scholarly journals Natural vibrations of nanostrips with cracks

2021 ◽  
Vol 25 (1) ◽  
pp. 87-105
Author(s):  
Mainul Hossain ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Material Behavior ◽  
Rotational Inertia ◽  
Natural Vibrations ◽  
Piecewise Constant ◽  
Theory Of Plates ◽  
Local Compliance

Employing the main equations of the theory of plates accounting for the rotational inertia the transverse vibrations of nanobeams and nanostrips are investigated. The nano strips under consideration have piecewise constant dimensions of cross sections. The nanosheets are weakened by cracks at re-entrant corners of steps. While the material behavior corresponds to the Eringen’s nonlocal theory of elasticity it is assumed that the cracks produce additional local compliance, which can be evaluated with the aid of the stress intensity factor at the cracktip. A numerical algorithm for determination of natural frequencies of nanosheets is developed.

scholarly journals Natural vibrations of stepped nanobeams with defects

2019 ◽  
Vol 23 (1) ◽  
pp. 143-158 ◽  
Author(s):  
Jaan Lellep ◽  
Artur Lenbaum
Keyword(s):  
Stress Intensity Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Vibration ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Natural Vibrations ◽  
Piecewise Constant ◽  
Local Compliance

Exact solutions for the transverse vibration of nanobeams based on the nonlocal theory of elasticity are presented. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with crack-like defects. It is assumed that the stationary cracks occur at the re-entrant corners of steps and that the mechanical behaviour of the nanomaterial can be modelled with the Eringen's nonlocal theory. The influence of cracks on the natural vibration is prescribed with the aid of additional local compliance at the weakened cross section. The local compliance is coupled with the stress intensity factor at the crack tip. A general algorithm for determination of eigenfrequencies is developed. It can be used in the case of an arbitrary finite number of steps and cracks.

scholarly journals Buckling of nanobeams and nanorods with cracks

2019 ◽  
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Piecewise Constant ◽  
Cracklike Defects ◽  
General Method

Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

scholarly journals Free vibration of rectangular nanoplate strips

2019 ◽  
Author(s):  
Jaan Lellep ◽  
Mainul Hossain
Keyword(s):  
Free Vibration ◽  
Cross Sections ◽  
Vibration Analysis ◽  
Theory Of Elasticity ◽  
Local Theory ◽  
Natural Vibrations ◽  
Size Dependent ◽  
Nano Structures ◽  
Non Local ◽  
Local Compliance

Natural vibrations of nanobeams and nanosheets are investigated with the help of nonlocal theories of elasticity. The vibration analysis is based on the size-dependent non-local theory of elasticity developed by A. C. Eringen. It is assumed that the nano-structures under consideration have rectangular cross sections with piece wise constant dimensions and that the nanoplates are weakened with defects. The influence of the crack on the vibration of the nanoplate is assessed with the aid of additional local compliance developed in previous papers. Numerical results are presented for one- and two-stepped nanoplates.

scholarly journals Stability of nanobeams and nanoplates with defects

2021 ◽  
Vol 25 (2) ◽  
pp. 221-238
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Critical Stress ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Physical Parameters ◽  
Axial Loads ◽  
Critical Buckling Load ◽  
Support Conditions ◽  
The Impact

The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.

Determination of Stress Distribution around Two Carbon Nonotubes Embedded in Infinite Metal Matrix Using Nonlocal Theory of Elasticity

2011 ◽  
Vol 110-116 ◽  
pp. 1696-1700
Author(s):  
Sina Amini Niaki ◽  
Reza Naghdabadi
Keyword(s):  
Stress Distribution ◽  
Hoop Stress ◽  
Potential Method ◽  
Nonlocal Theory ◽  
Complex Stress ◽  
Theory Of Elasticity ◽  
Reinforced Composites ◽  
Hoop Stresses ◽  
As Effects

Stress distribution in Carbon Nanotube (CNT) reinforced composites is studied using nonlocal theory of elasticity. Two nearby CNTs are modeled as two circular inclusions embedded in an infinite elastic medium, and classical stresses are obtained using the complex stress potential method. Nonlocal stresses are calculated using nonlocal integral elasticity equation. Effects of the distance between CNTs as well as effects of the nonlocal parameters on the stress distribution and stress concentration are studied. For unit normal stress at infinity, stress at the interface of the CNT and matrix increases from 0.1 for classical analysis to 0.85 for nonlocal analysis. Furthermore, when two CNTs approach to each other radial and hoop stresses across the interface increases. It is interesting that, results of the nonlocal and classical elasticity for the hoop stress are different completely.

Analysis of STEM micrographs of thick objects

1978 ◽  
Vol 36 (2) ◽  
pp. 106-107
Author(s):  
S. Golladay
Keyword(s):  
Inelastic Scattering ◽  
Multiple Scattering ◽  
Mass Distribution ◽  
Cross Sections ◽  
Phase Contrast ◽  
Image Point ◽  
Contrast Effects ◽  
Total Cross Sections ◽  
Elastic And Inelastic Scattering

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Preparation And elemental analysis of ancient fibers

1987 ◽  
Vol 45 ◽  
pp. 410-411
Author(s):  
Allen Angel ◽  
Kathryn A. Jakes
Keyword(s):  
Cross Sections ◽  
Physical Structure ◽  
Energy Dispersive ◽  
Archaeological Sites ◽  
X Ray ◽  
Long Term Storage ◽  
Backscattered Electron ◽  
Electron Imaging

Fabrics recovered from archaeological sites often are so badly degraded that fiber identification based on physical morphology is difficult. Although diagenetic changes may be viewed as destructive to factors necessary for the discernment of fiber information, changes occurring during any stage of a fiber's lifetime leave a record within the fiber's chemical and physical structure. These alterations may offer valuable clues to understanding the conditions of the fiber's growth, fiber preparation and fabric processing technology and conditions of burial or long term storage (1).Energy dispersive spectrometry has been reported to be suitable for determination of mordant treatment on historic fibers (2,3) and has been used to characterize metal wrapping of combination yarns (4,5). In this study, a technique is developed which provides fractured cross sections of fibers for x-ray analysis and elemental mapping. In addition, backscattered electron imaging (BSI) and energy dispersive x-ray microanalysis (EDS) are utilized to correlate elements to their distribution in fibers.

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

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