Size-dependent buckling analysis of Euler–Bernoulli nanobeam under non-uniform concentration

Li, Chenlin; Tian, Xiaogeng; He, Tianhu

doi:10.1007/s00419-020-01700-8

Cited by 12 publications

(6 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Nonlocal spatial influences [37] have been extensively examined in various domains. These include the realm of thermal conductivity within nanoscale systems [34,10,23], as well as in metals exposed to ultra-brief laser irradiation, spanning picoseconds and femtoseconds [39,38,31,27,45]. Furthermore, nonlocal spatial effects have garnered attention in contexts such as biological systems, cf.…”

Section: Introductionmentioning

confidence: 99%

A problem with periodic boundary conditions for the non-Fourier heat equation

Takhirov

2023

GJOM

View full text Add to dashboard Cite

All diffusion equations are based on the infinite velocity of potential fields, which leads to well-known paradoxes. Consequently, in non-stationary processes, the evolution of these quantities do not completely obey the above equations due to the lack of parameters in them that take into account the finite rate of potential growth.In the heat conduction theory, numerous generalizations of the Fourier law are used as a remedy for these issues. The article gives a brief overview of generalizations of the Fourier law. Some mathematical issues of well-posed boundary value problems for the Guyer-Krumhansl model are discussed. As an application, a boundary value problem for a general quasilinear equation with periodic boundary conditions is considered. Schauder-type a priori estimates are established and the uniqueness of the solution is proved.

show abstract

Section: Introductionmentioning

confidence: 99%

A problem with periodic boundary conditions for the non-Fourier heat equation

Takhirov

2023

GJOM

View full text Add to dashboard Cite

show abstract

“…The interest is largely motivated by technological needs such as thermal management in microelectronics and the ultra-fast laser processing of advanced metamaterials [1,4], i.e., artificial materials and media of designed properties, such as layered correlated materials [5,6]. Moreover, the heat transport at ultrashort space and time scales leads to unusual non-Fourier phenomena such as wavelike temperature propagation [4][5][6]12,13], size [14,15] and distance [15] dependent thermal conductivity, and boundary temperature jumps [1,14,15], which have raised an extensive body of literature concerning different conceptual questions of these phenomena [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. The problem is that when the characteristic length of the process is of the order of the mean free path (MFP) of energy carriers and/or the characteristic time scale of the process is of the order of the mean free time (MFT) of energy carriers, the thermal dynamics occur under far from local equilibrium conductions and cannot be described by classical Fourier law based on the local equilibrium assumption [31].…”

Section: Introductionmentioning

confidence: 99%

“…However, the HHCE cannot be used to describe heat conduction in nanosized systems where the nonlocal space effects [14][15][16][17][18]21,22,[26][27][28]31] and ballistic component of heat transport [14][15][16][17]19,23,24] lead to non-Fourier phenomena such as size-dependent thermal conductivity [1,9,[14][15][16][17] and boundary temperature jumps [14][15][16][17]19], which can be observed even in the steady-state [14][15][16][17]. Note that the HHCE in the steady-state reduces to the classical heat conduction equation of the parabolic type, and consequently, cannot describe these effects.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlocal space effects [1,7,26,31] have been extensively studied in the context of heat conduction in nanosized systems [10,11,[14][15][16][17][18][21][22][23][24]28], in metals under ultrashort (pico-and femtosecond) laser irradiation [4,[31][32][33][34][38][39][40][41][42][43][44][45][46][47], and in biological [48][49][50] and heterogeneous systems [51][52][53]. Comprehensive reviews of different nonlocal heat conduction theories are presented in [41,42].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

Соболев

Dai

2022

Materials

View full text Add to dashboard Cite

The non-Fourier effects, such as wave-like temperature propagation and boundary temperature jumps, arise in nanosized systems due to the multiple time and space scales nature of out-of-equilibrium heat transport. The relaxation to equilibrium occurs in successive time and space scales due to couplings between different excitations, whose relaxation times have different physical meanings and may differ significantly in magnitude. The out-of-equilibrium temperature evolution is described by a hierarchy of partial differential equations of a higher order, which includes both the diffusive and wave modes of heat transport. The critical conditions of transition from wave to diffusive modes are identified. We demonstrate that the answer to the question concerning which of these modes would be detected by experimental measurements may also depend on the accuracy of the experimental setup. Comparisons between the proposed approach and other non-Fourier models, such as the Guyer–Krumhansl and Jeffreys type, are carried out. The results presented here are expected to be useful for the theoretical and experimental treatment of non-Fourier effects and particularly heat wave phenomena in complex nanosized systems and metamaterials.

show abstract

“…Because it is difficult to solve the integrodifferential equations, a differential constitutive model proposed by Eringen in Eringen (1983) is widely used to analyze the size-dependent behaviors of structures (Ebrahimi and Barati, 2018; Ghadiri and Shafiei, 2017; Li et al, 2020a, 2020b Preethi et al, 2017; Raghu et al, 2020; Reddy, 2007; Srividhya et al, 2018; Vila et al, 2016). However, some paradoxes appear when solving the cantilever beam in the differential form of Eringen’s model.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of Euler–Bernoulli curved beams using two-phase nonlocal integral models

Zhang

Qing

2021

Journal of Vibration and Control

View full text Add to dashboard Cite

Eringen’s nonlocal elastic model has been widely applied to address the size-dependent response of micro-/nanostructures, which is observed in experimental tests and molecular dynamics simulation. However, several recent studies have pointed out that some inconsistent results appear while applying it in the analysis of bounded structures, which indicates that it is necessary to adopt other suitable models. In this work, both the well-posed strain-driven and stress-driven two-phase local/nonlocal integral models are used to study the size effect in the free vibration of Euler–Bernoulli curved beams. The governing equations of motion and the associated boundary conditions are derived on the basis of Hamilton’s principle. The two-phase nonlocal integral relation is transformed into an equivalent differential law with two constitutive boundary conditions. Using the generalized differential quadrature method, the governing equation in terms of displacements is solved numerically. The vibration frequencies of the beam under different boundary conditions are obtained and validated by comparing with those existing results. For all boundary conditions, the nonlocal related parameters of the two types of two-phase nonlocal strategies show consistent softening and stiffening effects on vibration response, respectively. Moreover, the effect of the curvature radius of the beam is also investigated.

show abstract

Size-dependent buckling analysis of Euler–Bernoulli nanobeam under non-uniform concentration

Cited by 12 publications

References 40 publications

A problem with periodic boundary conditions for the non-Fourier heat equation

A problem with periodic boundary conditions for the non-Fourier heat equation

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

Free vibration analysis of Euler–Bernoulli curved beams using two-phase nonlocal integral models

Contact Info

Product

Resources

About