Nonlocal Parameter Research Articles

Impact of weak nonlocal nonlinearity on modulational instability and chirp-free soliton trains in parabolic law optical fiber

This study considers the generation and evolution of chirp-free soliton trains in a focusing cubic-quintic nonlinear optical fiber media (by utilizing experimental parameters), under the influence of weak nonlocal nonlinearity. Analysis of modulational instability (MI) reveals that the MI gain exist only in the anomalous dispersion regime, with the quintic nonlinear term increasing the maximum gain and sideband frequencies. The nonlocal nonlinearity parameter generally suppresses the impact of MI, because the maximum gain is greatly reduced with increase in nonlocality. By using the subsidiary ordinary differential equation method, stationary periodic soliton trains are obtained; with the intensity of the optical beam greatly reduced and frequency increased as nonlocality is gradually stepped up. However, an increase in nonlocality instead reduces the frequency of the traveling optical signals; derived via an efficient transformation method. Our results strongly suggest that nonlocal nonlinearity has potential applications in the control of laser beams; as nonlinear periodic optical signals can be easily transformed to very weak quasi-plane waves.

A nonlocal higher-order shear deformation approach for nonline ar static analysis of magneto-electro-elastic sandwich Micro/Nano-plates with FG-CNT core in hygrothermal environment

In this study, the nonlocal static analysis of Magneto-Electro-Elastic (MEE) sandwich micro/nano-plates with Functionally Graded Carbon Nanotubes (FG-CNTs) core in a hygrothermal environment is studied. The nonlocal static formulation is developed based on Reddy's High-order Shear Deformation theory (HSDT). The von Kármán nonlinear strains are used and the governing equations of the HSDT are derived accounting for Eringen's nonlocal stress-gradient model. The governing equations are solved using the Galerkin method, which involves expanding the displacement field based on orthogonal functions. The variation of the volume fractions through the thickness of FG-CNTs core layer has been computed using two different homogenization techniques: the rule of mixtures and the Mori–Tanaka scheme. A detailed parametric study to show the characteristics of the FG-CNTs core, nonlocal parameters, thermal and moisture changes, types of CNT reinforcement and volume fraction, electric and magnetic potentials, and geometric parameters. The results are compared with the first-order shear deformation theory (FSDT) and classical plate theory to show the accuracy of nonlocal High-order Shear Deformation theory(NHSDT) formulation.

Effect of non-local thermoelasticity on diffusion under hydrostatic pressure

AbstractIn this paper, thermoelastic diffusion theory is demonstrated on a two-dimensional half-space problem. The surface is subjected to thermal shock and hydrostatic loads. The chemical potential must be a known function of time. The solution is obtained by the direct method using the Laplace technique and the Fourier exponential transform. Local and non-local thermoelasticity are discussed, and the influence of non-local parameters on the general theory of thermoelastic diffusion is investigated. Chemical potential, concentration, temperature, stress and displacement distributions are calculated numerically and displayed graphically.

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

PurposeThis paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.Design/methodology/approachThe analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.FindingsComputational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.Research limitations/implicationsThe results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.Practical implicationsThis investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.Originality/valueThis study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

Characterizing elastic wave reflection in a semiconducting isotropic diffusive medium with temperature rate-dependent nonlocal theory

In this paper, we explore the application of nonlocal theory to analyze the phenomenon of coupled thermoelastic wave reflection in a semiconducting diffusive medium, considering its temperature rate dependence. The governing equations are deconstructed using the Helmholtz vector rule, allowing us to delve into the behavior of the system. By calculating the dispersion relation in terms of propagation speed, we investigate four coupled longitudinal waves alongside an independent nondispersive transverse wave within the local medium. The cut-off frequencies for each wave are discussed, shedding light on their characteristics. Furthermore, we delve into the phenomenon of coupled longitudinal displacement waves at the medium’s boundary. Analytical derivations of amplitude ratios are presented, accompanied by graphical representations of their behavior, focusing on a semiconductor material such as copper. We examine the effects of physical parameters, including the nonlocal and diffusive parameters, on the obtained results. It is important to note that the existing literature primarily lacks consideration of diffusivity and plasma transportation. Lastly, we validate our findings by investigating the conservation of energy within the system.

Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes

In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases.

A novel FFT framework with coupled non-local elastic-plastic damage model for the thermomechanical failure analysis of UD-CF/PEEK composites

A novel FFT-based computational framework for coupling non-local elastic-plastic damage model is proposed in this paper, which is employed to accurately simulate the transverse tensile behaviors of unidirectional (UD) CF/PEEK composite materials under different temperatures. To address the distinct material properties exhibited by different microscopic constituents within the composite, two approaches are employed: (i) an integral-type regularized traction-separation damage model is applied to the interphase debonding, and (ii) an implicit gradient regularization technique for Lemaitre-type damage (matrix cracking) of the PEEK. By coupling the non-local damage model capable of accurately characterizing different failure modes within composites with an FFT computational framework, accurate predictions of the transverse tensile performance of UD-CF/PEEK composites at different temperature conditions can be achieved. Furthermore, the influence of non-local feature parameters and interphase mechanical properties on the composite's mechanical behavior is thoroughly discussed. Comparisons with experimental results affirm the accurate prediction of the transverse tensile behavior of UD-CF/PEEK composites through the proposed computational framework. Ultimately, based on this framework, the transverse tensile modulus and strength of UD-CF/PEEK composites, considering different fiber volume fractions and temperatures, are predicted, successfully demonstrating the effectiveness and applicability of the proposed approach in forecasting the mechanical behavior of composites.

Electromagnetic thermo-viscoelastic response of piezoelectric rods considering memory dependent effects

Based on the theory of nonlocal elasticity and nonlocal heat conduction, a new dual-phase-lag heat conduction model with memory dependent effect is proposed in this article to explore the thermodynamic behavior of functionally graded rotating piezoelectric rods under the action of moving heat sources. Assuming that the material properties of functionally graded piezoelectric rods vary exponentially along the length direction, the end of the rod is rigid and fixed without voltage. Use Laplace transform to transform the problem into the spatial domain and perform analytical solutions, then use inverse Laplace transform to obtain the time-domain solution. Numerical solutions were performed for dimensionless displacement, temperature, electric potential, and stress, and the variation patterns of the physical quantities involved were described in graphical form. The calculation provides the effects of functional gradient non-uniformity index, thermal nonlocal parameters, kernel function, and viscoelastic parameters on the physical quantities involved.

A new model of rotating nonlocal fiber-reinforced visco-thermoelastic solid using a modified Green–Lindsay theory

The effect of rotation on a nonlocal fiber-reinforced visco-thermoelastic media was examined in this work using an modified Green and Lindsay theory (MGL). The problem was resolved by using normal mode method to derive the precise expressions of field quantities. In this technique, one gets exact solution without any assumed restrictions on the field variables. The normal mode technique is applicable to a wide range of problems in thermodynamics and thermoelasticity. Graphical representations of the thermal temperature, displacements and stresses are obtained. Comparisons of the physical quantities are shown in figures to study the effects of nonlocal parameter, rotation, viscosity and reinforcement parameters. Some special cases of interest have also been inferred from the present problem. The results indicate that rotation, nonlocal parameter, viscosity and reinforcing factors have a considerable impact on the fluctuations of the variables under consideration. These impacts are examined and described in depth.

Isogeometric Analysis for Nonlocal Vibration Characteristics of BFGP Curved Nanobeams with Variable Nonlocal Parameters

Isogeometric Analysis for Nonlocal Vibration Characteristics of BFGP Curved Nanobeams with Variable Nonlocal Parameters

A thermodynamically consistent strain difference-based nonlocal damage mechanics approach for failure analysis of quasi-brittle materials

The nonlocal integral approaches are established methods known for their effectiveness in dealing with the challenges of ill-posed behaviour and mesh sensitivity during the strain softening process, especially within classical continuum theories. The present work extends the strain difference-based nonlocal approach to continuum damage mechanics (CDM) theories for predicting the failure behaviour of quasi-brittle materials. The strain difference approach is adopted for two reasons: (i) it maintains physical realism and indirectly incorporates nonlocal effects while computing both the damage variable and the damage energy release rate, and (ii) the constitutive model maintains a symmetry nature in constructing the nonlocal part of the stiffness matrix, reducing the computational cost in strain-softening problems. The state and damage evolution equations for the present nonlocal approach are formulated within the thermodynamic framework. Numerical examples involving 2D and 3D cases are solved: (i) to study the influence of nonlocal parameter ‘α’ on the damage distribution while capturing the post-peak behaviours, (ii) to demonstrate the effectiveness of the present methodology by obtaining mesh-independent results and accurately predicting damage propagation paths, and (iii) to compare the experimental results and numerical structural response for coarse mesh, highlighting both computational efficiency and reduction of mesh-bias dependency. The results obtained by the strain difference-based nonlocal damage model agree well with the experimental results in the literature.

ZPEKTR: A code for spectral synthesis of fast-rotating stars

Estimating the physical states of the surfaces of fast-rotating stars is challenging due to several intrinsic processes, which include radiative flux inhomogeneities on the photosphere induced by rotation and circumstellar signatures in their spectra. The analysis of their spectra ultimately requires the use of synthetic grids of spectra accounting for all these physical processes. In this paper, we present the `von ZeiPEl's code for gravity darKening specTRal synthesis' (ZPEKTR) code, which is designed to perform the spectral synthesis of fast-rotating stars, accounting for gravity darkening, limb-darkening effects in the continuum and geometrical deformation induced by fast rotation. We consider colatitudinal temperature and surface-gravity variations, assuming both the classical prescription developed by von Zeipel and the new formulation by Espinosa-Lara. The code runs either with a rectangular or a triangular mesh on the stellar surface. We compare the temperature and gravitational distribution as a function of the stellar latitude arising from both models. The line profiles of 4388, 4471, 4922, and 6678 produced with both formalisms are compared at three different rotation rates and illustrate differences in shape and central intensity. We also illustrate the fittings of 31 line spectra of classical Be stars averaged from the Be Stars Observation Survey (BeSOS) database and make a comparison among their apparent physical parameters and ages determined from plane-parallel non-local thermodynamical equilibrium (non-LTE) models and parameters determined from classical von Zeipel models, finding a displacement of more evolved objects towards the zero-age main sequence. We also compare the distributions of projected rotation velocities of these objects obtained with and without the inclusion of gravity-darkening effects with ZPEKTR. We observe a shift of the histogram of rotation velocities calculated accounting for effects of gravity darkening concerning rotation velocities obtained through the fittings with classical plane-parallel non-LTE models. We show that models that do not account for gravity darkening can underestimate the rotation velocity, because the stellar latitudes that contribute the higher velocities are those in the equator with the least radiative flux. We envisage near-future improvements to the code, such as the inclusion of differential rotation and treatment of tidal forces in binary stellar systems.

Jacobian elliptic wave trains in fourth-order dispersive nonlinear Schrödinger equation and the modulational instability

We analytically and numerically explore the existence of explicit exact Jacobian elliptic solutions of a nonlinear Schrödinger model with fourth-order dispersion and weak nonlocality. We delineate the parameter domain in which these highly dispersive doubly periodic waves balanced by the weak nonlocality and Kerr nonlinearity exist. Additionally, we have studied the modulational instability (MI) of these waves with the aid of linear stability analysis. We observe that in the presence of fourth-order dispersion, the MI gain increases with increasing the nonlocality parameter.

Small-dependent nonlinear analysis of functionally graded triply periodic minimal surface nanoplates

This paper introduces an effective and simple approach to analyze functionally graded triply periodic minimal surface (FG-TPMS) nanoplates, taking advantage of a novel nonlocal strain gradient nonlinear analysis. TPMS has recently gained attention as an extraordinary solution for constructing structures, drawing inspiration from natural architectures. It offers remarkable features, including high interconnectivity porous architectures, smooth surfaces, and the ability to achieve mathematically controllable geometry features. However, the extensive potential and benefits of TPMS structures have not been fully explored in current research. Hence, this study aims to address this limitation and unlock new possibilities for FG-TPMS nanoplates. Three patterns of FG-TPMS nanoplates, namely Primitive (P), Gyroid (G), and I-gragh and Wrapped Package-graph (IWP), are utilized in this investigation. The proposed model effectively incorporates the nonlocal,strain gradient and nonlinear effects into nanoplate structures. It enables a comprehensive understanding of the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate by fine-tuning the nonlocal and strain gradient parameters. This research offers promising prospects for future design and optimization, providing a robust approach to address the intricate nonlinear behavior observed in FG-TPMS nanoplates.

Nonlocal and dual‐phase‐lag effects in a transversely isotropic exponentially graded thermoelastic medium with voids

AbstractThe aim of the present work is to examine the thermally induced disturbances in a transversely isotropic nonlocal exponentially graded (nonhomogeneous) thermoelastic half‐space with voids within the framework of dual‐phase‐lag (DPL) theory. It is supposed that the material's properties are graded in ‐direction. By employing normal mode technique, the exact expressions of the temperature field, the change in volume fraction field, displacement and stress components are obtained. The obtained results are computed numerically for a magnesium crystal‐like material and depicted graphically to display the effects of material's anisotropy, non‐homogeneity parameter, generalized theories, nonlocal parameter, void parameter and time on the variations of different physical fields. Certain limiting cases of interest have been deduced from the present investigation.

Vibration analysis of functionally graded carbon nanotubes reinforced composite nanoplates

This work presents the analytical analysis for free linear vibration behavior of functionally graded-carbon nanotubes reinforced composite (FG-CNTRC) nanoplates in the framework of nonlocal strain gradient theory (NSGT) and the first-order shear deformation plate theory (FSDPT). The nanoplate is considered made of a mixture of an isotropic polymer matrix and reinforced carbon nanotubes (CNTs). Four different distributions of CNTs are examined including uniformly distributed and FG reinforcements (FG-O, FG-X, and FG-V). The governing equations of motion are established based on the Hamilton’s principle. The closed-form analytical solution for the natural frequency of FG-CNTRC nanoplates with simply supported all edges is carried out by using the Navier-type solution. The impact of some key parameters on the natural frequencies of FG-CNTRC nanoplates is also studied and discussed. The result shows that FG-CNTRC nanoplates reveal the softening- or hardening-stiffness effects depending on the relationship between the nonlocal parameter and the material length scale parameter. The aspect ratios of FG-CNTRC nanoplates, the volume fraction, and the distribution pattern of CNTs have also an important impact on the vibration behavior of FG-CNTRC nanoplates.

Realizing Minimally Perturbed, Nonlocal Chiral Metasurfaces for Direct Stokes Parameter Detection.

Recent development in nonlocal resonance based chiral metasurfaces draws great attention due to their abilities to strongly interact with circularly polarized light at a relatively narrow spectral bandwidth. However, there still remain challenges in realizing effective nonlocal chiral metasurfaces in optical frequency due to demanding fabrications such as 3D-multilayered or nanoscaled chiral geometry, which, in particular, limit their applications to polarimetric detection with high-Q spectra. Here, we study the underlying working principles and reveal the important role of the interaction between high-Q nonlocal resonance and low-Q localized Mie resonance in realizing effective nonlocal chiral metasurfaces. Based on the working principles, we demonstrate one of the simplest types of nonlocal chiral metasurfaces which directly detects a set of Stokes parameters without the numerical combination of transmitted values presented from typical Stokes metasurfaces. This is achieved by minimally altering the geometry and filling ratio of every constituent nanostructure in a unit cell, facilitating consistent-sized nanolithography for all samples experimentally at a targeted wavelength with relatively high-Q spectra. This work provides an alternative design rule to realizing effective polarimetric metasurfaces and the potential applications of nonlocal Stokes parameters detection.

Thermoelastic transient memory response analysis of non-localized nano-piezoelectric plates based on Moore-Gibson-Thompson thermoelasticity theory

With their abilities to induce electric charge, stress or deformation in response to external forces as well as the ease of fabrication, design flexibility and excellent electromechanical properties, piezoelectric materials have been widely used in actuators, sensors and even in nano/micro-electro-mechanical systems. With the rapid advancement of nano/micro-technology, from the perspective of theoretical analysis, the priority is to develop applicable models to describe the piezoelectric-thermoelastic responses of piezoelectric nano/micro-structures suffering transient heat conduction by taking the size-dependent effect and the memory-dependent effect into consideration. In this work, a new model based on the existing piezoelectric-thermoelastic model is established by introducing the nonlocality into the constitutive equations and the memory-dependent derivative into Moore-Gibson-Thompson (MGT) heat conduction equation respectively. Then, this new model is applied to investigating the dynamic responses of a piezoelectric nanoplate subjected to thermal shock. The corresponding governing equations are formulated and then solved by Laplace transform and its numerical inversion. In calculation, the influences of the time delay factor and the kernel function of MDD and the non-local parameter on the thermal, electric and elastic fields in the piezoelectric nanoplate are examined. Meanwhile, the predictions of transient response among different thermoelastic models are compared. The numerical results are illustrated graphically and discussed in detail. The obtained results show that MDD has a significant effect on the transient response, where the effect of the kernel function is more pronounced. This work may provide a theoretical reference for strength design, thermal protection and thermal processing strategies for piezoelectric nanodevices.

Mechanical behavior of nanocircular plates under coupled surface and nonlocal effects by using molecular dynamics simulations

The equations of control for a circular thin plate under simple support are obtained by coupling the surface effect and non-local effect using the equilibrium method. Molecular dynamics simulations were used to calculate the residual surface strain energies at different crystal orientations. Different crystal orientations of the same material would affect its surface energy and thus result in different mechanical behaviors. The effects of residual surface strain energy and non-local parameters on the mechanical behavior of circular thin plates were analyzed. The analysis reveals that the surface effect and non-local effect on the deflection of the nanoplates are significant. The surface effect parameter of tensile stress increases the deflection, while the opposite is true for the surface effect parameter of compressive stress, and the non-local parameter decreases the deflection. The influence of surface effect and non-local effect is significant for smaller thicknesses and weakens for larger thicknesses.

Nonlocal theory on plane waves in a higher-order thermo-diffusive semiconducting medium under the gravitational field

This article explores the reflection of elastic waves in nonlocally generalized thermo-diffusive semiconducting elastic solids under the influence of gravity. The problem is framed within the higher-order fractional derivative heat equation. The frequency dispersion relation reveals the presence of five coupled waves. The wave speeds are graphed against angular frequency for the nonlocal parameter under the influence of gravity, and the cut-off frequency of the waves is visually represented. The incident wave at the free surface of the solid is the coupled longitudinal P-wave, and its reflection coefficients are computed. The study investigates the impact of gravity, fractional order, and nonlocal parameters on propagation speed and amplitude ratios, revealing their significant influence. The findings are substantiated in the context of energy conservation. This research provides valuable insights for scientists engaged in geophysics and various branches of mechanics.