Nonlocal Parameter Research Articles

Application of Surface Stress-Driven Model for Higher Vibration Modes of Functionally Graded Nanobeams.

This paper employs a surface stress-driven nonlocal theory to investigate the synergistic impact of long-range interaction and surface energy on higher vibration modes of Bernoulli-Euler nanobeams made of functionally graded material. It takes into account surface effects such as the surface modulus of elasticity, residual surface stresses, surface density, and rotary inertia. The governing equation is derived through the application of Hamilton's principle. The novelty of this work lies in its pioneering approach to studying higher-order vibrations, carefully considering the combination of long-range interactions and surface energy in nanobeams of functionally graded materials through a well-posed mathematical model of nonlocal elasticity. This study conducts a parametric investigation, examining the effects of the nonlocal parameter and the material gradient index for four static schemes: Cantilever, Simply-Supported, Clamped-Pinned and Clamped-Clamped nanobeams. The outcomes are presented and discussed, highlighting the normalized nonlocal natural frequencies for the second through fifth modes of vibration in each case under study. In particular, this study illustrates the central role of surface effects in the dynamic response of nanobeams, emphasizing the importance of considering them. Furthermore, the parametric analysis reveals that the dynamic response is influenced by the combined effects of the nonlocal parameter, the material gradient index, the shapes of the cross-sections considered, as well as the static scheme analyzed.

Revealing incommensurability between device-independent randomness, nonlocality, and entanglement using Hardy and Hardy-type relations

A comprehensive treatment of the quantification of randomness certified device-independently by using the Hardy and Cabello-Liang-Li (CLL) nonlocality relations is provided in the two parties-two measurements per party-two outcomes per measurement (2-2-2) scenario. For the Hardy nonlocality, it is revealed that for a given amount of nonlocality signified by a particular non-zero value of the Hardy parameter, the amount of Hardy-certifiable randomness is not unique, unlike the way the amount of certifiable randomness is related to the CHSH nonlocality. This is because any specified non-maximal value of Hardy nonlocality parameter characterises a set of quantum extremal distributions. Then this leads to a range of certifiable amounts of randomness corresponding to a given Hardy parameter. On the other hand, for a given amount of CLL-nonlocality, the certifiable randomness is unique, similar to that for the CHSH nonlocality. Furthermore, the tightness of our analytical treatment evaluating the respective guaranteed bounds for the Hardy and CLL relations is demonstrated by their exact agreement with the Semi-Definite-Programming based computed bounds. Interestingly, the analytically evaluated maximum achievable bounds of both Hardy and CLL-certified randomness have been found to be realisable for non-maximal values of the Hardy and CLL nonlocality parameters. In particular, we have shown that even close to the maximum 2 bits of CLL-certified randomness can be realised from non-maximally entangled pure two-qubit states corresponding to small values of the CLL nonlocal parameter. This, therefore, clearly illustrates the quantitative incommensurability between randomness, nonlocality and entanglement.

Nonlinear Vibration of Truncated Open Conical Nanoshells Under Harmonic Excitation

The nonlinear forced vibration behavior of truncated open conical nanoshells is investigated in this paper. Nonlocal elasticity theory has been employed to modify the size-dependent effect of micro/nanostructure. Von Karman nonlinear strains are used to consider the geometric nonlinearity of the nanoshells. Using Hamilton’s principle, the equations of motion and boundary conditions of truncated open conical nanoshells are derived. Galerkin method is used to solve the governing equations. Then, to determine the nonlinear forced vibration behavior of truncated open conical nanoshells, complex averaging and arc-length continuation methods are employed. Finally, the effect of nonlocal parameters, cone apex angle, the amplitude of harmonic excitation, structural damping coefficient, and geometrical parameters on the nonlinear frequency response of the truncated open conical nanoshells are discussed.

Nonlocal nonlinear higher-order finite element model for static bending of curved nanobeams including graphene platelets reinforcement

The aim of this work is concerned with the nonlocal nonlinear bending characteristics of non-classical isotropic and composite curved beams based on graphene platelets reinforcement, viz., nano size/micro beams. The size-dependant effect prominent in micro/nanobeams is incorporated in the formulation based on the nonlocal theory using size-dependent continuum approach. The proposed structural model includes both moderately large displacement and rotations, respectively. The system governing equations are established in terms of displacement functions using the principle of virtual work statements. A three-noded shear deformable curved beam finite element using a higher-order sinusoidal function based beam theory is employed; the solutions are obtained by adopting direct iterative procedure. The efficacy of the model is tested against the analytical studies available for the nano-size beams. A detailed analysis is made to highlight the influence of various design variables like thickness ratio, curvature of beam, nonlocal parameter, and the support conditions on the nonlinear bending behavior of curved nano/micro-size beams.

Gravitational Influence on a Nonlocal Thermoelastic Solid with a Heat Source via L–S Theory

PurposeThe purpose is to obtain precise expressions of physical fields using the appropriate non-dimensional variables and normal mode analysis.MethodsBased on the Lord–Shulman (L-S) theory and taking into account gravitational influences as well as temperature-dependent features, the fundamental equations for a nonlocal thermoelastic solid are developed.ResultsWhen a nonlocal thermoelastic media is swapped out for a thermoelastic one, this approach still holds true. Comparisons are done between the outcomes obtained and those expected for various nonlocal parameter values and for an empirical material constant. Additionally, comparisons are done between the outcomes for various gravity field values.ConclusionThe nonlocal parameter plays a big part in how the physical fields are distributed. The distributions of the physical fields are significantly influenced by the gravity field.

The effect of the viscoelastic support and GRPL-reinforced foam material on the thermomechanical vibration response of piezomagnetic sandwich nanosensor plates

This paper investigates the vibration characteristics of a sandwich nanosensor plate composed of piezoelectric materials, specifically barium and cobalt, in the upper and lower layers, and a core material consisting of either ceramic (silicon nitride) or metal (stainless steel) foams reinforced with graphene (GPRL). The study utilized the novel sinosoidal higher-order deformation theory and nonlocal strain gradient elasticity theory. The equations of motion for nanosensor sandwich graphene were derived using Hamilton's principle, considering the thermal, electroelastic, and magnetostrictive characteristics of the piezomagnetic surface plates. These equations were then solved using the Navier method. The core element of the sandwich nanosensor plate can be represented using three distinct foam variants: a uniform foam model, as well as two symmetric foam models. The investigation focused on analyzing the dimensionless fundamental natural frequencies of the sandwich nanosensor plate. This analysis considered the influence of three distinct foam types, the volumetric graphene ratio, temperature variation, nonlocal parameters, porosity ratio, electric and magnetic potential, as well as spring and shear viscoelastic support. Furthermore, an analysis was conducted on the impact of the metal and ceramic composition of the central section of the sandwich nanosensor plate on its dimensionless fundamental natural frequencies. In this context, the use of ceramic as the central material results in a mean enhancement of 33% in the fundamental natural frequencies. In contrast, the incorporation of graphene into the core material results in an average enhancement of 27%. The thermomechanical vibration behavior of the nanosensor plate reveals that the presence of graphene-supported foam and a viscoelastic support structure in the core layer leads to an increase in thermal resistance. This increase is dependent on factors such as the ratio of graphene, porosity ratio of the foam, and parameters of the viscoelastic support. Metal foam or ceramic foam has been found to enhance thermal resistance when compared to solid metal or ceramic core materials. The analysis results showed that it is important to take into account the temperature-dependent thermal properties of barium and cobalt, which are piezo-electromagnetic materials, and the core layer materials ceramics and metal, as well as the graphene used to strengthen the core. The research is anticipated to generate valuable findings regarding the advancement and utilization of nanosensors, transducers, and nano-electromechanical systems engineered for operation in high-temperature environments.

Surface effects on wave propagation in piezoelectric–piezomagnetic loosely bonded bilayer system using nonlocal theory of elasticity

This study investigates nonlocal and surface effects on the dispersion behaviors of Shear horizontal (SH) waves in piezoelectric(PE)-piezomagnetic(PM) bilayer systems. The interface between these two layers is imperfectly bonded. The general governing equations are derived from the nonlocal magnetoelectroelastic (MEE) theory by adding an inherent length. The G-M model and generalized Young-Laplace equations have been used to incorporate surface effects into the boundary conditions of the bilayer systems. The closed-form dispersion equation is obtained analytically for electrically open and magnetically short conditions. Numerical solutions are utilized to investigate the effects of nonlocal scale parameters and surface parameters on SH surface wave propagation. Contrary to the results of classical theory, the coupling effects of nonlocal small-scale and surface piezoelectricity are more significant than individual effects. Also, it has been observed that the imperfectness parameter across the interface and the thickness ratio of the bilayer significantly affect the phase velocity. Moreover, 2D and 3D plots of the mode shapes of field variables for the propagation of SH waves are presented graphically. These results are validated by conducting analyses excluding nonlocal effects. This allows us to isolate the specific impact of surface effects in the piezoelectric–piezomagnetic bilayer system, drawing connections to existing results and enhancing the robustness of our findings. This study provides valuable insights into complex wave dynamics, helping to optimize the performance and functionality of such smart composites in various engineering applications.

Twice hidden string order and competing phases in the spin-1/2 Kitaev–Gamma ladder

Finding the Kitaev spin liquid in candidate materials involves understanding the entire phase diagram, including other allowed interactions. One of these interactions, called the Gamma (Γ) interaction, causes magnetic frustration and its interplay with the Kitaev (K) interaction is crucial to comprehend Kitaev materials. Due to the complexity of the combined KΓ model, quasi-one-dimensional models have been investigated. While several disordered phases are found in the 2-leg ladder, the nature of the phases are yet to be determined. Here we focus on the disordered phase near the antiferromagnetic Γ limit (denoted by AΓ phase) next to the ferromagnetic Kitaev phase. We report a distinct non-local string order parameter characterizing the AΓ phase, different from the string order parameter in the Kitaev phase. This string order parameter becomes evident only after two unitary transformation, referred to as a twice hidden string order parameter. The related entanglement spectrum, edge states, magnetic field responses, and the symmetry protecting the phase are presented, and its relevance to the two-dimensional Kitaev materials is discussed. Two newly identified disordered phases in the phase diagram of KΓ ladder is also reported.

Reflection phenomena of plane wave at a nonlocal monoclinic micropolar generalized thermoelastic half-space

In this study, we examined the reflection phenomena of plane wave occurring at the thermally insulated and stress-free surface of a nonlocal monoclinic micropolar generalized thermoelastic half-space. We have derived the reflection coefficients, phase velocities, and energy ratios of all the reflected waves. We explored the variation of phase velocity and reflection coefficients in presence and absence of nonlocal parameter against incident angle under LS and GL theory. The variation of energy ratios against incident angle in presence of nonlocal parameter is also obtained.

Scale-dependent torsional frequency analysis of right triangle anisotropic advanced composite microscale rods

Despite several theoretical investigations on the torsional dynamic behavior of non-circular micro/nanorods, the torsional behavior of right triangle cross-section is still unevaluated. Therefore, Timoshenko-Gere theory in conjunction with nonlocal strain gradient theory is developed for modeling the scale-dependent torsional dynamic of right triangle microscale rods. Various anisotropic materials, i.e. hexagonal, trigonal, triclinic, and monoclinic materials are regarded as the constituent material of microscale rods. The shear stress function is developed for right triangle shape and according to the calculated shear stress function, the warping function of right triangle shape is obtained. The nonlocal governing equation of the torsional dynamic of anisotropic microrods is obtained with the help of the energy approach and solved using an analytical method by regarding two different boundary conditions. The accuracy of the proposed model is validated with recent similar investigations. Because of the lack of mechanical research on right triangle microrods, the proposed methodology was validated with equilateral triangle nanowire reported in the literature. Eventually, the various remarkable variants’ effects on change of scale-dependent torsional frequency are assessed comprehensively. It is found that hexagonal and triclinic materials have the largest and smallest values of frequency. Also, nonlocal parameter, b/h ratio play a decreasing role and length scale parameters and mode number plays an increasing role.

Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method

This study investigates the free vibration behavior of a double cracked nanobeam composed of bi-directional functionally graded material. The analysis incorporates Eringen’s nonlocal elasticity theory and the Euler–Bernoulli theory. The material properties are considered to vary in both the thickness and length directions. The cracked nanobeam is modeled as a series of interconnected sub-beams, with rotational springs placed at the cracked sections. This modeling approach accounts for the discontinuities in rotational displacement resulting from bending, which is directly related to the bending moment transmitted by the cracked section. The problem is solved using the differential quadrature method, which approximates the derivatives of the field quantities by employing a weighted linear sum of the nodal values. By doing so, the problem is transformed into a linear algebraic system. Various supporting cases are examined, and a parametric study is conducted to analyze the impact of the axial and transverse gradient indices, nonlocal parameter, and crack severity on the obtained results.

Quantitative De Giorgi methods in kinetic theory for non-local operators

We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permits to quantitatively prove the Intermediate Value Lemma for the full range of non-locality parameter s∈(0,1). Our results recover the results from Imbert and Silvestre, The weak Harnack inequality for the Boltzmann equation without cut-off, 2020. The paper is self-contained.

Three-to-one internal resonances of stepped nanobeam of nonlinearity

Abstract In this study, vibrations of stepped nanobeams were investigated according to Eringen’s nonlocal elasticity theory. Multi-time scale method, which is one of the perturbation methods, has been applied to solve dimensionless state equations. The solution is considered in two steps. First-order terms obtained from the perturbation expansion formed the linear problem in the first step. In the second step, the solution of the second order of the perturbation expansion was made and nonlinear terms emerged as corrections to the linear problem from this solution. The main issue that the study wants to emphasize is the examination of the mechanical effects of the steps, which are discontinuities encountered at the nanoscale, on the system. For this purpose, while the findings of the research were obtained, various nonlocal parameter values were obtained to capture the nano-scale effect, and frequency-response and nonlinear frequency-amplitude curves corresponding to the 1st Mode values of the beam for different step ratios and step locations were obtained to capture the step effect. One of the important features of the nonlinear system is the formation of internal resonance between the modes of the system. How this situation affects the characteristics of the system has also been examined and results have been given by graphs. The obtained data show that taking into account the nanoscale step is essential for the accuracy and sensitivity of many nanostructures such as sensors, actuators, biostructures, switches, etc. that are likely to be produced at the nanoscale in practice.

A Hybrid ANN Multiaxial Fatigue Model for the Assessment of Fretting Fatigue under Variable Amplitude Shear Loading.

To foresee the life of fretting fatigue with variable shear amplitude loading, a hybrid model incorporating non-local multiaxial fatigue parameters and artificial neural networks (ANN) in conjunction with cumulative damage models has been proposed. The model has been developed based on equivalent stress parameters associated with crack nucleation and Miner's cumulative damage rule-inspired models, enabling the assessment of the impact of variable amplitude loading. To validate the models, fretting fatigue tests conducted under variable shear loading amplitude are employed to compare the predictions of four different models. The results demonstrate that while all models provide satisfactory estimates falling within the two-band limit, the hybrid model combining two ANN models outperforms the others and emerges as the most effective in predicting fretting fatigue life under these conditions. The proposed methodology effectively addresses the inherent complexities of fretting fatigue under variable amplitude stress, while also examining the influence of load block order on material behavior. Additionally, these types of fatigue ANN models have been demonstrating a strong capacity for generalization, making them highly promising for future industrial applications.

A novel model of nonlocal photoacoustic and plasmaelastic heated by laser pulsed excitation of nanoscale semiconductor medium

The study takes into account the diffusion of photo-excited carriers in the presence of a laser pulse and theoretically investigates photoacoustic wave propagation in the thermoelastic domain. In a nonlocality medium, the phenomena of thermomechanical and acoustic wave interaction are considered. Thermoelasticity, photothermal, and photoacoustic theories provide the controlling formulas. Photoacoustic waves are not dependent on electron–phonon or electron–hole thermalization processes; rather, they are produced by thermoelastic stress resulting from the temperature increase induced by the laser. The optical, elastic, and thermoelastic characteristics of nanoscale semiconductor materials are taken into account and photoacoustic signals are predicted by solving a thermal diffusion issue and a thermoelastic problem in combination. The mathematical model can be solved using the harmonic wave approach. By obtaining numerical solutions, all the physical fields of the physical domain, such as thermal, acoustic, mechanical, and carrier density diffusion, as well as displacements and temperatures, can be derived. The influences of nonlocal parameters, thermal delay, and laser pulse effect are investigated and compared using two- and three-dimensional visual representations, corresponding to two-dimensions and three-dimensions domains, respectively.

Wave propagation analysis in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory

The purpose of this research is to study the propagation of surface waves in transversely isotropic piezoelastic medium based on nonlocal strain gradient theory. A characteristics equation for the existence of surface waves is discussed. This equation could be easily reduced to the ones of the gradient strain theory, nonlocal theory, and classical theory. It has also been concluded that there exist cut-off frequency for the wave propagating in size-dependent materials based on the nonlocal strain gradient theory. The dispersion equation which surface wave speed satisfies is derived from the free traction condition on the surface of half-space with consideration of electrically open circuit conditions. The effect of the nonlocal parameter, the strain gradient parameter on the existence of surface waves as well as the Rayleigh wave propagation is illustrated through some numerical examples.

Nonlocal dual-phase-lag thermoelastic damping analysis in functionally graded sandwich microbeam resonators utilizing the modified coupled stress theory

Functionally graded (FG) sandwich structures stand as one of the most representative composite structures owing to the thermal resistance and the energy absorption property in non-unfiorm thermal environment. Additionally, accurately estimating thermoelastic damping (TED) is of great importance for the design of high-performance micro/nano-resonators. Nevertheless, the classical TED models fail on the micro/nano-scale structures due to without considering the influences of the spatial size-dependent effects related to heat transfer and elastic deformation. The nonlocal heat conduction model and modified coupled stress theory are responsible for the size-dependent effects. To address this issue, present study aims to conduct the size-dependent TED model of FG sandwich microbeam resonators for TED analysis by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are formulated, and then, the analytical solution is solved by complex frequency method. Exact and closed-form expressions for TED can be obtained through the complex frequency method. The results are validated, and the parameter effects of the nonlocal thermal parameter, the material length-scale parameter, the power-law index and the vibration modes on the TED are analyzed. The results show that the energy dissipation can be reduced by the size-dependent effects resulting in improving the quality factor of microstructures. It is expected that these results may provide a theoretical basis for predicating TED in the design of FG sandwich micro/nano-resonators with high quality factor in extreme heat transfer environment.

Nonlinear Vibration of Function Graded Magneto-electro-elastic Microplates using Nonlocal Stress Theory

This work presents an analysis of nonlinear vibration in Function Graded Magneto-Electro-Elastic (FG-MEE) plates subjected to mechanical, electrical, and magnetic loads using the nonlocal stress theory approach. In this study two types of MEE plates, namely BaTiO3 and CoFe2O4 were considered. The basic equations are derived using classical plate theory with nonlocal stress theory and are solved using the Galerkin method and Runge-Kutta method. We investigated the effects of nonlocal parameters, materials, and geometrical characteristics on the natural frequencies and nonlinear vibration of the FG-MEE microplates.
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Numerical solutions of nonlocal heat conduction technique in tumor thermal therapy

The heat transport that takes place in living tissue during magnetic tumor hyperthermia is described in this study using the nonlocal bioheat model in spherical coordinates. In magnetic fluid hyperthermia, it is crucial to regulate the therapeutic temperature. This paper suggests a hybrid numerical approach that employs the Laplace transforms, change of variables, and modified discretization techniques, coupled with nonlocal hyperbolic shape function, to tackle the present problem. This study investigates the impacts of nonlocal parameter and the disparity in thermophysical properties between diseased and healthy tissue. A graph is displayed to represent the numerical temperature results. The validity of the numerical findings is demonstrated by comparing them with the results reported in previous literature.

Constraints on non-local gravity from binary pulsars gravitational emission

Non-local theories of gravity are considered extended theories of gravity, meaning that when the non-local terms are canceled out, the limit of General Relativity (GR) is obtained. Several reasons have led us to consider this theory with increasing interest, but primarily non-locality emerges in a natural way as a ‘side’ effect of the introduction of quantum corrections to GR, the purpose of which was to cure the singularity problem, both at astrophysical and cosmological level. In this paper we studied a peculiar case of the so called Deser-Woodard theory consisting in the addition of a non-local term of the form R□−1R to the Hilbert-Einstein lagrangian, where R is the Ricci scalar, and derived, for the first time, constraints on the dimensionaless non-local parameter A by exploiting the predicted gravitational wave emission in three binary pulsars, namely PSR J1012+5307, PSR J0348+0432 and PSR J1738+0333. We discovered that the instantaneous flux strongly depends on A and that the best constraints (0.12<A<0.16) come from PSR J1012+5307, for which the GR prediction is outside the observational ranges. However, since for PSR J1012+5307 scintillation is suspected, as emerged in a recent census by LOFAR corruptions in pulsar timing could be hidden. We finally comment on the usability and reliability of this type of test for extended theories of gravity.