Search Results (43)

The free vibration of functionally graded (FG) beams under thermal environments is fundamental to understanding forced vibration, flutter, and thermal buckling in high-temperature structures. However, current research primarily focuses on theoretical modeling and numerical solutions, with limited mechanistic insights into temperature-dependent frequency variations and multi-factor effects. This study presents an analytical investigation coupled with experimental validation to characterize the vibration behavior of FG beams under thermal environments. First, governing equations for thermal vibration of FG beams are derived under uniform, linear, and nonlinear temperature fields based on the power-law assumption, the rule of mixtures, Timoshenko beam theory, and Hamilton’s principle. Subsequently, analytical expressions for natural frequencies and mode shapes are obtained using the state-space method. Then, experimental validation is performed to verify the model’s accuracy. Finally, the combined effects of temperature field, power-law index, slenderness ratio, and boundary conditions on the natural frequencies are systematically analyzed. Full article

We study an infinite-horizon consumption–investment problem in which an investor endogenously manages a consumption comfort zone above a fixed subsistence benchmark. Consumption can move freely within the prevailing admissible interval, while upward expansions of the upper endpoint are irreversible and costly. This captures downward rigidity not through a single ratcheting reference level but through the endogenous management of a sustainable expenditure range. Using the dual martingale method together with singular stochastic control, we reduce the problem to a one-sided singular control problem for the comfort-zone width process. The associated dual Hamilton–Jacobi–Bellman equation becomes a gradient-constrained free-boundary problem, which admits a one-dimensional reduction under CRRA utility. We characterize the optimal comfort-zone expansion rule, consumption policy, risky portfolio rule, and value function. Economically, the model implies infrequent upward revisions of the sustainable consumption ceiling, smoother consumption than in the frictionless Merton benchmark, and state-dependent portfolio behavior. A key implication of the additive specification is that proportional consumption flexibility shrinks as the upper endpoint rises, so higher consumption states become endogenously tighter and require a larger wealth buffer to sustain. The infinite-horizon formulation is interpreted as a stationary benchmark that isolates the economics of costly lifestyle upgrading. Full article

This paper develops a dynamic asset allocation strategy for defined contribution pension funds using a stochastic control framework under the Heston stochastic volatility model. By solving the associated Hamilton–Jacobi–Bellman partial differential equation, we derive optimal equity allocations that adapt to changing market volatility and investor risk aversion using a constant relative risk aversion utility function (parameter $\gamma$). The strategy increases equity exposure during stable periods and reduces it during volatile regimes, capturing both myopic and intertemporal hedging demands. We test the model using historical U.S. data from 2006 to 2025 and benchmark its performance against a traditional static 60/40 stock–bond portfolio, as well as rule-based strategies such as volatility targeting and constant proportion portfolio insurance. Our results show that with moderate risk aversion, the dynamic strategy achieves long-term wealth comparable to the 60/40 benchmark while substantially reducing drawdown risk. As risk aversion increases, drawdown risk is further reduced and risk-adjusted returns remain competitive. Although higher aversion yields lower final wealth, certainty-equivalent returns are highest at moderate aversion levels. These results demonstrate that volatility responsive dynamic policies grounded in realistic stochastic volatility modeling can substantially enhance downside protection and risk-adjusted utility, especially for long-horizon, risk-averse pension participants. Full article

The intelligent transformation of the wastewater treatment industry, as a core component of the modern environmental governance system, is of decisive significance for achieving sustainable development goals. This study focuses on the issue of multi-stakeholder collaborative governance in the intelligent transformation of the wastewater treatment industry, with differential game theory as the core framework. A tripartite game model involving the government, wastewater treatment enterprises, and digital twin platforms is developed to depict the dynamic interrelations and mutual influences of strategy choices, thereby capturing the coordination mechanisms among government regulation, enterprise technology adoption, and platform support in the transformation process. Based on the dynamic optimization properties of differential games, the Hamilton–Jacobi–Bellman (HJB) equation is employed to derive the long-term equilibrium strategies of the three parties, presenting the evolutionary paths under Nash non-cooperative games, Stackelberg games, and tripartite cooperative games. Furthermore, the Sobol global sensitivity analysis is applied to identify key parameters influencing system performance, while the response surface method (RSM) with central composite design (CCD) is used to quantify parameter interaction effects. The findings are as follows: (1) compared with Nash non-cooperative and Stackelberg games, the tripartite cooperative strategy based on the differential game model achieves global optimization of system performance, demonstrating the efficiency-enhancing effect of dynamic collaboration; (2) the most sensitive parameters are β, α, μ₃, and η₃, with β having the highest sensitivity index (ST_i = 0.459), indicating its dominant role in system performance; (3) significant synergistic enhancement effects are observed among α–β, α–μ₃, and β–μ₃, corresponding, respectively, to the “technology stability–benefit conversion” gain effect, the “technology decay–platform compensation” dynamic balance mechanism, and the “benefit conversion–platform empowerment” performance threshold rule. Full article

In this study, the free vibration characteristics of a functionally graded (FG) shear-deformable Timoshenko beam were investigated both analytically and numerically. The work is notable for its significant contribution to the literature, particularly in addressing analytically challenging problems related to complex FGM structures using advanced computer-aided finite element methods. For the analytical approach, the governing equations and associated boundary conditions were derived using Hamilton’s principle of minimum potential energy. These equations were then solved using the Navier solution method to determine the natural frequencies of the beam. In the numerical analysis, a 3D FG beam model was developed in the ABAQUS finite element software (2023, Dassault Systèmes, Providence, RI, USA)using the second-order hexahedral (HEX20/C3D20) and 1D three-node quadratic beam (B32) elements. The material gradation was defined layer-by-layer along the thickness direction in accordance with the rule of mixtures. Modal analysis was subsequently performed to extract the natural frequency values. The results show a high level of agreement between the analytical and numerical solutions. and were consistent with previously published studies in the literature. Full article

This work breaks a 180-year-old framework created by Hamilton both with regard to the use of imaginary quantities and the definition of a quaternion product. The general quaternionic algebraic structure we are considering was provided by the author in a previous work with a commutative product and will be provided here with a non-commutative product. We replace the imaginary units usually used in the theory of quaternions by linearly independent vectors and the usual Hamilton product rule by a Hamiltonian-adapted vector-valued vector product and prove both a new geometric property of this product and a vectorial adopted Euler type formula. Full article

This paper investigates the stability and Hopf bifurcation problems of fractional-order quaternion-valued neural networks (FOQVNNs) with leakage delay and communication delay. Utilizing the Hamilton rule of quaternions, the fractional-order quaternion-valued time-delay neural network model is transformed into an equivalent fractional-order real-valued time-delay neural network system. Then, employing the stability theory and bifurcation theory of fractional-order dynamical systems, novel sufficient criteria are derived to ensure system stability and to induce Hopf bifurcation, respectively, using the leakage delay and the communication delay as bifurcation parameters. Furthermore, the influences of both delay types on the bifurcation behavior of FOQVNNs are analyzed in depth. To verify the correctness of the theoretical results, bifurcation diagrams and simulation results generated using MATLAB are presented. The theoretical results established in this paper provide a significant theoretical basis for the analysis and design of FOQVNNs. Full article

This article focuses on the study of elastic beams with fractional-order inertial damping structures at both ends, with the aim of exploring their dynamic characteristics, damping effects, and parameter selection rules in depth, providing theoretical and practical support for engineering applications. Firstly, using the generalized Hamilton principle, two dynamic models of an elastic beam are established for two different boundary conditions. Next, using the complex modal analysis method, a design method for the critical damping of the first and second modes of an elastic beam was proposed for the first time, and the accuracy of the critical damping calculation formula was verified. Simulation analysis shows that the higher the derivative order and inertance, the lower the main resonance frequency, and the greater the critical damping. Then, using the main resonance amplitude and frequency attenuation rate (R_A and R_Ω) as indicators, an analysis was conducted on the impact of damper parameters on vibration suppression effects. The results indicate that the introduction of fractional-order inerter can reduce the main resonance amplitude and frequency, and critical damping plays a significant role in the vibration suppression process. Based on the optimal average R_A range (95–98%) and higher cost-effectiveness, selecting a damping value of 0.05~0.6 times the critical damping ensures better overall vibration suppression performance, providing an important reference for the vibration suppression design of elastic beams in practical engineering. Full article

Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies. This paper introduces the generalized notion of Pauli Fibonacci polynomial quaternions, a definition that incorporates the advantages of the Fibonacci number system augmented by the Pauli matrix structure. With the concept presented in the study, it aims to provide material that can be used in a more in-depth understanding of the principles of coding theory and quantum physics, which contribute to the confidentiality needed by the digital world, with the help of quaternions. In this study, an approach has been developed by integrating the advantageous and consistent structure of quaternions used to solve the problem of system lock-up and unresponsiveness during rotational movements in robot programming, the mathematically compact and functional form of Pauli matrices, and a generalized version of the Fibonacci sequence, which is an application of aesthetic patterns in nature. Full article

Old growth forests are increasingly rare but important carbon sinks which harbour rich biodiversity. Chronic browsing by the white-tailed deer (Odocoileus virginianus) is a threat to the sustainability of the services provided by these forests, particularly in northern temperate forests where deer numbers have increased in recent decades (driven by stricter hunting rules and reduced predation) and necessitating local monitoring of vegetation responses. The objective of this study was to determine the effects of deer exclusion on tree regeneration dynamics and soil nutrients in an old growth Carolinian forest. This was performed using exclusion fencing and tip-up mounds at McMaster Forest Nature Preserve and the Sheelah Dunn Dooley Nature Sanctuary in Hamilton Ontario. Tree regeneration was surveyed from thirty 1 m × 1 m quadrats within exclusion plots and another thirty quadrats from deer-browsed areas adjacent to the exclusion plots. Soil samples were taken from each quadrat to analyze browsing impacts on nitrate, phosphate and soil organic matter. Red oak (Quercus rubra) was planted at the top and base of tip-up mounds of varying heights and widths and monitored for deer access and browsing activity. Results show a significantly higher density of woody plants within exclosures compared to non-exclosures (p = 0.0089) and twice more abundance of highly palatable species within the exclosures. However, species richness (p > 0.05) and diversity (p > 0.05) were minimally impacted by deer browsing, showing a resilient old growth forest. Soil nitrate was consistently higher in the non-exclosures, while phosphate was consistently higher within deer exclosures. Finally, more seedlings survived at the top of mounds than the bases, showing the potential of tip-up mounds to be a natural method of deer exclusion and a critical avenue for restoring over-browsed forests. Full article

With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhile, quaternions enable image encryption algorithm (IEA) to be more secure by providing a higher-dimensional mathematical system. Therefore, considering the importance of IEA and quaternions, this paper explores the global exponential synchronization (GES) problem for a class of quaternion-valued neural networks (QVNNs) with discrete time-varying delays. By using Hamilton’s multiplication rules, we first decompose the original QVNNs into equivalent four real-valued neural networks (RVNNs), which avoids non-commutativity difficulties of quaternions. This decomposition method allows the original QVNNs to be studied using their equivalent RVNNs. Then, by utilizing Lyapunov functions and the matrix measure method (MMM), some new sufficient conditions for GES of QVNNs under designed control are derived. In addition, the original QVNNs are examined using the non-decomposition method, and corresponding GES criteria are derived. Furthermore, this paper presents novel results and new insights into GES of QVNNs. Finally, two numerical verifications with simulation results are given to verify the feasibility of the obtained criteria. Based on the considered master–slave QVNNs, a new IEA for color images Mandrill (256 × 256), Lion (512 × 512), Peppers (1024 × 1024) is proposed. In addition, the effectiveness of the proposed IEA is verified by various experimental analysis. The experiment results show that the algorithm has good correlation coefficients (CCs), information entropy (IE) with an average of 7.9988, number of pixels change rate (NPCR) with average of 99.6080%, and unified averaged changed intensity (UACI) with average of 33.4589%; this indicates the efficacy of the proposed IEAs. Full article

This study investigates the sensitivity of dynamic properties in coupled curved beams reinforced with carbon nanotubes (CNTs) to thermal variations. Temperature-dependent (TD) mechanical properties are considered for poly methyl methacrylate (PMMA) to be strengthened with single-walled CNTs (SWCNTs), employing the basic rule of mixture to define the equivalent mechanical properties of nanocomposites. The governing equations of motion are derived using a first-order shear deformation theory (FSDT) and Hamilton’s principle, accounting for elastic interfaces modeled using elastic springs. A meshfree solution method based on a generalized differential quadrature (GDQ) approach is employed to discretize the eigenvalue problem and to obtain the frequency response of the structure. The proposed numerical procedure’s accuracy is verified against predictions in the literature for homogeneous structural cases under a fixed environmental temperature. The systematic investigation assesses the impact of various geometric and material properties, including curvature, boundary conditions, interfacial stiffness, and CNT distribution patterns, on the vibrational behavior. Full article

This research is concerned with the free vibration and buckling analysis of carbon nanotube-reinforced beams (CNT-RBs) using a novel high-order shear deformation theory (HSDT). The current HSDT is modeled by a trigonometric function without a shear correction factor, and the displacement field has only four variables. Several different carbon nanotube distributions, including two uneven CNT distributions (X-CNT and O-CNT), are considered. The mixture rule is applied to express the effective material properties of carbon nanotube-reinforced beams. The CNTR beams are rested on two springs and a shear layer (Kerr foundation). Hamilton’s principle is employed to derive the governing equations, which are then solved using the Navier technique. The current theory and several parameter effects are studied and validated in comparison to benchmark studies and theories. The main purpose of this study is to enhance understanding of high-order shear theories, such as third order, sinusoidal, exponential, etc. In this context, our theory yields excellent results when compared to other theories. The difference between our theory and the exact solution is so minimal that it is superior to other theories. The second part of the study focuses on investigating the distribution of carbon nanotubes to enhance understanding. This knowledge can assist panel manufacturers in determining the appropriate distribution shape. Our results indicate that the third distribution (X-CNT) significantly influences mechanical behavior, unlike the first and second distributions (UD-CNT and O-CNT). Full article

The aim of the present study is to examine the acute effects of a specially designed musicokinetic (MSK) program for patients with Parkinson’s disease (PD) on (a) anxiety levels, (b) select kinematic and kinetic parameters, and (c) frontal cortex hemodynamic responses, during gait initiation and steady-state walking. Methods: This is a blind cross-over randomized control trial (RCT) in which 13 volunteers with PD will attend a 45 min MSK program under the following conditions: (a) a synchronous learning format and (b) an asynchronous remote video-based format. Changes in gait biomechanics and frontal cortex hemodynamic responses will be examined using a 10-camera 3D motion analysis (Vicon T-series, Oxford, UK), and a functional near-infrared spectroscopy (f-NIRS-Portalite, Artinis NL) system, respectively, while anxiety levels will be evaluated using the Hamilton Anxiety Rating Scale. Expected results: Guided by the rules of music, where periodicity is distinct, our specially designed MSK program may eventually be beneficial in improving motor difficulties and, hence, reducing anxiety. The combined implementation of f-NIRS in parallel with 3D gait analysis has yet to be evaluated in Parkinsonian patients following a MSK intervention. It is expected that the aforementioned intervention, through better rhythmicity, may improve the automatization of motor control, gait kinematics, and kinetics—supported by decreased frontal cortex hemodynamic activity—which may be linked to reduced anxiety levels. Full article

Based on the Hamilton principle combined with the Timoshenko beam theory, the authors developed a mixed finite element (FE) method for the nonlinear free vibration analysis of functionally graded (FG) beams under combinations of simply supported, free, and clamped edge conditions. The material properties of the FG beam gradually and smoothly varied through the thickness direction according to the power-law distributions of the volume fractions in the constituents, and the effective material properties of the FG beam were estimated using the rule of mixtures. The von Kármán geometrical nonlinearity was considered. The FE solutions of the amplitude-frequency relations of the FG beam were obtained using an iterative process. Implementing the mixed FE method showed that its solutions converged rapidly and that the convergent solutions closely agreed with the accurate solutions reported in the literature. A multilayer perceptron (MP) back propagation neural network (BPNN) was also developed to predict the nonlinear free vibration behavior of the FG beam. After appropriate training, the prediction of the MP BPNN’s amplitude-frequency relations was entirely accurate compared to those obtained using the mixed FE method, and its central processing unit time was less time-consuming than that of the mixed FE method. Full article