Search Results (1,001)

Practical applications of piezoelectric vibration energy harvesting systems are required to produce a stable DC output through the nonlinear process of AC-DC rectification. In most simulation studies of such systems, the diodes have been idealised as switches, an assumption that is valid only if the vibration-induced voltage is high enough, which is frequently not the case in practice. This paper presents an experimentally validated simulation of a base excited vibration energy harvester connected to a full wave rectified load, combining the analytical modal transformation of the Euler–Bernoulli model of a piezoelectric beam with the nonlinear current-voltage characteristic of a real (non-ideal) diode. Three types of diodes with significantly different model parameters sourced from industry-standard datasets are considered. Discrepancies between simulated and measured resonant voltage levels are found to be less than 10% on average, and the discrepancy in resonant frequency is less than 1%, demonstrating the reliability of the Shockley diode model despite its omission of the dynamic behaviour of the diode. Full article

This study comprehensively investigates the dynamic vibration behavior of multilayer carbon nanotubes with stepped cross-sectional geometries under various boundary conditions, which is crucial for their advanced engineering applications. The methodology integrates classical molecular dynamics simulations to determine the bending stiffness of single-walled and multi-walled atomistic structures, which are subsequently utilized in the Euler–Bernoulli beam theory based on nonlocal elasticity for vibration analysis. The research focuses on elucidating the influence of the μ/L ratio (a key length parameter) and different support conditions on the natural frequencies and mode shapes of these nanostructures. Key findings reveal that the cross-sectional geometry significantly impacts the vibrational characteristics. A consistent trend observed across all examined boundary conditions is a decrease in natural frequencies as the μ/L ratio increases, indicating that increased free length or reduced fixed length leads to lower stiffness and, consequently, reduced natural frequencies. The study presents Frequency Response Functions (FRFs) and the first four mode shapes, which visually confirm these dynamic characteristics. Graphical representations further reinforce the sensitivity of natural frequencies to both the μ/L ratio and support conditions. The systematic analysis presented in this work provides vital data for predicting resonance phenomena, optimizing structural stability, and enabling precise control over the vibrational response of these advanced nanomaterials in diverse engineering applications. Full article

Fatigue damage of yawed wind turbine components can be caused by repeated long-term unsteady asymmetric inflow loads across the rotor swept area, necessitating fatigue load analysis to ensure the in-operation safety of wind turbines. This study investigates the impact of geometric nonlinearity on the fatigue loads of wind turbine components. The geometrically exact beam theory (GEBT), implemented in BeamDyn of OpenFAST, is employed to model full geometric nonlinearity. For comparison, ElastoDyn in OpenFAST, which uses the generalized Euler–Bernoulli beam theory for straight isotropic beams, is also utilized. Aeroelastic simulations were conducted for the national renewable energy laboratory (NREL 5 MW) and international energy agency (IEA) 15 MW wind turbines. Fatigue loads, quantified by the damage equivalent load (DEL) based on Palmgren–Miner’s rule, were analyzed for critical components, including blade out-of-plane (OOP) moments, low-speed shaft (LSS) torque, LSS bending moment (LSSBM), and tower base bending moment (TBBM). Results indicate that geometric nonlinearity significantly influences fatigue damage in critical turbine components, with significant differences observed between BeamDyn and ElastoDyn simulations. Full article

The Kronecker product has been commonly seen in various scientific fields to formulate higher-dimensional spaces from lower-dimensional ones. This paper presents a generalization of the Cannon–Kronecker product bases by introducing generalized Kronecker product bases of polynomials within an analytic framework. It investigates the convergence behavior of infinite series formed by these generalized products in various polycylindrical domains, including both open and closed configurations. The paper also delves into essential analytic properties such as order, type, and the ${\mathbb{T}}_{\rho }$-property to analyze the growth and structural characteristics of these bases. Moreover, the theoretical insights are applied to a range of classical special functions, notably Bernoulli, Euler, Gontcharoff, Bessel, and Chebyshev polynomials. Full article

In this study, the nonlinear forced vibration response of fiber-reinforced laminated composite beams coated with functionally graded materials (FGMs) is investigated under the combined action of aero-thermoelastic loads and a concentrated harmonic excitation. The mathematical formulation is established using the Euler–Bernoulli beam theory, where von Kármán geometric nonlinearities are taken into account, along with the modified third-order piston theory to represent aerodynamic effects. By neglecting axial inertia, the resulting set of nonlinear governing equations is simplified into a single equation. This equation is discretized through the Galerkin procedure, yielding a nonlinear ordinary differential equation. An analytical solution is, then, obtained by applying the method of multiple time scales (MTS). Furthermore, a comprehensive parametric analysis is carried out to evaluate how factors such as the power-law index, stacking sequence, temperature field, load amplitude and position, free-stream velocity, and Mach number influence both the lateral dynamic deflection and the frequency response characteristics (FRCs) of the beams, offering useful guidelines for structural design optimization. Full article

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, r-Whitney numbers, and hyperharmonic polynomials, as well as Bernoulli numbers and polynomials. We also provide formulas for the higher-order derivatives of Cauchy polynomials and obtain corresponding formulas and identities for poly-Cauchy polynomials. Furthermore, we introduce a multiparameter framework for poly-Cauchy polynomials, unifying earlier generalizations like shifted poly-Cauchy numbers and polynomials with a q parameter. Full article

A probabilistic version of geometry is introduced. The fifth postulate of Euclid (Playfair’s axiom) is adopted in the following probabilistic form: consider a line and a point not on the line—there is exactly one line through the point with probability P, where $0\le P\le 1$. Playfair’s axiom is logically independent of the rest of the Hilbert system of axioms of the Euclidian geometry. Thus, the probabilistic version of the Playfair axiom may be combined with other Hilbert axioms. $P=1$ corresponds to the standard Euclidean geometry; $P=0$ corresponds to the elliptic- and hyperbolic-like geometries. $0<P<1$ corresponds to the introduced probabilistic geometry. Parallel constructions in this case are Bernoulli trials. Theorems of the probabilistic geometry are discussed. Given a triangle and a line drawn from a vertex parallel to the opposite side, the event that this line is actually parallel occurs with probability P. Otherwise, the line may intersect the side or diverge. Parallelism is not transitive in the probabilistic geometry. Probabilistic geometry occurs on the surface with a stochastically variable Gaussian curvature. Alternative geometries adopting various versions of the probabilistic Playfair axiom are introduced. Probabilistic non-Archimedean geometry is addressed. Applications of the probabilistic geometry are discussed. Full article

This study introduces a novel mathematical framework for a machine learning algorithm tailored to address linear regression problems in the presence of non-Gaussian estimation noise. In particular, we focus on Bernoulli–Gaussian noise, which frequently occurs in practical scenarios such as wireless communication channels and signal processing systems. We apply our framework within the context of wireless systems, particularly emphasizing its utility in channel estimation tasks. This article demonstrates the efficacy of linear regression in estimating wireless channel fading coefficients under the influence of additive Bernoulli–Gaussian noise. Through comparative analysis with Gaussian noise scenarios, we underscore the indispensability of the proposed framework. Additionally, we evaluate the performance of the maximum-likelihood estimator using gradient descent, highlighting the superiority of estimators tailored to non-Gaussian noise assumptions over those relying solely on simplified Gaussian models. Full article

In recent years, special functions have played a significant role in the investigation of different subclasses within the class of bi-univalent functions. In this work, we present and investigate two new subclasses of bi-univalent functions defined in $\mathfrak{U}=$$\{\varsigma \in \mathbb{C}:|\varsigma |<1\}$, characterized by Bernoulli polynomials associated with imaginary error functions. For functions belonging to these subclasses, we establish bounds for their initial coefficients. For these classes, we also tackle the Fekete–Szegö problem. Several new results are also obtained as special cases by specifying certain parameter values in the general findings. Full article

Leader–follower neural networks deployed over wireless platforms are subject to parameter uncertainties and stochastic channel fading. The combined impact of these effects on quasi-synchronization control remains largely unexplored. The paper addresses the problem of quasi-synchronization performance degradation in discrete-time leader–follower neural networks caused by randomly occurring parameter uncertainties and stochastic channel fading. Discrete leader–follower neural networks are constructed in state-space form. Randomly occurring parameter uncertainties in the leader neural networks are described using a Bernoulli probability distribution and time-varying parameter matrices. Channel fading is represented by a finite-state Markovian model that captures state switching. For the follower neural networks, an intermittent impulsive control strategy is designed based on linear matrix inequalities and the Lyapunov stability principle. A computable bound on the synchronization error is derived as well. A simulation study validates that the proposed impulsive control strategy effectively suppresses synchronization error caused by parameter uncertainties and Markovian channel fading, thereby ensuring mean-square boundedness. Compared with an existing method, the proposed approach consumes less control energy but achieves better performance in terms of synchronization error. The average norms of the synchronization error and the control input signal are reduced by 24.00% and 58.64%, respectively. Full article

Target tracking in typical radar applications faces critical challenges in complex environments, including nonlinear dynamics, non-Gaussian noise, and sensor outliers. Current robustness-enhanced approaches remain constrained by empirical kernel tuning and computational trade-offs, failing to achieve balanced noise suppression and real-time efficiency. To address these limitations, this paper proposes the variational Bayesian-based maximum correntropy criterion cubature Kalman filter (VBMCC-CKF), which integrates variational Bayesian inference with CKF to establish a fully adaptive robust filtering framework for nonlinear systems. The core innovation lies in constructing a joint estimation framework of state and kernel size, where the kernel size is modeled as an inverse-gamma distributed random variable. Leveraging the conjugate properties of Gaussian-inverse gamma distributions, the method synchronously optimizes the state posterior distribution and kernel size parameters via variational Bayesian inference, eliminating reliance on manual empirical adjustments inherent to conventional correntropy-based filters. Simulation confirms the robust performance of the VBMCC-CKF framework in both single and multi-target tracking under non-Gaussian noise conditions. For the single-target case, it achieves a reduction in trajectory average root mean square error (Avg-RMSE) by at least 14.33% compared to benchmark methods while maintaining real-time computational efficiency. Integrated with multi-Bernoulli filtering, the method achieves a 40% lower optimal subpattern assignment (OSPA) distance even under 10-fold covariance mutations, accompanied by superior hit rates (HRs) and minimal trajectory position RMSEs in cluttered environments. These results substantiate its precision and adaptability for dynamic tracking scenarios. Full article

This article presents a newly defined subclass of univalent functions that are starlike with respect to a boundary point, closely related to the Robertson class and specifically associated with a vertical strip domain. Additionally, this study derives generalized coefficient estimates for these classes, as well as for the Robertson class linked to the Nephroid domain and the Lemniscate of Bernoulli. Full article

This study presents an exact analytical investigation into the static response of helical single-walled carbon nanotube (SWCNT) beams based on Eringen’s differential nonlocal elasticity theory, which captures nanoscale effects arising from interatomic interactions. A key contribution of this work is the derivation of the governing equations for helical SWCNT beams, based on the nonlocal Euler–Bernoulli theory, followed by their exact analytical solution using the initial value method. To the best of the authors’ knowledge, this represents the first closed-form formulation for such complex nanostructures using this theoretical framework of nonlocal elasticity theory. The analysis considers both cantilevered and clamped–clamped boundary conditions, under various concentrated force and moment loadings applied at the ends and midpoint of the helical beam. Displacements and rotational components are expressed in the Frenet frame, enabling direction-specific evaluation of the deformation behaviour. Parametric studies are conducted to investigate the influence of geometric parameters—such as the winding angle ($\alpha$) and aspect ratio ($R/d$) and the nonlocal parameter ($R/\gamma$). Results show that nonlocal elasticity theory consistently predicts higher displacements and rotations than the classical local theory, revealing its importance for accurate modelling of nanoscale structures. The proposed analytical framework serves as a benchmark reference for the modelling and design of nanoscale helical structures such as nano-springs, actuators, and flexible nanodevices. Full article

This paper explores the eigenfunctions of specific Laguerre-type parametric operators to develop multi-parametric models, which are associated with a class of the generalized Mittag-Leffler type functions, for dynamical systems and population dynamics. By leveraging these multi-parametric approaches, we introduce new concepts in number theory, specifically those involving multi-parametric Bernoulli and Euler numbers, along with other related polynomials. Several numerical examples, which are generated by using the computer algebra program Mathematica© (Version 14.3), demonstrate the effectiveness of the models that we have presented and analyzed in this paper. Full article

Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness. Full article