scholarly journals Small length scale coefficient for Eringen’s and lattice-based continualized nonlocal circular arches in buckling and vibration

2017 ◽  
Vol 165 ◽  
pp. 148-159 ◽  
Author(s):  
H. Zhang ◽  
C.M. Wang ◽  
N. Challamel
Keyword(s):  
Length Scale ◽  
Small Length ◽  
Small Length Scale ◽  
Scale Coefficient

Nonlocal Approaches for the Vibration of Lattice Plates Including Both Shear and Bending Interactions

2018 ◽  
Vol 18 (07) ◽  
pp. 1850094 ◽  
Author(s):  
F. Hache ◽  
N. Challamel ◽  
I. Elishakoff
Keyword(s):  
Natural Frequencies ◽  
Scale Effects ◽  
Dynamical Behavior ◽  
Mindlin Plate ◽  
Length Scale ◽  
Small Length ◽  
Simply Supported ◽  
Small Length Scale ◽  
Plate Models ◽  
Scale Coefficient

The present study investigates the dynamical behavior of lattice plates, including both bending and shear interactions. The exact natural frequencies of this lattice plate are calculated for simply supported boundary conditions. These exact solutions are compared with some continuous nonlocal plate solutions that account for some scale effects due to the lattice spacing. Two continualized and one phenomenological nonlocal UflyandMindlin plate models that take into account both the rotary inertia and the shear effects are developed for capturing the small length scale effect of microstructured (or lattice) thick plates by associating the small length scale coefficient introduced in the nonlocal approach to some length scale coefficients given in a Taylor or a rational series expansion. The nonlocal phenomenological model constitutes the stress gradient Eringen’s model applied at the plate scale. The continualization process constructs continuous equation from the one of the discrete lattice models. The governing partial differential equations are solved in displacement for each nonlocal plate model. An exact analytical vibration solution is obtained for the natural frequencies of the simply supported rectangular nonlocal plate. As expected, it is found that the continualized models lead to a constant small length scale coefficient, whereas for the phenomenological nonlocal approaches, the coefficient, calibrated with respect to the element size of the microstructured plate, is structure-dependent. Moreover, comparing the natural frequencies of the continuous models with the exact discrete one, it is concluded that the continualized models provide much more accurate results than the nonlocal Uflyand–Mindlin plate models.

scholarly journals Eringen’s small length scale coefficient for vibration of axially loaded nonlocal Euler beams with elastic end restraints

2017 ◽  
Vol 1 (2) ◽  
Author(s):  
C. M. Wang ◽  
H. Zhang ◽  
N. Challamel ◽  
W. H. Duan
Keyword(s):  
Length Scale ◽  
Small Length ◽  
Small Length Scale ◽  
Axially Loaded ◽  
Scale Coefficient

AbstractThis paper presents the calibration of Eringen’s small length scale coefficient

Visualization of buoyancy opposing flow structures in a small length scale fluidic junction

2005 ◽  
Vol 8 (4) ◽  
pp. 288-288 ◽  
Author(s):  
P. A. Walsh ◽  
M. R. D. Davies ◽  
T. Dalton
Keyword(s):  
Flow Structures ◽  
Length Scale ◽  
Small Length ◽  
Small Length Scale

Small Length-Scale Analysis of Transport Phenomena in Oil-Wells Formation with Drilling Fluid Losses

2009 ◽  
Vol 27 (3) ◽  
pp. 345-356 ◽  
Author(s):  
G. Espinosa-Paredes ◽  
R. Vázquez-Rodriguez ◽  
R. Ramos-Alcantara ◽  
R. Varela-Ham ◽  
H. Romero-Paredes ◽  
...  
Keyword(s):  
Drilling Fluid ◽  
Transport Phenomena ◽  
Oil Wells ◽  
Length Scale ◽  
Scale Analysis ◽  
Small Length ◽  
Small Length Scale ◽  
Fluid Losses
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