Nonlinear longitudinal deformations of an elastic rod under the action of a non-stationary singular source

2020 ◽  
Vol 124 ◽  
pp. 103514
Author(s):  
Yu.A. Chirkunov
Keyword(s):  
Elastic Rod ◽  
Singular Source

Effects of the Fractional Laplacian Order on the Nonlocal Elastic Rod Response

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Giuseppina Autuori ◽  
Federico Cluni ◽  
Vittorio Gusella ◽  
Patrizia Pucci
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Coefficient Of Variation ◽  
Fractional Laplacian ◽  
Numerical Procedure ◽  
Elastic Rod ◽  
The Mean ◽  
Distributed Forces ◽  
Nonlinear Fashion

In this paper, we yield with a nonlocal elastic rod problem, widely studied in the last decades. The main purpose of the paper is to investigate the effects of the statistic variability of the fractional operator order s on the displacements u of the rod. The rod is supposed to be subjected to external distributed forces, and the displacement field u is obtained by means of numerical procedure. The attention is particularly focused on the parameter s, which influences the response in a nonlinear fashion. The effects of the uncertainty of s on the response at different locations of the rod are investigated by the Monte Carlo simulations. The results obtained highlight the importance of s in the probabilistic feature of the response. In particular, it is found that for a small coefficient of variation of s, the probability density function of the response has a unique well-identifiable mode. On the other hand, for a high coefficient of variation of s, the probability density function of the response decreases monotonically. Finally, the coefficient of variation and, to a small extent, the mean of the response tend to increase as the coefficient of variation of s increases.

scholarly journals The magneto-elastica : from self-buckling to self-assembly

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130609 ◽  
Author(s):  
Dominic Vella ◽  
Emmanuel du Pontavice ◽  
Cameron L. Hall ◽  
Alain Goriely
Keyword(s):  
Self Assembly ◽  
Permanent Magnets ◽  
Energy Estimates ◽  
Dimensional Chain ◽  
Elastic Rod ◽  
Straight Chain ◽  
One Dimensional ◽  
Vibration Dynamics ◽  
Magnetic Strength ◽  
A Chain

Spherical neodymium–iron–boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.

scholarly journals Self-Excited Vibration of an Elastic Rod in Swirling Flow

2011 ◽  
Vol 77 (779) ◽  
pp. 2566-2575
Author(s):  
Hiroki MORI ◽  
Takuo NAGAMINE ◽  
Tatsumi ICHIMURA ◽  
Yuichi SATO
Keyword(s):  
Swirling Flow ◽  
Elastic Rod ◽  
Excited Vibration

Statics Analysis of the Mechanical Model of Nucleosome

2011 ◽  
Vol 343-344 ◽  
pp. 661-667 ◽  
Author(s):  
Yun Xue ◽  
De Wei Weng ◽  
Gang Ming Gong
Keyword(s):  
Mechanical Model ◽  
The Other ◽  
Elastic Rod ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Precession Angle ◽  
Nutation Angle ◽  
Analytic Expression ◽  
Set Up ◽  
Calculated Analysis

Mechanical model of nucleoside and its equilibrium equations are set up, and the mechanical properties on the equilibrium position are analyzed. In the case constraint force and electrostatic attraction between cylinder OH and elastic rod are balanced, the analytic expression of nutation angle of the section and its conditions of existence are given. It is show that the cylinder OH can maintain equilibrium at any range of the precession angle. In the other case when unbanced, there is phenomenon of separation of elastic rod from cylinder OH in the spiral wound 2 circles, and numerical solution of the precession angle at separation points are calculated. Analysis of equilibrium of cylinder H1 illustrates that the generatrix of cylinder H1 and OH are not parallel, and the angle between them is obtained

Energy Harvesting With Piezoelectric Nanobrushes: Analysis and Design Principles

2009 ◽  
Author(s):  
Carmel Majidi ◽  
Mikko Haataja ◽  
David J. Srolovitz
Keyword(s):  
Energy Harvesting ◽  
Design Space ◽  
Electronic Devices ◽  
Wearable Electronics ◽  
Nanostructured Surface ◽  
Elastic Rod ◽  
Analysis And Design ◽  
Rod Theory ◽  
Piezoelectric Energy ◽  
Self Powered

The development of self-powered electronic devices is essential for emerging technologies such as wireless sensor networks, wearable electronics, and microrobotics. Of particular interest is the rapidly growing field of piezoelectric energy harvesting (PEH), in which mechanical strains are converted to electricity. Recently, PEH has been demonstrated by brushing an array of piezoelectric nanowires against a nanostructured surface. The piezoelectric nanobrush generator can be limited to sub-micron dimensions and thus allows for a vast reduction in the size of self-powered devices. Moreover, energy harvesting is controlled through contact between the nanowire tips and nanostructured surface, which broadens the design space to a wealth of innovations in tribology. Here we propose design criteria based on principles of contact mechanics, elastic rod theory, and continuum piezoelasticity.

scholarly journals XII. On the cause of the discrepancies observed by Mr. Baily with the Cavendish apparatus for determining the mean density of the earth

1847 ◽  
Vol 137 ◽  
pp. 217-229 ◽  
Keyword(s):  
Mathematical Theory ◽  
Full Account ◽  
Astronomical Society ◽  
Royal Astronomical Society ◽  
The Earth ◽  
Singular Source ◽  
The Mean ◽  
The Masses ◽  
Source Of Error ◽  
Different Parts

In the Fourteenth Volume of the Transactions of the Royal Astronomical Society will be found a full account of the Cavendish apparatus, and of the mode of experimenting followed by Mr. Baily. It will therefore not be necessary for me, in this place, to enter into any detail as to the different parts of the instrument, and the various precautions adopted in order to avoid that singular source of error 'currents of air in the torsion box arising from unequal temperature,’ which had been discovered by Cavendish. It will be sufficient for me to state that all the arrangements are of a highly satisfactory kind, and that I am of opinion that no aerial currents could have existed in the torsion box. The deduction of the mean density of the earth from the observed vibrations of the balls influenced by the torsion force and the attraction of the masses, is founded on a mathematical theory of the motion of the balls given by the Astronomer Royal, Mr. Airy ; and as this theory is certainly insufficient to account for the discrepancies, it will here be necessary to give a brief sketch of it.

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