Dynamics, Volume 6, Issue 2 (June 2026) – 12 articles

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