Eigenvalue Approach Research Articles

Understanding population dynamics and management strategies for a newly emerging pest Carea sp. in Eucalyptus plantations in Indonesia through a mathematical model

In this current study, we investigate the population dynamics of Carea sp. (Lepidoptera: Nolidae), a newly emerging pest in Indonesian Eucalyptus plantations, utilizing the MELP-SI-B mathematical model based on the first reported outbreak in 2022. The larval infestation of Carea sp. has been observed to stunt plant growth and can even lead to plant mortality. The proposed model incorporates pest management interventions, including chemical control with pesticides and biological control through the introduction of natural predators. Analysis of the deterministic compartment model revealed four locally asymptotically stable equilibrium points, validated using eigenvalue approach and application of the center manifold theorem. Bifurcation diagrams are presented to elucidate the relationships between all equilibrium points. An optimal control problem is explored within this model, considering three scenarios: chemical control without predators, simultaneous chemical control with predators, and chemical control followed by predator management. The results of the optimal control strategy analysis highlight the critical importance of timing the initial chemical control application for effective pest management. Notably, this study reveals that a combined approach involving chemical control (without predators) followed by predator management during the post-chemical control period yields the most favorable outcomes among the examined strategies.

Analysis of multi-phase lag gradients for a spherical cavity due to prescribed internal pressure

A refined multi-phase lag model is proposed here for a homogeneous unbounded thermoelastic spherical cavity in a curvilinear coordinate system. The associated solutions are obtained by forming non-dimensional vector matrix equations and applying Eigen value approach in the transform domain. The results have been verified using the valid boundary conditions associated with physical and field variables. Mathematica and MATLAB platforms are used for numerical analysis and graphical representation.

Eringen’s nonlocal elasticity theory for the analysis of two temperature generalized thermoelastic interactions in an anisotropic medium with memory

PurposeThe purpose of this paper is to investigate the thermoelastic interactions in a homogeneous, transversely isotropic infinite medium with a spherical cavity in the context of two temperature Lord-Shulman (2TLS) generalized theory of thermoelasticity considering Eringen’s nonlocal theory and memory dependent derivative (MDD). Memory-dependent derivative is found to be better than fractional calculus for reflecting the memory effect which leads us to the current investigation.Design/methodology/approachThe governing field equations of the problem are solved analytically using the eigenvalue approach in the transformed domain of Laplace when the cavity’s boundary is being loaded thermomechanically. Using MATLAB software the numerical solution in real space-time domain is obtained by Stehfest method.FindingsNumerical results for the different thermophysical quantities are presented in graphs and the effects of delay time parameter, non-local parameter and two temperature parameters are studied thereafter. The outcomes of this study convince that the displacement u, conductive temperature ϕ, thermodynamic temperature θ are concave upward whereas radial stress τrr is concave downward for every choice of delay time parameter ω, two temperature parameter η and non-local parameter “ζ”. As a specific instance of our findings, the conclusions of an equivalent problem involving integer order thermoelasticity theory can be obtained, and the corresponding results of this article can be readily inferred for isotropic materials.Originality/valueThe novelty of this research lies in the adoption of generalized thermoelastic theory with memory dependent derivative and Eringen’s nonlocality for analyzing the thermoelastic interactions in an infinite body with spherical cavity by employing eigenvalue approach. It has applications to many thermo-dynamical systems.

Thermo-elastic vibration analysis and optimization of a nanoresonator composed of a coupled nanotube system for acoustic liner application using the hybrid deep neural network–based white shark algorithm

This study explores the potential of nanoresonator systems composed of coupled nanotubes with graphene nanoparticles for enhancing the performance of acoustic liners in aircraft engines. The objective of this study is to develop an analytical model and predict its behavior under various conditions. The acoustic liners consist of perforated metal sheets and honeycomb cavities, which are essential for noise reduction in aircraft engines. The model is tested for variations in natural frequency, mode number (m), size effects (e0a), viscous constant (C), temperature (T), localness factor (L), and stiffness constant (K). A hybrid deep neural network–based white shark algorithm (DNN-WSA) is used to predict and optimize the performance of nanoresonator-coupled nanotube systems. Four theories were compared, such as wave propagation theory, nonlocal elasticity theory, polynomial eigenvalue approach, and governing equations with respect to natural frequencies in nanoresonator-coupled nanotube systems. The wave propagation theory yielded the lowest natural frequency, which was selected for detailed analysis. The optimized values of size effect of 2 nm, temperature of 5 K, and frequency of 1.971975 THz were obtained. When C = 0.3, K = 10, T = 300, and L = 10×e−9, the root mean square error (RMSE) value is 0.8421, which indicates improved predictive performance as it continues to decrease. The study’s findings showed that changes in viscous constants impact natural frequencies, while size effects have a minor influence. Temperature variations also affect natural frequencies, with higher temperatures leading to higher frequencies. The optimized model demonstrates enhanced predictive performance, which contributes to a better understanding of nanoresonator systems and their application in noise reduction for aircraft engines.

Longitudinal Air-Breathing Hypersonic Vehicle Nonlinear Dynamic Simulation with Different Control Inputs

<div>The air-breathing hypersonic vehicle (AHV) holds the potential to revolutionize global travel, enabling rapid transportation to low-Earth orbit and even space within the next few decades. This study focuses on investigating the nonlinear dynamic simulation, trim, and stability analysis of a three-degrees-of-freedom (3DOF) longitudinal model of a generic AHV for variable control surface deflection, <i>δ<sub>e</sub></i> and <i>δ<sub>r</sub></i>. A simulation is developed to analyze the burstiness of the AHV’s nonlinear longitudinal behavior, considering the complete flight envelope across a wide range of Mach numbers, from <i>M</i> = 0 to 24, for selected stable <i>M</i>. The presented simulation assesses trim analysis and explores the dynamic stability of the AHV through its flight envelope and bifurcation method analysis is carried out to gain insight and validate the dynamic stability using eigen value approach.</div>

Eigenvalue approach for investigating thermal and mechanical responses on living tissues during laser irradiation with experimental verification

This study provides analytical solutions for the non-Fourier theory, which accounts for bioheat transfer in biological tissue when exposed to laser irradiation. To perform thermal treatment procedures effectively, a thorough comprehension of both the heat transmission mechanism and the subsequent thermal and mechanical interaction within the patient's human tissue is essential. The assessment of thermal injuries to the tissue involves determining the extent of denatured proteins using the Arrhenius formulation. The bio-thermoelastic model presented employs Laplace transforms and analytical techniques to establish governing formulations. Subsequently, an eigenvalues scheme is utilized to derive solutions to these equations. Graphical representations of the results for temperature, displacements, and stress are provided. The analytical solution's accuracy is verified through a comparison with numerical and experimental data. Results indicate that, when both have zero thermal lag times, the generalized non-Fourier model aligns with the Pennes bioheat transfer model. Furthermore, the effectiveness of the mathematical model in evaluating bioheat transfer in biological tissues is validated by comparing it with established experimental data.

Flow separation and stability analysis for aligned magnetic field in a porous medium saturated by a titanium alloy nanofluid

ABSTRACT This article examines Joule heating and aligned magnetic field in a porous medium saturated by Ti-alloy nanofluid. The heat generation and first-order velocity slip towards an exponentially permeable shrinking surface are taken. Non-dimensional forms of the resulting flow equations are solved numerically for multiple solutions using the shooting technique along with the Runge–Kutta method of 4th order in MATLAB(R2021a). The stability of the resultant system of equations is verified through the smallest eigenvalue approach. Both the first and second solutions of correlation streamline profiles are extracted for appropriate values of physical parameters. By stability analysis, the first solution is unquestionably more stable than the second solution. The major outcome is that the Joule heating raises the fluid’s temperature. The presence of flow separation is identified in the shrinking regions and the delay of boundary layer separation is pointed out. These analyses play a significant role in the fields of aerodynamics, medicine, and space sciences.

Analytical study of micropolar thermoelastic rectangular plate under three theories

A three-dimensional micropolar thermoelastic problem is considered for an isotropic rectangular plate that is subjected to simply support and isothermal on its four adjacent edges. Normal mode analysis is applied to the governing equations to form a vector-matrix differential equation and the analytical solution of the vector-matrix differential equation is obtained by using eigenvalue approach methodology. Numerical results are presented graphically along with theoretical analysis for sinusoidal variation of the stresses applied on the top surface of the rectangular plate.

An FPGA-Based Adaptive Solution for Synchronous Configuration in UART Communication

To address the challenges associated with data reception failures, which arise due to abrupt alterations in the baud rate and the data format of the transmission signal in traditional Universal Asynchronous Receiver-Transmitter (UART) scenarios, this study presents an adaptive UART parameter solution underpinned by Field-Programmable Gate Array (FPGA) technology. Initially, this manuscript elucidates the underlying principles of UART communication and delineates the pivotal constituents of the UART protocol. Subsequently, it offers an in-depth analysis, from the transmission perspective, of how specific parameters influence the effectiveness of the UART protocol. Based on the software and hardware embodiments associated with the dual primary functions – baud rate adaptation and data format adaptation – this paper extensively details the flow chart for baud rate adaptation, the circuitry for edge detection, methodologies for baud rate computation, and the parameter eigenvalue approach. Following this, Verilog, a hardware description language, is employed for coding and subsequent simulation within the Quartus II environment. Empirical evidence corroborates the efficacy of the proposed design in achieving synchronous configuration between the baud rate and the data format. The findings of this research bear substantial implications for augmenting both the adaptability and dependability of UART communication systems.

Generalized thermomechanical interaction in two-dimensional skin tissue using eigenvalues approach

The aim of this work is to analytically study the thermo-mechanical response of two-dimensional skin tissues when subjected to instantaneous heating. A complete understanding of the heat transfer process and the associated thermal and mechanical effects on the patient's skin tissues is critical to ensuring the effective applications of thermal therapy techniques and procedures. The surface boundary of the half-space undergoes a heat flux characterized by an exponentially decaying pulse, while maintaining a condition of zero traction. The utilization of Laplace and Fourier transformations is employed, and the resulting formulations are then applied to human tissues undergoing regional hyperthermia treatment for cancer therapy. To perform the inversion process for Laplace and Fourier transforms, a numerical programming method based on Stehfest numerical inverse method is employed. The findings demonstrate that blood perfusion rate and thermal relaxation time significantly influence all the analyzed distributions. Numerical findings suggest that thermo-mechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model.

Non-linear stability characteristics of randomly distributed CNT-reinforced fiber composite beams under thermo-mechanical loadings

The aim of the present study is to elucidate the non-linear stability characteristics of randomly distributed carbon nanotube-reinforced fiber composite (RD-CNTRFC) beams subjected to thermo-mechanical loading. Effective material properties of RD-CNTRFC are estimated using the Eshelby-Mori-Tanaka approach and Halpin–Tsai micromechanical techniques. The material properties are considered to be temperature-dependent, and the influence of carbon nanotube (CNT) agglomeration is also incorporated in material properties estimation of hybrid matrix. The strain-displacement relations are assumed by incorporating the higher-order shear deformation theory and geometrical nonlinearity (von Kármán). The governing partial differential equations are obtained by minimizing the total potential energy of the beam. Buckling loads of beam subjected to in-plane compressive loads are estimated using Eigen value approach. Similarly, buckling temperatures are also determined by solving Eigenvalue problem iteratively due to temperature-dependent material properties. The non-linear equilibrium paths under thermal and mechanical loadings are traced through iterative Eigenvalue approach. Numerical results are presented to elucidate the influence of various parameters like CNT agglomeration, ply sequences, span-to-depth ratio, boundary conditions, and mass fraction of CNTs.

A unified buckling formulation for linear and nonlinear analysis of laminated plates using penalty based [formula omitted] FEM-HSDT model

In this paper, the effect of pre-buckling boundary conditions and the type of nonlinearity for stress stiffening used in different linear and nonlinear buckling approaches is studied for laminated composite plates. The study is conducted using a C0 finite element (FE) plate model, employing a unified C1 higher-order shear deformation theory (HSDT). The set of governing equations is derived using the principle of virtual displacement and solved using the tangent-based arc-length method in conjunction with a simple branch switching technique. The performance of the present C0 FE model is assessed through a validation exercise and comparison with results obtained via the use of ANSYS and, for linear analysis, Navier solution, as well as solutions available in the literature. The influence of the different in-plane loads, boundary conditions, side-to-thickness ratio, fiber orientation, types of imperfection and penalty stiffness matrix are also examined. The results show that the same boundary conditions must be utilized in both pre-buckling and linear eigenvalue analyses for accurate and realistic predictions of critical buckling loads, as confirmed from the nonlinear buckling analyses. Furthermore, the critical buckling loads obtained using Green–Lagrange nonlinearity are observed to be more conservative than those obtained using von Kármán nonlinearity. The nonlinear buckling approach is a generalized approach while the nonlinear eigenvalue approach has a limited range of application.

Reduced-Order Modal Solution of the Full-Wave Method of Moments Based on a Quasi-Static Eigenvalue Approach

Reduced-Order Modal Solution of the Full-Wave Method of Moments Based on a Quasi-Static Eigenvalue Approach

Dynamic response of a 1D semi-infinite piezoelectric rod with fractional order generalized thermoelasticity

In this work, the problem of a 1D semi-infinite piezoelectric rod in the context of fractional generalized thermoelasticity is considered. The rod with one end fixed is subjected to a moving heat source. The physical quantities are analytically given by the eigenvalue approach with the Laplace transform and the distribution of displacement, temperature, and stress can be obtained through the numerical inverse of Laplace transform. Numerical results show that the fractional order parameter has a great effect on all physical quantities, and it is necessary to take the fractional order thermoelasticity into account when dealing with the thermoelastic problems of piezoelectric materials.

Analytical solution for thermo-mechanical interactions in hyperthermia treatment of living tissue using eigenvalue approach

Analytical solution for thermo-mechanical interactions in hyperthermia treatment of living tissue using eigenvalue approach

Poroviscoelastic Gravitational Dynamics

AbstractGlobal‐scale periodic deformation has been studied using the (visco)elastic gravitational theory, which assumes a planetary body consists of solid or liquid layers. Recent planetary exploration missions, however, suggest that a global layer of a mixture of solid and liquid exists in several planetary bodies. This study provides a theory of periodic deformation of such a layer unifying the viscoelastic gravitational theory with the theory of poroelasticity without introducing additional constraints. The governing equation system and a formulation suitable for numerical calculation are given. Equations used to calculate the energy dissipation rate are also given. The analytical solutions for a homogeneous sphere are obtained using an eigenvalue approach. Simple numerical calculations assuming a homogeneous sphere reveal that a numerical instability occurs if a thick porous layer, a low permeability, or a high frequency is assumed. This instability can be avoided by choosing an appropriate interior structure model that is numerically equivalent. Different simple numerical calculations adopting a multilayered, radially varying interior profile reveal that the radial profile of the tidal heating rate for a fluid‐saturated porous layer and that for a low‐viscosity solid layer are completely different. In addition, the radial variation in porosity can lead to a factor of ∼100 increase in the local heating rate. These results indicate that future studies should consider a wider variety of detailed interior structure models.

Surface waves in piezoelectric semiconductor by using Eigen value approach

The article is about the propagation of surface waves through electrically conducting medium. The piezoelectric medium is an n-type semiconductor. The finite deformation caused in the medium results in generation of elastic disturbance that propagate through the medium in the form of surface waves. According to the theory of thermoelasticity, temperature also propagate in the medium in the form of thermal waves. The heat propagation through the medium is encountered by classical heat conduction model derived from Fourier’s law of heat conduction. The analytical solution for system of governing equations is obtained by using Normal mode analysis method along with Eigen value approach. Secular equation containing the information of surface waves is obtained for some specific boundary conditions at the surface . Furthermore, the theoretical results obtained are represented graphically for a particular medium.

Improved methodology for damping sub‐synchronous oscillation in a series‐compensated DFIG‐based wind farm

AbstractThe interaction between the wind farm and the series‐compensated transmission line may lead to the sub‐synchronous oscillation (SSO) phenomenon which affects the system stability and equipment safety. Among the presented methods for damping the SSO phenomenon, the supplementary damping controller (SDC) is the most prevalent method because of its low cost, effectiveness, and simplicity. In all previous studies, one input control signal is fed to the SDC for mitigating the SSO. Here, two input control signals (active power and reactive power deviation) are applied to the SDC for enhancing the system stability and damping the SSO quickly. The ability of the proposed method for damping the SSO has not been investigated before. The proposed SDC is embedded into the q‐axis of the rotor‐side converter (RSC) inner current loop. The modified IEEE first benchmark model (FBM) is used to analyze the performance of the proposed method under different compensation levels, variable wind speeds, and sub‐synchronous control interaction (SSCI). Small‐signal stability using the eigenvalue approach is carried out, where the impact of the proposed method on sub‐synchronous mode, and super‐synchronous mode is investigated. The results successfully prove the superiority of the proposed method for damping the SSO under various operating conditions compared to some previous methods, where the least overshoot and faster convergence have been achieved by the proposed method in all studied cases.

The Effect of Fractional Derivatives on Thermo-Mechanical Interaction in Biological Tissues during Hyperthermia Treatment Using Eigenvalues Approach

This article studies the effects of fractional time derivatives on thermo-mechanical interaction in living tissue during hyperthermia treatment by using the eigenvalues approach. A comprehensive understanding of the heat transfer mechanism and the related thermo-mechanical interactions with the patient’s living tissues is crucial for the effective implementation of thermal treatment procedures. The surface of living tissues is traction-free and is exposed to a pulse boundary heat flux that decays exponentially. The Laplace transforms and their associated techniques are applied to the generalized bio-thermo-elastic model, and analytical procedures are then implemented. The eigenvalue approach is utilized to obtain the solution of governing equations. Graphical representations are given for the temperature, the displacement, and the thermal stress results. Afterward, a parametric study was carried out to determine the best method for selecting crucial design parameters that can improve the precision of hyperthermia therapies.

Photothermal effects of semiconducting medium with non-local theory

A generalized magnetothermoelastic half-space problem is considered for a homogeneous, isotropic and semiconducting medium under the non-local heat equation with dual-phase-lag model. The boundary surface of the medium is subjected to a prescribed time-dependent and exponential order compression along with a prescribed temperature and carrier intensity gradient. Two integral transformations, Laplace transform for time variable and Fourier transform for space variable, are employed to the equations of motion and the heat conduction equation for formulation of a vector-matrix differential equation which is then solved by using eigenvalue approach. Inversion processes for the two integral transforms are carried out numerically. Finally, the effects of physical field variables and stress components are analyzed and illustrated graphically under the variation of different physical parameters.