Search Results (855)

Flexible circular shafts are critical components for power transmission in engineering systems. However, they are susceptible to complex three-dimensional coupled vibrations under multidirectional excitations, which can compromise operational stability and lead to structural fatigue. To address this issue, this paper presents an active control method for the three-dimensional vibration of a piezoelectrically driven flexible circular shaft via a fuzzy adaptive PID algorithm. The study begins by establishing a dynamic model of the system based on the Euler–Bernoulli beam theory and Lagrange equation. This model forms the foundation for the design of a fuzzy adaptive PID controller. The accuracy of the developed model is then validated through simulations and experiments. Subsequently, active vibration control (AVC) experiments are carried out to evaluate the vibration attenuation effectiveness of various control strategies (including a conventional PID controller as the benchmark for comparison) under different types of excitations applied at the shaft root. The results demonstrate that the proposed active control method has superior control performance, and exhibits excellent vibration suppression performance, especially under bidirectional excitation at the natural frequency, where the vibration suppression ratios in the two orthogonal directions reach 93.03% and 92.09%, respectively. Full article

We develop structure-preserving variational integrators for non-autonomous Lagrangian systems by extending the prolongation–collocation variational integrator framework to explicitly time-dependent dynamics. The proposed method is obtained by discretizing Hamilton’s principle for non-autonomous Lagrangians, leading to a family of discrete Lagrangian functions defined at a fixed time step. By combining Hermite interpolation, the Euler–Maclaurin quadrature formula, and collocation applied to the Euler–Lagrange equations and their prolongations, the resulting scheme retains key qualitative properties of variational integrators, including a discrete symplectic (or cosymplectic) structure and favorable long-time behavior. We clarify the relationship between the proposed integrator and classical variational integrators for autonomous systems, showing that the method naturally reduces to the standard prolongation–collocation formulation in the time-independent case. Numerical experiments on representative examples illustrate the effectiveness of the approach and demonstrate its advantages over standard integration methods for non-autonomous systems. Full article

We investigate the asymptotic behavior of a proposed ordinary differential equation (ODE) model for Genetic Toggle switches from Gardner et. al. and I. Rajapakse and S. Smale: ${\displaystyle \frac{dx}{dt}}={\displaystyle \frac{a}{1+y^m}}-x$ and ${\displaystyle \frac{dy}{dt}}={\displaystyle \frac{b}{1+x^n}}-y$ where $a,b,m,n>0$ and $x\left(t\right),y\left(t\right)\ge 0$. We also investigate the asymptotic behavior of the Euler discretization of this system: $x_{n+1}=a_1{x}_n+{\displaystyle \frac{b_1}{1+y_n^m}}=f(x_n,y_n)$ and $y_{n+1}=a_2{y}_n+{\displaystyle \frac{b_2}{1+x_n^n}}=g(x_n,y_n),$ where $1-h=a_1$, $1-k=a_2$, $ah=b_1$ and $bk=b_2$, $a_1,a_2\in (0,1)$ and $h,k>0$ are steps of discretizations. Here, x and y represent protein concentrations at a particular time in both genes and $a,b,m,n>0$, respectively, above. We will apply the theory of competitive maps to find the basins of attractions of different equilibrium points and period-two solutions of systems of difference equations. Full article

This paper presents a theoretical approach based on the FSDT to study the acoustic vibration performance of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases when submerged in water. The complex core layer with reinforcing and weakening phases is homogenized to an equivalent orthotropic layer. Building upon this framework, the governing equations of motion for rib-stiffened PVC foam sandwich structures under the boundary conditions of a simply supported type are derived, incorporating the coupling interaction between the reinforcing ribs and the sandwich plates. Considering the influence of the underwater environment, with the Helmholtz equation governing the continuity of the acoustic pressure field and the Euler equation regulating the fluid–structure interaction interface continuity, the Navier method is subsequently employed to solve for the natural frequencies and acoustic vibration responses. For the purpose of verifying the proposed approach, the predicted results are contrasted with both the literature-derived data and numerical simulation results. Finally, parametric research is further conducted to explore the effect of the parameters of the rib and core layers on the underwater acoustic vibration characteristics. The conclusions drawn from this study can provide meaningful guidance for engineering design and optimization of such rib-stiffened sandwich structures, incorporating both reinforcing and weakening phases in underwater engineering applications. Full article

We develop a unified Koopman–von Neumann (KvN) operator and Weyl–Wigner phase-space framework for inviscid ideal (barotropic) Euler flows. Our approach reformulates the nonlinear fluid dynamics as a linear KvN evolution on an enlarged field phase space, thereby enabling us to apply tools developed for quantum mechanics (Weyl quantization, Moyal ⋆-products, and Wigner functionals) to a classical fluid. We construct the appropriate KvN generator (including the required Jacobian term for unitarity) and derive the evolution equation for the corresponding Wigner functional. This framework clarifies when the classical Liouville (Vlasov) description is exact—namely, in quadratic or linear regimes where the Moyal bracket reduces to the Poisson bracket—and when higher-order quantum-like corrections become significant in fully nonlinear regimes. As an analytic example, we obtain a closed-form Wigner solution for a one-dimensional Burgers flow (pressureless Euler) and verify, term by term, that it reproduces the expected Liouville transport (with distributional contributions at the shock). We also compare the phase-space approach with a kinetic (Vlasov–monokinetic) formulation and outline the extension of the framework to three-dimensional flows using a Clebsch variable representation. Full article

To solve the problems of high-precision attitude control and vibration isolation of satellite payloads, this paper conducts in-depth research on satellite attitude dynamics and maglev active vibration isolation control technology. A dual-super collaborative control scheme is proposed, which consists of payload module ultra-high precision and ultra-high stability control, relative position control of two modules, and service module attitude control. The target attitude and angular velocity obtained by maneuver path planning and attitude guidance are transmitted to the attitude and orbit control management unit, and the total control command torque is formed by combining feedback control and feedforward control, which is then distributed to each maglev actuator to realize high-precision control of the payload module. The architecture of the maglev vibration isolation system is designed, and its dynamic model is established based on the Newton–Euler equation. Meanwhile, the dynamic model of the maglev actuator is constructed, and the active control strategy is designed by adopting PID control. The models of output force and torque are established, system parameters are set for simulation analysis of dynamic responses such as displacement, attitude and electromagnetic force, and a 20% pull-bias robustness test is carried out. Simulation results show that the system has high isolation accuracy, stability, and can effectively suppress the interference and shaking of the platform and load, with strong robustness. Full article

Accurate and long-horizon forecasting is essential for reliable planning of solar and wind power generation. Most existing models rely on high-resolution meteorological data, which are often unavailable in practical microgrid environments. This study proposes SNORF, a solar–wind neural ordinary differential equation model that uses only basic meteorological variables such as solar radiation, cloud cover, and wind speed together with lagged generation values. However, reliance on lagged generation inherently limits the effective forecasting horizon of conventional models. To address this limitation, SNORF extends the forecasting horizon while maintaining accuracy and stability through a rolling forecasting framework with a bounded input-dependent drift function and repeated Euler integration that promotes smooth hidden-state dynamics. SNORF supports both deterministic point forecasting and probabilistic forecasting through quantile-based loss functions. Experiments on solar and wind power datasets show that SNORF consistently outperforms representative time-series forecasting models. For solar forecasting, SNORF reduces RMSE and MAE by 15.35% and 16.93% on average compared with baseline models. For wind forecasting, the improvements reach 44.77% in RMSE and 52.85% in MAE on average. Furthermore, when evaluated under the official protocol of the 2024 IEEE Hybrid Energy Forecasting and Trading Competition, SNORF achieves a top 4% ranking using only the officially provided basic weather dataset, demonstrating its practical applicability to renewable energy forecasting in microgrids and virtual power plants. Full article

Fractional calculus and distribution theory share a common conceptual origin in the symbolic interpretation of differentiation and integration. Despite this connection, most developments in fractional calculus have traditionally been formulated within the framework of ordinary functions, while the systematic use of distributions remains limited. In this work, a novel distributional framework is developed by constructing a fractional Taylor representation of the product of Euler gamma and Riemann zeta functions in terms of fractional derivatives of the Dirac delta distribution. The proposed formulation enables the derivation of new fractional identities via Laplace transformation and facilitates the analytical solution of fractional differential equations containing such functions. Closed-form solutions are obtained in both classical and generalized distributional senses, allowing the extension of solutions from the positive real axis to the entire real line. Furthermore, the framework is applied to fractional operators of Erdélyi–Kober type, yielding new integral and derivative transforms. Fractional differential and integral equations with singular terms arise naturally in several engineering models involving memory effects, impulsive responses, and anomalous transport phenomena. However, the presence of nonremovable singularities—such as those associated with Euler gamma and Riemann zeta functions—significantly restricts the applicability of classical analytical methods. Overall, the proposed distributional framework bridges the gap between abstract fractional calculus and practical engineering models by enabling analytical solutions of fractional systems with singular memory kernels that were previously inaccessible using classical methods. Full article

Functionally graded porous beams are increasingly used in lightweight engineering structures, where thermal effects and material inhomogeneity significantly influence vibration behavior. In this study, the thermoelastic free vibration of functionally graded porous Euler–Bernoulli beams with temperature-dependent material properties is investigated by considering uniform and symmetric porosity distributions, together with uniform, linear, and nonlinear temperature fields. The governing equations are derived based on classical Euler–Bernoulli beam theory and solved using the Differential Transformation Method, while the accuracy of the semi-analytical formulation is verified through a Hermite-based finite element model. The results show that increasing temperature reduces the bending stiffness due to thermal axial forces and leads to a rapid decrease in natural frequency as the critical buckling temperature is approached. Increasing porosity generally decreases the natural frequency, although a slight increase may occur in symmetric distributions because of the accompanying reduction in mass density. The present study provides a computational framework for the thermo-vibration analysis of functionally graded porous beams in lightweight structural applications. Full article

This study investigates the common assumption that segmental inertial parameters remain constant during manual lifting using a model-based experimental approach. The primary objective was to evaluate the variability in these parameters and the subsequent effects on biomechanical calculations. The research was conducted with 20 participants (10 females and 10 males) who performed lifting tasks in the two-dimensional sagittal plane under three distinct load conditions: 2.5 kg, 5.0 kg, and 7.5 kg. Angular variations of the hand, arm, and leg joints were recorded using video-based image processing techniques. These kinematic data, integrated with anthropometric measurements, were incorporated into Newton–Euler-based equations of motion to determine joint reaction forces and net joint moments. During the initial forward dynamics stage, the solvability of the problem was tested using constant mass ratios from the established literature. In the following inverse dynamics stage, genetic algorithms were utilized to overcome solution diversity and identify the variable inertial parameters responsible for the observed motion. The results indicate that changes in segment moments of inertia reached 18–37%, leading to variations of 0–19% in net joint moments. These findings highlight the critical necessity of incorporating dynamic inertial parameters into accurate biomechanical moment calculations for manual materials handling. Full article

Pricing multi-peril agricultural insurance under compound climate hazards demands a framework that captures stochastic dependence among heterogeneous perils, accommodates non-stationary loss dynamics, and supports adaptive policy optimisation. We demonstrate that backward stochastic differential equations, combined with copula dependence, recurrent neural networks, and reinforcement learning, provide a unifying language for this task; the contribution lies in their principled integration. The dynamic premium is the unique adapted solution of a BSDE whose driver encodes compound-risk dependence through a Student-t copula, forward loss dynamics through a jump-diffusion process, and a green-finance adjustment through an optimal control variable. Within this framework we derive three progressive results by adapting standard BSDE theory to the compound-dependence and policy-control setting. First, existence and uniqueness hold under Lipschitz and square-integrability conditions. Second, a comparison theorem guarantees that a larger correlation matrix yields higher premiums; the degrees-of-freedom effect enters separately through the risk-loading magnitude. Third, the Euler discretisation converges at a rate of one half of the time-step size, with copula estimation, LSTM conditional expectation approximation, and Q-learning HJB solution as sequential components. Applied to eleven Zhejiang cities (2014–2023, $N \times T=110$), in this illustrative application the framework reduces premium variance by 43.5 percent (bootstrap 95% CI: $[38.2\%,48.7\%]$) while maintaining actuarial adequacy with a mean loss ratio of 0.678, though the modest sample size warrants caution in generalising these findings. Each component contributes statistically significant improvements confirmed by the Friedman test at the 0.1 percent significance level. Full article

We obtain improved regularity estimates on solutions of partial differential equations by combining the method of Fuchsian Reduction with geometric transformations. Examples include the meron problem and the regularity of the conformal radius. In each case, Reduction needs to be combined with a reinterpretation of the underlying geometry. We argue that the geometric meaning assigned to a problem has an influence, positive or negative, on the range of methods envisioned for its solution, and that the Euler–Poisson–Darboux (EPD) equation cannot be properly understood within a single geometric framework. This explains the central position of EPD-like equations. Full article

This study addresses the challenge of consistently transferring atomistic parameters of the C–C bond into phenomenological material characteristics within the framework of continuum mechanics. Particular attention is given to determining the effective transverse diameter of the covalent C–C bond in carbon nanostructures. The dependence of this diameter on Poisson’s ratio ν is examined, and the influence of the interatomic stiffness constants ${\mathrm{k}}_{\mathrm{r}},{\mathrm{k}}_{\mathsf{\theta }}\mathrm{and}{\mathrm{k}}_{\tau }$ is systematically analyzed. Classical representative-volume models of the C–C bond based on the Euler–Bernoulli beam hypothesis violate thermodynamic stability conditions and lead to nonphysical Poisson’s ratio values exceeding 0.5, due to the neglect of shear deformation effects. To overcome this limitation, an approach based on Timoshenko beam theory is proposed, accounting for both bending and shear deformations. This approach enables estimation of energetically equivalent states between the phenomenological representative volume and the corresponding atomistic C–C bond model. As a result, a sixth-order algebraic equation is derived linking the effective bond diameter, the Poisson’s ratio, and the molecular mechanics force constants. Analysis of this equation reveals a narrow range of effective bond diameters and Poisson’s ratios for which thermodynamic stability conditions are satisfied. Within this range, physically consistent macroscopic material parameters can be directly expressed in terms of atomistic force constants. Full article

Professors, students, and researchers from universities around the world use software distributed under licenses for numerical simulation purposes, which requires a computer with considerable hardware capabilities. This implies a high cost of simulations in engineering applications that require dynamic modeling using numerical methods, particularly in robotics and nonlinear control. This article compares and analyzes the performance of a frugal simulation scheme based on the use of low-cost, free, and open-source technology, specifically a low-power, single-board minicomputer (Raspberry Pi) in conjunction with GNU-Octave software. The benchmark is a numerical simulation of trajectory tracking control in the joint space of a Selective Conformal Assembly Robot Arm (SCARA). To perform this task, a system of coupled nonlinear differential equations is solved in matrix form using a numerical method known as an ODE solver. This solution includes the control law and the dynamic system model derived from Euler–Lagrange formalism. The time complexity and accuracy are analyzed to compare the performance of the frugal simulation tool with that of a conventional simulation setup consisting of a personal computer and MATLAB^TM running the same simulation code. The analysis shows minimal deviations in the numerical solutions and reasonable time complexity. Moreover, the frugality score of this approach and the low acquisition cost of the simulation tool enable the creation of simulation laboratories at universities with limited budgets for education and research. Full article

This manuscript presents a study of the Stress-Driven integral Model (SDM) for the bending response of Bernoulli–Euler nanobeams. Unlike conventional approaches that reformulate the nonlocal integral problem into an equivalent differential form, a direct numerical strategy is developed to solve the integral equation. The proposed framework enables a systematic comparison of six different convolution kernels (Helmholtz, Gaussian, Lorentzian, triangular, Bessel and hyperbolic cosine), highlighting how their mathematical properties influence the structural response. To address issues related to long-range interactions and the potential ill-posedness of the integral operator, an adaptive regularization procedure based on the Morozov discrepancy principle is introduced. Furthermore, a local clipping and renormalization technique is proposed to properly account for boundary effects while preserving the weighted averaging property of the kernels. Validation against available analytical solutions for the Helmholtz kernel demonstrates high accuracy, with errors below 1%. The results show that the nonlocal parameter significantly affects structural rigidity depending on the kernel shape and that the proposed approach ensures consistent convergence to the local solution as the nonlocal parameter tends to zero. Full article