may fail to generalize beyond training data, are often treated as “black boxes”, and may predict physically inconsistent results. In response to these limitations, Physics-Informed Machine Learning (PIML) has emerged as a new area that integrates domain knowledge, such as energy or mass conservation, directly into data-driven algorithms. This review paper examines the foundations and main strategies of PIML, organizing the approaches into three categories: automated discovery and system identification, continuous-time modeling, and operator learning. In addition, Physics-Informed Neural Networks are analyzed in a dedicated section that covers architecture fundamentals, forward and inverse problem formulations, loss function design and implementation challenges. The paper also presents a survey of interdisciplinary applications of PIML in materials science, biomedical engineering, and fractional calculus. In this context, the review also analyzes open challenges and outlines future directions in the field. Full article

The physical characteristics of a heated non-Newtonian Eyring–Powell fluid in a conduit with sinusoidally moving ciliated walls are highlighted in this analytical study. The impact of mass transmission is considered in this model. The dimensional form of the governing equations is simplified using the long-wavelength estimation and suitable transformations to produce a set of dimensionless partial differential equations with pertinent boundary conditions. To solve it, the perturbation technique is utilized applying polynomial solutions. The solutions of temperature, concentrations, and velocity profiles are obtained, and then are further analyzed through graphical results. An accurate mathematical solution for the pressure gradient is achieved by integrating the velocity profile over the elliptic cross-section. The non-Newtonian Eyring–Powell fluid flows quicker through this vertical ciliated elliptic duct than the Newtonian fluid. Moreover, the cilia elliptic movement eccentricity and the wave number for metachronal wave have a dual effect on the velocity profile. Increasing the dimensionless flow rate and occlusion leads to an increase in closed contour size, as seen in the streamline description. Full article

A graph-theoretical approach to the analysis of motion and rest in many-body systems is developed. Point bodies are represented as vertices of a complete bi-colored graph, termed the motion–rest graph (MRG). Two vertices are connected by a rust-colored edge when the corresponding bodies are at rest relative to each other; that is, when their mutual distance remains constant in time, bodies moving relative to each other are connected by a cyan edge. It is shown that the logical structure of the relation “to be at rest relative to each other” determines the combinatorial structure of the graph. For one-dimensional motion in classical mechanics and special relativity, this relation is reflexive, symmetric, and transitive, and therefore defines an equivalence relation. As a result, rust edges form disjoint complete cliques corresponding to rest-clusters, and the MRG becomes a semi-transitive complete bi-colored graph that is completely determined by the partition of the bodies into equivalence classes. It is proven that any such graph on five vertices necessarily contains a monochromatic triangle. For two- and three-dimensional motion, the transitivity of relative rest generally fails because constant mutual distance does not imply an equality of velocities in the presence of rotational degrees of freedom. In this case, the MRG is non-transitive, and the Ramsey threshold becomes the classical value R(3, 3) = 6. The approach is extended to mixed sets containing moving bodies and reference points, including the center of mass of the system. Generalizations to general relativity and quantum mechanics are also discussed. In general relativity, transitivity of relative rest is generically lost because global rigid congruences do not generally exist. In quantum mechanics, exact transitivity survives only at the level of idealized delocalized eigenstates, whereas for physically realizable localized states, the notion of mutual rest becomes only approximate. The results demonstrate that the interplay between kinematics, logical properties of relational motion, and Ramsey-type combinatorial constraints gives rise to unavoidable ordered substructures in many-body systems. Full article

The results of the development and practical application of a comprehensive system for studying gear cutting processes are presented. The processes are traditional hobbing, modern power skiving, and radial-circular methods. Carrying out these processes is based on the gear teeth continuous generating method using complex kinematics. This complicates the analysis, description and modeling of the processes. The developed system provides for a logical sequence of step-by-step modeling and simulation of interrelated processes and phenomena accompanying gear processing. Reproducing volumetric chips and calculating their parameters provides the basis for determining deformation and contact processes, cutting forces, elastic deformations, machining accuracy and energy costs per operation. After establishing the operation to overcome friction and heat flows, the degree of heating and the temperature of the working surfaces are calculated to predict tool wear and its service life. Based on the parametric non-uniformity of the considered processes, the intensity of oscillations and vibrations of gear cutting machines is predicted, and their impact on the quality of gear surfaces and the accuracy of gears is determined. These approaches enable the study of such processes at the level of individual teeth and blades during cutting. They also allow gear cutting technology and cutting tools to be optimized according to the most important criteria and performance assessments. Full article

The Rössler system is a paradigmatic chaotic oscillator widely used to investigate synchronization phenomena. Existing studies on monovariate coupling almost exclusively rely on the x or y variables, while coupling through z is commonly regarded as ineffective. In this work, we report that complete synchronization through the z variable is indeed possible, provided that specific parameter values are chosen. We further consider a parameter regime in which the Rössler system exhibits multistability and show that synchronization via z-coupling occurs only when the dynamics evolve on a particular attractor. Although synchronization can be achieved, the admissible range of coupling strengths is very narrow as determined by the master stability function. For small networks, full connectivity is required, whereas larger networks can tolerate the removal of a limited number of links without losing synchronization. An analytical expression predicting the fraction of connections that must be preserved as a function of network size is derived and validated, revealing that a very high average degree is necessary. This effectively excludes common topologies such as small-world and scale-free networks. Numerical examples with up to 100 oscillators are presented, and potential challenges that may yield new insights are discussed. Full article

Simulated spiking neural networks have been explored for over a hundred years. Many of these networks are driven by biological considerations and an attempt to simulate brains, but others are used with little biological consideration. This paper gives some history of the development of spiking neural models, their use for modelling biological and cognitive phenomena, and for machine learning. It introduces the current state of the art in computational biological neuron and synapse modelling and plasticity. It introduces and reviews balanced spiking networks and their engineering applications. Spiking networks are also used for machine learning, with the hope that their implementation on neuromorphic hardware will bring energy and time savings. Similarly, neuromorphic hardware can enable massive parallelism, supporting larger spiking networks. The use of spiking nets for machine learning, both with biologically plausible models and without, is discussed, showing that effective models already exist. The paper concludes with some notes about implementing spiking nets and a discussion including open questions and future work. Full article

The growing need to safeguard sensitive data in various fields, including in relation to education, banking over the phone, private voice conferences, and the military, has grown as dependence on technology in daily life has increased. Encryption schemes based on chaotic systems are among the most commonly utilized approaches in the security field due to their high levels of safety and reliability. This study proposes a secure audio encryption framework based on the Chameleon chaotic algorithm implemented on a Xilinx ZedBoard Zynq-7000 FPGA. The system was designed using a fixed-point arithmetic format with 32-bit precision (eight integers; 24 fractional bits) with the Xilinx System Generator in MATLAB Simulink R2021b and verified using Vivado. The Chameleon Chaotic System, characterized by its transition from self-excited to hidden attractors through parameter variation, adds complexity to the system dynamics and strengthens the encryption algorithm. The Adaptive Feedback Control technique was applied to synchronize the signals. These methods enhance the security of audio data by ensuring robust and fast synchronization during transmission. The performance of the proposed system was assessed using correlation analysis, the mean squared error, histogram analysis, and audio spectrogram analysis. The system demonstrated strong encryption capabilities with low correlation values (−0.0033). In decryption, they achieved high fidelity with a correlation exceeding 0.999 in noise-free conditions and above 0.9933 under 20 dB AWGN. Adaptive Feedback Control showed superior decryption precision with lower MSEU and higher PSNR, confirming its effectiveness under noisy environments. Full article

This paper investigates the dynamics of a permanent magnet synchronous motor (PMSM) and controls its chaotic speed behavior using the synergetic control technique (SCT). The model includes electrical dynamics in the dq frame and mechanical speed dynamics, with a scalar parameter $\gamma$ capturing cross-coupling effects. The equilibrium structure and local stability properties of the PMSM are analyzed. For zero input voltages and zero load torque, the system exhibits a pitchfork-type bifurcation in the electrical–mechanical equilibrium as $\gamma$ crosses a critical value. Explicit expressions are derived for all equilibria, and their stability is characterized using eigenvalue analysis and the Routh–Hurwitz criterion, and a secondary loss of stability via a Hopf-type mechanism is identified. The case of nonzero input voltages with zero load torque is also discussed. Numerical simulations confirm the analytical results and highlight the parameter regions that admit stable operation. Bifurcation diagrams show the different PMSM behaviors as the parameter $\gamma$ varies. For a certain interval of $\gamma$, the PMSM speed undergoes chaotic oscillations. The SCT is introduced to control the chaos. Macro variables are chosen to design the SCT. The derived SCT is implemented to eliminate the chaotic speed. The controller provides good performance in suppressing the chaos. The controller is tested under sudden reference speed change where the controller gets the new reference speed accurately. It is also evaluated under sudden and sinusoidal load torque variations. Full article

We study the Cauchy problem for a loaded fractional integro-differential equation with a time-dependent diffusion coefficient. By reducing the problem to an equivalent Volterra integral equation of the second kind, we derive explicit analytical representations of solutions under appropriate regularity assumptions. The construction of the associated resolvent kernel allows us to establish existence and uniqueness results and to investigate the role of the fractional order and the loading term in the solution structure. Two illustrative examples are presented to demonstrate the applicability of the proposed approach. Full article

This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. This article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them. Full article

The dynamic behaviour of a column excited at the base, e.g., under an earthquake load, has been extensively studied. However, the column may also experience impact at the tip like a heavy-duty truck braking on a bridge. The caused base shear of the pier is very important. In this work, the dynamic behaviour, particularly the impact load from the tip to the base, was studied on two different composites: double basalt- and double flax fibre-reinforced polymer tube (DBFRP and DFFRP)-confined coconut fibre-reinforced concrete (CFRC). For each composite, two columns with a height of 1 m, an inner diameter of the outer tube of 100 mm, and an inner tube of 30 mm were fabricated. The column was fully fixed at the base and struck at the top with an impulse hammer. The base shear was calculated through an equivalent mass method using the acceleration at the tip. The results show that both DBFRP-CFRC and DFFRP-CFRC can dissipate a portion of the impact force, resulting in a reduction in force at the base of the specimens. The base shear of DFFRP-CFRC columns is larger and dissipates energy faster than that of DBFRP-CFRC columns. Full article