Search Results (9,449)

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

A symbolic method is presented for examining the solvability and constructing the exact solution to boundary value problems for systems of linear ordinary loaded differential equations and loaded integro-differential equations with nonlocal boundary conditions. The method uses the inverse of the differential operator involved in the system of loaded differential or integro-differential equations. A solvability criterion based on the determinant of a matrix and an exact analytical matrix-form solution formula are presented. For the implementation of the method into computer algebra system software, two algorithms are provided. The effectiveness of the method is demonstrated by solving several problems. The theoretical and practical results obtained complement the existing literature on the subject. Full article

Integral-form nonlocal elasticity provides a mechanically meaningful approach to describing size effects, yet it leads to Volterra-type integro-differential equations that are difficult to solve analytically and numerically challenging for boundary layers and high-order modes. In this work, we developed a symplectic numerical integration framework for Eringen’s two-phase (local/nonlocal mixture) integral model by embedding the constitutive operator into a Hamiltonian formulation and discretizing the influence domain in a belt-wise manner. A step-increase strategy was incorporated to allow flexible spatial marching while preserving the geometric (symplectic) structure of the transfer operation. In addition, a symmetry-explicit, element-level stiffness representation was derived for the discretized integral operator; it exposes a mirrored long-range coupling pattern and enables symmetric, energy-consistent assembly. The resulting kernel-agnostic algorithm accommodates both smooth and finite-range kernels. Static benchmarks and longitudinal vibrations are investigated for exponential, Gaussian, and triangular kernels over representative length ratios and mixture parameters. Comparisons with available analytical and asymptotic solutions show good agreement within their validity ranges, and the method yields stable higher-order eigenfrequencies when asymptotic expansions may be unreliable. The current study is limited to a linear one-dimensional rod setting, and validation is restricted to published analytical/asymptotic solutions rather than experimental calibration. Full article

Numerous applications from electrical engineering and mechanical structures are mathematically modeled using dynamical systems theory. Our paper concerns the behaviors of a 3D dynamic system in terms of damped or periodical oscillations and asymptotic representation, considering the dependence on three physical parameters. This system is explicitly integrated via a smooth-function solution of a third–order nonlinear differential equation, which means that the obtained exact parametric solutions describe a heteroclinical orbit. The modified Optimal Parametric Iteration Method (mOPIM) is used to study the influence of the physical parameters. The advantages of the applied method include the small number of iterations due to due to the appropriate choice of auxiliary convergence control functions. The mOPIM solutions are in good agreement with the corresponding numerical results and this aspect is highlighted qualitatively by figures and quantitatively by tables, respectively, in this work. The accuracy of the obtained solutions is assessed via a comparison with the OPIM method and the iterative solutions using 5–8 iterations, via an iterative method. A qualitative analysis of errors is performed. Full article

Soil salinization poses a severe threat to global wheat production, yet the physiological mechanisms underlying photosynthetic responses to neutral, alkaline, and combined salt stress remain poorly understood. This study systematically evaluated the photosynthetic physiology and salt tolerance of six spring wheat genotypes under three types of salt stress at varying concentrations. By integrating phenotypic data, gas exchange parameters, chlorophyll fluorescence indices, and biomass measurements, and applying structural equation modeling and multivariate analysis, key traits regulating biomass were identified. The results revealed significant interactions among salt stress type, genotype, and concentration on photosynthetic parameters. Structural equation modeling analysis revealed that under neutral salt stress, both gas exchange parameters and chlorophyll content had significant direct effects on seedling biomass, with standardized path coefficients of 0.421 and 0.400, respectively. Under alkaline and combined salt stresses, only chlorophyll content showed a significant direct effect on biomass, with standardized path coefficients of 0.873 and 0.790, respectively. Multiple regression analysis further identified key photosynthetic factors influencing growth under different stress types. Under neutral salt stress, phi (Ro) and E significantly affected biomass, whereas under alkaline and combined salt stresses, biomass was primarily co-regulated by phi (Ro) and phi (Eo). Based on a comprehensive evaluation of salt tolerance index, damage index, and biomass response, genotypes W06 and W02 exhibited the strongest overall salt tolerance. This study systematically elucidates the differential response mechanisms of photosynthesis in spring wheat under distinct salt stress types, providing an important theoretical basis and elite germplasm resources for breeding salt-tolerant wheat varieties. Full article

We revisit a hyperbolic wildfire model based on reaction–diffusion dynamics with relaxation effects and extend it by incorporating an advection transport term that accounts for wind-driven fire spread. After a planar two-dimensional reformulation and non-dimensionalization of the model, the analysis is restricted to the minimal ignition regime characterized by the presence of a logistic reaction term governing the evolution of the fire-affected tree fraction. The focus of the study is to assess the influence of the effective wind velocity on the propagation dynamics of the fire-affected tree fraction. For this purpose, analytical solutions of the extended wildfire model are derived by applying the Simple Equations Method (SEsM) in its (1,1) variant using a Riccati-type ordinary differential equation as a simple equation. The obtained families of exact solutions describe physically relevant transition fronts connecting fire-unaffected and fully fire-affected states, or vice versa. Numerical simulations of the derived analytical solutions are performed to demonstrate how the internal front thickness and the profile morphology depend on the specific variant of the Riccati-type solution and on the magnitude of the effective wind velocity. A phase-plane stability and bifurcation analysis of the reduced traveling wave system is carried out. Hopf bifurcation thresholds with respect to the effective wind velocity parameter are identified, revealing transitions between monotone front propagation and oscillatory regimes. A regime map is constructed in the parameter plane spanned by the effective wind velocity and the traveling wave speed. This regime diagram delineates regions of qualitatively different propagation behavior, including monotone advancing fronts, possible oscillatory regimes, and regimes in which traveling wave fronts cease to exist. Full article

Finger seals operate over extended periods under complex conditions involving high-pressure differentials, elevated rotational speeds, and rotor radial runout. Intense convective heat transfer arises within the seal, significantly impacting its structural deformation. To elucidate the influence of temperature on finger-seal deformation during convective heat transfer, the present study derives heat transfer energy equations for finger seals based on the Local Thermal Non-Equilibrium (LTNE) model. A three-dimensional porous-media flow-field model incorporating the LTNE framework, along with a solid thermal-deformation model, is developed. The effects of pressure differential and interference-fit magnitude on the structural deformation and average contact pressure of finger seals are analyzed under both the Local Thermal Equilibrium (LTE) and LTNE models. The results indicate that the LTNE model predicts a higher maximum seal temperature and a lower leakage rate compared to the LTE model. In both models, the deformation of individual seal-blade layers increases with rising pressure differentials and interference-fit magnitudes. Furthermore, the overall blade deformation is more pronounced under the LTNE model, suggesting a substantial thermal influence on sealing performance. The effects of pressure difference and interference fit on the thermal deformation of the seal plate are similar: both have the greatest impact on radial deformation, followed by circumferential deformation and axial deformation. Within the pressure difference range, the radial deformation of the third-layer seal plate in the LTNE model increases by 14.55%. When the interference fit increases from 0.05 mm to 0.2 mm, the radial deformation of each layer of the seal plate in the LTNE model increases by 0.18 mm. The average contact pressure increases with both pressure differential and interference-fit magnitude across both models. At a given pressure differential, the LTNE model yields a higher average contact pressure than the LTE model, with a maximum observed difference of 0.01 MPa. When the interference-fit magnitude is small, the pressure difference between the models remains minimal; however, at the maximum interference-fit, the difference reaches 0.08 MPa. Full article

This study introduces a modified computational scheme for handling linear and nonlinear fractal time-dependent partial differential equations. The method is constructed using three different stages that provide third-order accuracy in the fractal time variable. The stability of the approach is examined using scalar fractal models and Fourier analysis, while convergence is established for coupled convection–diffusion systems. The numerical algorithm is applied to analyze the mixed convective flow of a Carreau–Yasuda non-Newtonian fluid over stationary and oscillating plates under the influence of viscous dissipation and magnetic field effects. For spatial discretization, the incompressible continuity equation is handled by a first-order difference scheme, whereas higher-order compact schemes are implemented for the momentum, thermal, and concentration equations. The numerical findings show that increasing the Weissenberg number and magnetic field inclination reduces the velocity distribution. An accuracy assessment against existing numerical techniques demonstrates that the present method yields smaller computational errors, particularly when central difference schemes are used in space. In addition, a surrogate machine learning model is developed to predict the skin friction coefficient and local Nusselt number using Reynolds, Weissenberg, Prandtl, and Eckert numbers as input features. The predictive capability of the model is validated through Parity plots, bar charts for sensitivity analysis, scatter visualization, and Taylor Diagrams, confirming strong agreement with the numerical results. Full article

This work aims to introduce the concept of graphic rational contractions in the framework of extended $\mathcal{F}$-metric spaces and to establish fixed point theorems related to these mappings. In addition, we define and examine the class of interpolative Ćirić–Reich–Rus-type cyclic contractions in the same setting, deriving several new fixed point results that broaden existing theories. To illustrate the validity and originality of the obtained results, appropriate examples are presented. Furthermore, the developed theoretical results are applied to study the existence of solutions for fractional differential equations and nonlinear mixed Volterra–Fredholm integral equations, highlighting their effectiveness and practical importance. Full article

We study the complex point spectral distribution of the underlying operator of the system consisting of a reliable machine, a storage buffer with infinite capacity and an unreliable machine. This system is described by infinitely many partial differential equations with integral boundary conditions. The known literature proved that all points in a set in the left half of the complex plane are eigenvalues of the underlying operator and indicated that all points outside of the set remain undetermined. In this paper, we study the spectrum outside of the set and, under certain conditions, prove that some points outside the set are eigenvalues of the underlying operator, whereas other points are not. By combining our result with the results in the existing literature, we give a description of the point spectral distribution of the underlying operator on the whole complex plane. Our idea and method are suitable for studying point spectral distribution of the underlying operators of some queueing models described by infinitely many partial differential equations with integral boundary conditions. Full article

Fractional differential equations provide a flexible framework for describing evolutionary processes in complex media, where nonlocality and memory effects play central roles, and classical integer-order models are frequently inadequate to capture these behaviors. In this work, we revisit the time-fractional Harry Dym (HD) evolution equation in the Caputo sense and construct high-precision analytical approximations using the recently developed Tantawy technique (TT). The method generates a rapidly convergent fractional-power series in time without resorting to perturbative assumptions, auxiliary decomposition polynomials, linearization procedures, or integral transforms, and it remains computationally economical even at high approximation orders. Closed, compact expressions are derived up to the fifth-order approximation and can be systematically extended, yielding excellent agreement with the known exact solution of the classical/integer HD model and with approximations obtained via the new iterative method. A detailed error analysis is carried out by computing absolute and maximum residual errors over the entire computational domain, demonstrating the accuracy, stability, and robustness of the TT for the HD-type fractional nonlinear evolution equation. From a physical perspective, the proposed framework offers a reliable tool for modeling nonlinear wave structures in dispersive media with significant memory and, more generally, for treating a broad class of fractional nonlinear wave equations arising in physics and engineering. Full article

In this paper, we extend some existing models of the Ebola virus disease through a hybrid impulsive conformable approach. The base of the introduced model is a class of partial differential equations that incorporate diffusion terms to describe the development of the Ebola virus disease in time and space. In the extended model, we have considered impulsive effects at fixed moments of time, which is of high significance in investigating opportunities for impulsive vaccination strategies and impulsive control drug treatment on disease evolution. In addition, conformable setting is proposed, which provides modeling flexibility without the complications inherent in classical fractional derivatives. Instead of studying the global stability of an equilibrium, the more general notion of stability of sets is introduced and analyzed. The main stability of sets results are obtained by using the impulsive conformable Lyapunov technique and comparison principle. The proposed framework, concepts and techniques may serve as effective tools for analyzing numerous phenomena in medicine and biology. Full article

In this paper, we investigate the (1 + 1)-dimensional nonlinear truncated M-fractional FitzHugh–Nagumo model. The main objective is to analyze the dynamical behavior and obtain exact solutions for the model. First, a fractional transformation is applied to convert the governing partial differential equation into an ordinary differential equation. Subsequently, a Galilean transformation is employed to reduce the resulting equation to a dynamical system. The bifurcation structure and chaotic dynamics of the model are then examined. The presence of chaos is further confirmed through the phase portrait, basin of attraction, return map, Lyapunov exponent, permutation entropy, Poincaré map, power spectrum, attractor, fractal dimension, multistability, time analysis, and recurrence plot. In addition, the sensitivity of the system to the initial conditions is analyzed. Finally, exact solutions for the model are constructed using the unified Riccati equation expansion method. The obtained results are illustrated using two-dimensional, three-dimensional, and contour plots. Full article

With the increasing importance of cultural consumption and the sustainable revitalization of intangible cultural heritage (ICH), visual communication has become a key mechanism for translating cultural meanings into contemporary branding contexts. This study develops a semiotics-informed structural model that integrates semiotic theory with consumer behavior frameworks to explain how cultural visual symbols influence brand preference through cultural cognition and cultural identity. Using Wufangzhai as an empirical case, partial least squares structural equation modeling (PLS-SEM) is applied to survey data from 274 consumers. The results indicate that different visual elements exert differentiated effects on cultural cognition, with color and packaging showing stronger influences, while typography plays a more significant role in shaping cultural identity. Cultural identity is also found to mediate the relationship between cultural cognition and brand preference. These findings contribute to cultural branding research and provide practical insights for the design of ICH visual communication systems. Full article

Vessel vibrations have serious safety risks and must be effectively mitigated. This study investigates the reduction in ship pitch–roll vibrations modeled as a two degrees of freedom of nonlinear spring–pendulum system subjected to multi-parametric excitation, using proportional–derivative controller. The main objective is to develop a rapid and efficient analytical approach to nonlinear vibration analysis. A non-perturbative approach is employed to transform weakly nonlinear oscillators of ordinary differential equations into equivalent linear ones without using Taylor expansions. He’s frequency formula plays a central role in this transformation. The resulting parametric solutions are validated using Mathematica Software (v13) and show a strong agreement with the original nonlinear model. The effects of various parameters on stability are examined. Theoretical analysis is conducted using the multiple time scales method to identify worst resonance conditions and derive frequency response equations. Stability near simultaneous sub-harmonic resonance is assessed using Routh–Hurwitz criterion. Numerical simulations based on the fourth-order Runge–Kutta method confirm the effectiveness of proportional–derivative control. Excellent agreement between analytical and numerical results demonstrates the accuracy, efficiency, and practical applicability of the proposed method. Full article