Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

scholarly journals Surface Effects on the Vibration and Buckling of Double-Nanobeam-Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Dong-Hui Wang ◽  
Gang-Feng Wang
Keyword(s):  
Natural Frequency ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Nanoelectromechanical Systems ◽  
Beam Model ◽  
Cross Sectional ◽  
Axial Buckling ◽  
Cross Sectional Size ◽  
Euler Bernoulli Beam ◽  
Deformation Modes

Surface effects on the transverse vibration and axial buckling of double-nanobeam-system (DNBS) are examined based on a refined Euler-Bernoulli beam model. For three typical deformation modes of DNBS, we derive the natural frequency and critical axial load accounting for both surface elasticity and residual surface tension, respectively. It is found that surface effects get quite important when the cross-sectional size of beams shrinks to nanometers. No matter for vibration or axial buckling, surface effects are just the same in three deformation modes and usually enhance the natural frequency and critical load. However, the interaction between beams is clearly distinct in different deformation modes. This study might be helpful for the design of nano-optomechanical systems and nanoelectromechanical systems.

scholarly journals Static analysis of tall buildings based on Timoshenko beam theory

2019 ◽  
Vol 11 (4) ◽  
pp. 455-461
Author(s):  
Seyed Mozafar Davari ◽  
Mohsen Malekinejad ◽  
Reza Rahgozar
Keyword(s):  
Numerical Models ◽  
Lateral Displacement ◽  
Tall Buildings ◽  
Beam Theory ◽  
Flexural Behavior ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Lag Effects ◽  
Euler Bernoulli Beam ◽  
The Continuum

Abstract In this paper, the continuum model, which is known as Kwan model, has been presented for the analysis of tall buildings that have been as an appropriate approximation of the overall behavior of the structure. Tall building was modeled as a cantilever beam and analyzed with the assumption of flexural behavior based on Euler–Bernoulli Beam Theory, then the displacement of floors was calculated. o consider the shear lag effects in the overall displacement of the structure, Timoshenko’s beam model has been considered and related relations were extracted. The lateral displacement formulas obtained and calculated for the framed tube system modeled by Kwan’s method. To verify the results, numerical models were created in software (ETABS) and statically were analyzed for lateral loading. Finally the results were compared with those obtained by computer analysis and the corresponding diagrams were presented. At the end, the shape factor formula has been developed to improve the results of the Timoshenko’s theory.

On the forced vibration of carbon nanotubes via a non-local Euler—Bernoulli beam model

2010 ◽  
Vol 224 (2) ◽  
pp. 497-503 ◽  
Author(s):  
P Karaoglu ◽  
M Aydogdu
Keyword(s):  
Carbon Nanotubes ◽  
Forced Vibration ◽  
Beam Theory ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
Non Local ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Walled Cnts

This article studies the forced vibration of the carbon nanotubes (CNTs) using the local and the non-local Euler—Bernoulli beam theory. Amplitude ratios for the local and the non-local Euler—Bernoulli beam models are given for single- and double-walled CNTs. It is found that the non-local models give higher amplitudes when compared with the local Euler—Bernoulli beam models. The non-local Euler—Bernoulli beam model predicts lower resonance frequencies.

Nonlinear Free Vibration of Nanobeams With Surface Effects Considerations

2011 ◽  
Author(s):  
Ali Fallah ◽  
Keikhosrow Firoozbakhsh ◽  
Mohammad Hossein Kahrobaiyan ◽  
Abdolreza Pasharavesh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Partial Differential Equation ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Nonlinear Ordinary Differential Equation ◽  
Euler Bernoulli Beam ◽  
Analytical Expressions ◽  
Equations Of Motions

In this paper, simple analytical expressions are presented for geometrically non-linear vibration analysis of thin nanobeams with both simply supported and clamped boundary conditions. Gurtin-Murdoch surface elasticity together with Euler-Bernoulli beam theory is used to obtain the governing equations of motions of the nanobeam with surface effects consideration. The governing nonlinear partial differential equation is reduced to a single nonlinear ordinary differential equation using Galerkin technique. He’s variational approach is employed to obtain analytical solution for the resulted nonlinear governing equation. The effects of different parameters such as vibration amplitude, boundary conditions, and beam dimensions on the natural frequencies of nanobeams are investigated and results are presented for future studies.

Damping Improvement in Layered and Jointed Beams by Finite Element Analysis

2012 ◽  
Vol 505 ◽  
pp. 501-505 ◽  
Author(s):  
D.N. Thatoi ◽  
R.C. Mohanty ◽  
A.K. Acharya ◽  
B.K. Nanda
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Element Model ◽  
Damping Capacity ◽  
Bernoulli Beam ◽  
Element Analysis ◽  
Linear Elastic ◽  
Mass Matrices ◽  
Euler Bernoulli Beam

Damping in built-up structures is produced by the energy dissipation due to micro-slip along the frictional interfaces. A finite element model of the linear elastic system has been formulated using the Euler-Bernoulli beam theory to investigate the damping phenomena in riveted connections. The discrete element system having two degrees of freedom per node representing v and has been used for the analysis. The generalized stiffness and mass matrices for this element has been derived. Extensive experiments have been conducted for the validation of the analysis. From this study, it is established that the damping capacity increases and the natural frequency decreases due to the joint effects.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

scholarly journals Numerical Solution of Bending of the Beam with Given Friction

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 898
Author(s):  
Michaela Bobková ◽  
Lukáš Pospíšil
Keyword(s):  
Sliding Friction ◽  
Quadratic Function ◽  
Building Construction ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Sustainable Building ◽  
Construction Design ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Fixed Beam

We are interested in a contact problem for a thin fixed beam with an internal point obstacle with possible rotation and shift depending on a given swivel and sliding friction. This problem belongs to the most basic practical problems in, for instance, the contact mechanics in the sustainable building construction design. The analysis and the practical solution plays a crucial role in the process and cannot be ignored. In this paper, we consider the classical Euler–Bernoulli beam model, which we formulate, analyze, and numerically solve. The objective function of the corresponding optimization problem for finding the coefficients in the finite element basis combines a quadratic function and an additional non-differentiable part with absolute values representing the influence of considered friction. We present two basic algorithms for the solution: the regularized primal solution, where the non-differentiable part is approximated, and the dual formulation. We discuss the disadvantages of the methods on the solution of the academic benchmarks.

Fatigue Life Prediction of Drill-String Subjected to Random Loadings

2014 ◽  
Author(s):  
Jiahao Zheng ◽  
Hongyuan Qiu ◽  
Jianming Yang ◽  
Stephen Butt
Keyword(s):  
Fatigue Life ◽  
Time History ◽  
Beam Theory ◽  
Drill String ◽  
Finite Element Models ◽  
Bernoulli Beam ◽  
Stress Cycles ◽  
Rainflow Counting ◽  
Euler Bernoulli Beam ◽  
Random Nature

Based on linear damage accumulation law, this paper investigates the fatigue problem of drill-strings in time domain. Rainflow algorithms are developed to count the stress cycles. The stress within the drill-string is calculated with finite element models which is developed using Euler-Bernoulli beam theory. Both deterministic and random excitations to the drill-string system are taken into account. With this model, the stress time history in random nature at any location of the drill-string can be obtained by solving the random dynamic model of the drill-string. Then the random time history is analyzed using rainflow counting method. The fatigue life of the drill-string under both deterministic and random excitations can therefore be predicted.

Experimental and Theoretical Study of a Dual-Beam Piezoelectric Energy Harvester With Misaligned Magnets

2018 ◽  
Author(s):  
Wei-Jiun Su ◽  
Hsuan-Chen Lu
Keyword(s):  
Energy Harvester ◽  
Theoretical Study ◽  
Beam Theory ◽  
Main Beam ◽  
Bernoulli Beam ◽  
Potential Wells ◽  
Piezoelectric Energy ◽  
Dual Beam ◽  
Frequency Sweeps ◽  
Euler Bernoulli Beam

In this study, a dual-beam piezoelectric energy harvester is proposed. This harvester consists of a main beam and an auxiliary beam with a pair of magnets attached to couple their motions. The potential energy of the system is modeled to understand the influence of the potential wells on the dynamics of the harvester. It is noted that the alignment of the magnets significantly influences the potential wells. A theoretical model of the harvester is developed based on the Euler-Bernoulli beam theory. Frequency sweeps are conducted experimentally and numerically to study the dynamics of the harvester. It is shown that the dual-beam harvester can exhibit hardening effect with different configurations of magnet alignments in frequency sweeps. The performance of the harvester can be improved with proper placement of the magnets.

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