Determination of Transverse Amplitude of Microbeam Vibrating Accounting for Nonlinear Effects

2012 ◽  
Vol 446-449 ◽  
pp. 1190-1193
Author(s):  
Cheng Li ◽  
Wei Guo Huang
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Effects ◽  
Nonlocal Theory ◽  
Basic Element ◽  
Small Scale ◽  
Problem Model ◽  
Axial Tension ◽  
Small Scale Effect ◽  
Mechanical Devices

The nonlinear dynamics of a microbeam with initial axial tension is presented. The nonlocal theory with a small scale effect is applied to the problem model. Considering the axial protraction due to the transverse deformation of the microbeam, a nonlinear partial differential equation that governs the dynamic motion is derived. Explicit solution of transverse amplitude is obtained by the method of multiscale analysis. Both nonlinear and nonlocal effects are found to play significant roles in the vibration behaviors of a microbeam. The results may be helpful for the application and design of various micro-electronic-mechanical devices, where a microbeam acts as a basic element.

Computing Buckling Characteristics of Double-Layered Graphene Film Embedded in an Elastic Foundation

2019 ◽  
Vol 19 (06) ◽  
pp. 1950065
Author(s):  
Zhengtian Wu ◽  
Yang Zhang ◽  
Weicheng Ma
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Graphene Film ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Type Model ◽  
Classical Plate Theory ◽  
Buckling Behavior ◽  
Small Scale Effect ◽  
Simulation Results

Given the unique and extremely valuable properties, research has significantly focussed on graphene sheets (GSs). To premeditate the small-scale effect, the present work applies the nonlocal theory to study the buckling behavior of a double-layered GS (DLGS) embedded in an elastic foundation. To derive the equation, classical plate theory is adopted. For the elastic foundation, Pasternak-type model is used. In terms of buckling response, a meshless method is utilized to compute simulation results. Accordingly, we examine the effects of aspect ratio, geometry, boundary conditions and nonlocal parameters on the buckling responses of DLGSs.

NONLOCAL THEORY FOR BUCKLING OF NANOPLATES

2011 ◽  
Vol 11 (03) ◽  
pp. 411-429 ◽  
Author(s):  
S. C. PRADHAN ◽  
J. K. PHADIKAR
Keyword(s):  
Elasticity Theory ◽  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Plate Theory ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Theoretical Development ◽  
Small Scale ◽  
Classical Plate Theory ◽  
Small Scale Effect

Classical plate theory (CLPT) and first-order shear deformation plate theory (FSDT) of plates are reformulated using the nonlocal elasticity theory. Developed nonlocal plate theories have been applied to study buckling behavior of nanoplates. Nonlocal elasticity theory, unlike traditional elasticity theory introduces a length scale parameter into the formulation to take into account the discrete structure of the material to some extent. Both single-layered and multilayered nanoplates have been included in the analysis. Navier's approach has been used to obtain exact solutions for buckling loads for simply supported boundary conditions. Dependence of the small scale effect on various geometrical and material parameters has been investigated. Present study reveals the presence of significant small scale effect on the buckling response of nanoplates. The theoretical development and the numerical results presented in the present work are expected to promote the use of nonlocal theories for more accurate prediction of stability behavior of nanoplates and nanoshells.

A Nonlinear Approach for Dynamic Responses of a Nano-Beam Based on a Strain Gradient Nonlocal Theory

2014 ◽  
Vol 609-610 ◽  
pp. 1483-1488
Author(s):  
Cheng Li ◽  
Shuang Li
Keyword(s):  
Strain Gradient ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Continuum Theory ◽  
Nonlocal Theory ◽  
Dynamic Responses ◽  
Transverse Motion ◽  
Small Scale ◽  
Transverse Displacement ◽  
Nonlocal Continuum Theory

The transverse nonlinear vibration of a nanobeam fully clamped at both two ends was investigated using a strain gradient type of nonlocal continuum theory. The small scale effect was considered to the mechanical model at nanoscale. The axial elongation of the nanobeam was taken into account and the nonlinear partial differential equation governing the transverse motion was derived. Subsequently, a perturbation method was applied to the nonlinear governing equation. The dynamical responses of the nanobeam such as transverse displacement and resonant angular frequency were obtained and they were compared with those by a numerical method. The comparison indicated the validity of the present nonlinear model and the multiple-scales analysis method.

BUCKLING OF NANO-RINGS/ARCHES BASED ON NONLOCAL ELASTICITY

2012 ◽  
Vol 04 (03) ◽  
pp. 1250025 ◽  
Author(s):  
C. M. WANG ◽  
Y. XIANG ◽  
J. YANG ◽  
S. KITIPORNCHAI
Keyword(s):  
Scale Effect ◽  
Nonlocal Elasticity ◽  
Radial Pressure ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Mode Shapes ◽  
Small Scale ◽  
Small Scale Effect ◽  
Bifurcation Buckling

This paper is concerned with the bifurcation buckling of nano-rings and nano-arches where the allowance for small scale effect is catered for by using Eringen's nonlocal theory of elasticity. Exact buckling solutions for nano-rings and nano-arches under uniform radial pressure are derived and the influence of small scale effect on the buckling pressures and mode shapes is investigated. The new results presented will be useful to engineers who are designing nano-rings and nano-arches to be used in MEMS and NEMS devices.

Nonlocal Size Dependence of a Softness Nanobeam with Large Axial Tension under Various Boundary Conditions

2012 ◽  
Vol 490-495 ◽  
pp. 3226-3230
Author(s):  
Cheng Li ◽  
Wei Guo Huang
Keyword(s):  
Natural Frequency ◽  
Scale Parameter ◽  
Separation Of Variables ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Problem Model ◽  
Various Boundary Conditions ◽  
Size Dependent ◽  
Axial Tension ◽  
Dependent Theory

The transverse dynamical behaviors of softness Euler-Bernoulli nanobeams subjected to a biggish initial axial force based on nonlocal elasticity theory are investigated in this paper. The size-dependent theory is considered and a small intrinsic length scale parameter unavailable in classical continuum mechanics is adopted into the problem model as a size parameter. The linear partial differential governing equation is derived from the Newton’s second law and the ordinary equation and its dispersion relation are gained from by the method of separation of variables. Five sets of supporting conditions are presented respectively including simply supported, fully clamped, flexible fixed ends, sliding supports ends and completely free ends. Vibration frequencies are obtained approximately and correlations between the natural frequency and the dimensionless small scale parameter are also analyzed and discussed in detail. It shows that an increase in small scale parameter and dimensionless initial axial tension causes natural frequency to increase, while an increase in the dimensionless stiffness of nanostructures causes natural frequency to decrease, or the nanostructural bending stiffness is enhanced when nonlocal effects are considered.

scholarly journals A Perturbation Approach for Lateral Excited Vibrations of a Beam-like Viscoelastic Microstructure Using the Nonlocal Theory

2021 ◽  
Vol 12 (1) ◽  
pp. 40
Author(s):  
Cheng Li ◽  
Chengxiu Zhu ◽  
Suihan Sui ◽  
Jianwei Yan
Keyword(s):  
Lateral Displacement ◽  
Nonlocal Parameter ◽  
Nonlinear Partial Differential Equation ◽  
Excitation Amplitude ◽  
Nonlocal Theory ◽  
Harmonic Excitation ◽  
Small Scale ◽  
Perturbation Approach ◽  
Stress Theory ◽  
Excited Vibration

In this paper, we investigate the lateral vibration of fully clamped beam-like microstructures subjected to an external transverse harmonic excitation. Eringen’s nonlocal theory is applied, and the viscoelasticity of materials is considered. Hence, the small-scale effect and viscoelastic properties are adopted in the higher-order mathematical model. The classical stress and classical bending moments in mechanics of materials are unavailable when modeling a microstructure, and, accordingly, they are substituted for the corresponding effective nonlocal quantities proposed in the nonlocal stress theory. Owing to an axial elongation, the nonlinear partial differential equation that governs the lateral motion of beam-like viscoelastic microstructures is derived using a geometric, kinematical, and dynamic analysis. In the next step, the ordinary differential equations are obtained, and the time-dependent lateral displacement is determined via a perturbation method. The effects of external excitation amplitude on excited vibration are presented, and the relations between the nonlocal parameter, viscoelastic damping, detuning parameter, and the forced amplitude are discussed. Some dynamic phenomena in the excited vibration are revealed, and these have reference significance to the dynamic design and optimization of beam-like viscoelastic microstructures.

Tribology of rail bogie

2018 ◽  
Vol 77 (4) ◽  
pp. 230-240
Author(s):  
D. P. Markov
Keyword(s):  
Contact Fatigue ◽  
Basic Element ◽  
Difficult Problem ◽  
Railway Track ◽  
Rolling Stock ◽  
Kinematic Parameters ◽  
Approximate Estimation ◽  
Railway Bogie ◽  
Classical Calculation

Railway bogie is the basic element that determines the force, kinematic, power and other parameters of the rolling stock, and its movement in the railway track has not been studied enough. Classical calculation of the kinematic and dynamic parameters of the bogie's motion with the determination of the position of its center of rotation, the instantaneous axes of rotation of wheelsets, the magnitudes and directions of all forces present a difficult problem even in quasi-static theory. The paper shows a simplified method that allows one to explain, within the limits of one article, the main kinematic and force parameters of the bogie movement (installation angles, clearance between the wheel flanges and side surfaces of the rails), wear and contact damage to the wheels and rails. Tribology of the railway bogie is an important part of transport tribology, the foundation of the theory of wheel-rail tribosystem, without which it is impossible to understand the mechanisms of catastrophic wear, derailments, contact fatigue, cohesion of wheels and rails. In the article basic questions are considered, without which it is impossible to analyze the movement of the bogie: physical foundations of wheel movement along the rail, types of relative motion of contacting bodies, tribological characteristics linking the force and kinematic parameters of the bogie. Kinematics and dynamics of a two-wheeled bogie-rail bicycle are analyzed instead of a single wheel and a wheelset, which makes it clearer and easier to explain how and what forces act on the bogie and how they affect on its position in the rail track. To calculate the motion parameters of a four-wheeled bogie, it is represented as two two-wheeled, moving each on its own rail. Connections between them are replaced by moments with respect to the point of contact between the flange of the guide wheel and the rail. This approach made it possible to give an approximate estimation of the main kinematic and force parameters of the motion of an ideal bogie (without axes skewing) in curves, to understand how the corners of the bogie installation and the gaps between the flanges of the wheels and rails vary when moving with different speeds, how wear and contact injuries arise and to give recommendations for their assessment and elimination.

scholarly journals Metal artifacts in intraoperative O-arm CBCT scans

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Juha I. Peltonen ◽  
Touko Kaasalainen ◽  
Mika Kortesniemi
Keyword(s):  
Image Quality ◽  
Imaging Modality ◽  
Nonlinear Effects ◽  
Exposure Level ◽  
Metal Artifacts ◽  
Imaging Protocol ◽  
Metal Implants ◽  
Comprehensive Determination

Abstract Background Cone-beam computed tomography (CBCT) has become an increasingly important medical imaging modality in orthopedic operating rooms. Metal implants and related image artifacts create challenges for image quality optimization in CBCT. The purpose of this study was to develop a robust and quantitative method for the comprehensive determination of metal artifacts in novel CBCT applications. Methods The image quality of an O-arm CBCT device was assessed with an anthropomorphic pelvis phantom in the presence of metal implants. Three different kilovoltage and two different exposure settings were used to scan the phantom both with and without the presence of metal rods. Results The amount of metal artifact was related to the applied CBCT imaging protocol parameters. The size of the artifact was moderate with all imaging settings. The highest applied kilovoltage and exposure level distinctly increased artifact severity. Conclusions The developed method offers a practical and robust way to quantify metal artifacts in CBCT. Changes in imaging parameters may have nonlinear effects on image quality which are not anticipated based on physics.

Small-scale effect on the mechanical properties of metallic nanotubes

2012 ◽  
Vol 101 (9) ◽  
pp. 093109 ◽  
Author(s):  
Jin Zhang ◽  
Chengyuan Wang ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Mechanical Properties ◽  
Scale Effect ◽  
Small Scale ◽  
Small Scale Effect
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