scholarly journals Discrete mass-spring structure identification in nonlocal continuum space-fractional model

2019 ◽  
Vol 134 (9) ◽  
Author(s):  
Krzysztof Szajek ◽  
Wojciech Sumelka
Keyword(s):  
Nonlocal Parameter ◽  
Structure Identification ◽  
Nonlocal Continuum ◽  
Fractional Model ◽  
Optimization Task ◽  
The Masses ◽  
Mass Spring ◽  
Discrete Mass ◽  
Continuum Theories ◽  
First Time

Abstract. This paper considers discrete mass-spring structure identification in a nonlocal continuum space-fractional model, defined as an optimization task. Dynamic (eigenvalues and eigenvectors) and static (displacement field) solutions to discrete and continuum theories are major constituents of the objective function. It is assumed that the masses in both descriptions are equal (and constant), whereas the spring stiffness distribution in a discrete system becomes a crucial unknown. The considerations include a variety of configurations of the nonlocal parameter and the order of the fractional model, which makes the study comprehensive, and for the first time provides insight into the possible properties (geometric and mechanical) of a discrete structure homogenized by a space-fractional formulation.

The Biggest Ears in the Sky: LIGO

2020 ◽  
pp. 108-136
Author(s):  
John W. Moffat
Keyword(s):  
Black Holes ◽  
Gravitational Waves ◽  
Nobel Prize ◽  
Executive Director ◽  
Numerical Relativity ◽  
Washington State ◽  
Wave Form ◽  
Press Conference ◽  
The Masses ◽  
First Time

At a press conference on February 11, 2016, David Reitz, LIGO Executive Director, announced, “We did it!” They detected gravitational waves for the first time. Both LIGO sites, in Washington state and Louisiana, registered the incoming gravitational waves from two black holes colliding and merging far away. Over the following months, more mergers were detected. Gravitational waves are caused by the acceleration of a massive object, which stretches and compresses spacetime in a wave-like motion that is incredibly small and difficult to detect. Numerical relativity research over decades has produced over a quarter of a million template solutions of Einstein’s equations. The best template fit to the wave form data identifies the masses and spins of the two merging black holes. Much of this chapter describes the technology of the LIGO apparatus. On October 3, 2017, Barish, Thorne, and Weiss, the founders of LIGO, received the Nobel Prize for Physics.

The Hanging Column as a Dynamic Vibration Absorber

2018 ◽  
Vol 18 (07) ◽  
pp. 1871008 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Forced Vibration ◽  
Vibration Absorber ◽  
Initial Value ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Spring System ◽  
Simple Mass ◽  
Mass Spring ◽  
First Time

A simple mass–spring system with an attached hanging column is investigated. The problem is formulated and the frequencies obtained with an efficient initial value method. Under forced vibration, the amplitude of the mass may be greatly reduced by adding a hanging column. The possibility of using such a hanging column as a dynamic vibration absorber is shown for the first time.

scholarly journals Model of Close Packing for Determination of the Major Characteristics of the Liquid Dispersions Components

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Kiril Hristov Kolikov ◽  
Dimo Donchev Hristozov ◽  
Radka Paskova Koleva ◽  
Georgi Aleksandrov Krustev
Keyword(s):  
Dispersion Medium ◽  
Algebraic Method ◽  
Close Packing ◽  
Pure Substance ◽  
Sedimentation Stability ◽  
Dispersion Phase ◽  
Liquid Dispersion ◽  
The Masses ◽  
First Time

We introduce a close packing model of the particles from the disperse phase of a liquid dispersion. With this model, we find the sediment volumes, the emergent, and the bound dispersion medium. We formulate a new approach for determining the equivalent radii of the particles from the sediment and the emergent (different from the Stokes method). We also describe an easy manner to apply algebraic method for determining the average volumetric mass densities of the ultimate sediment and emergent, as well as the free dispersion medium (without using any pycnometers or densitometers). The masses of the different components and the density of the dispersion phase in the investigated liquid dispersion are also determined by means of the established densities. We introduce for the first time a dimensionless scale for numeric characterization and therefore an index for predicting the sedimentation stability of liquid dispersions in case of straight and/or reverse sedimentation. We also find the quantity of the pure substance (without pouring out or drying) in the dispersion phase of the liquid dispersions.

Buckling analysis of carbon nanotubes modeled using nonlocal continuum theories

2008 ◽  
Vol 103 (7) ◽  
pp. 073521 ◽  
Author(s):  
Devesh Kumar ◽  
Christian Heinrich ◽  
Anthony M. Waas
Keyword(s):  
Carbon Nanotubes ◽  
Buckling Analysis ◽  
Nonlocal Continuum ◽  
Continuum Theories

Mesoscopic fabric models using a discrete mass-spring approach: Yarn-yarn interactions analysis

2005 ◽  
Vol 40 (22) ◽  
pp. 5925-5932 ◽  
Author(s):  
Bilel Ben Boubaker ◽  
Bernard Haussy ◽  
Jean-Francois Ganghoffer
Keyword(s):  
Mass Spring ◽  
Discrete Mass

A Hybrid Inverse Mode Problem for Fixed-Fixed Mass-Spring Models

1996 ◽  
Vol 118 (4) ◽  
pp. 641-648 ◽  
Author(s):  
Izuru Takewaki ◽  
Tsuneyoshi Nakamura ◽  
Yasumasa Arita
Keyword(s):  
Inverse Problem ◽  
Closed Form ◽  
Sufficient Conditions ◽  
Eigenvalue Analysis ◽  
Spring Model ◽  
Mass Spring Model ◽  
Left And Right ◽  
The Masses ◽  
Mass Spring ◽  
Lowest Eigenvalue

A hybrid inverse mode problem is formulated for a fixed-fixed mass-spring model. A problem of eigenvalue analysis and its inverse problem are combined in this hybrid inverse mode formulation. It is shown if all the masses and the mid-span stiffnesses of the model are prescribed, then the stiffnesses of the left and right spans (side-spans) can be found for a specified lowest eigenvalue and a specified set of lowest-mode drifts in the side-spans. Sufficient conditions are introduced and proved for a specified eigenvalue and a specified set of drifts in the side-spans to provide positive stiffnesses of the side-spans and to be those in the lowest eigenvibration. A set of solution stiffnesses in the side-spans is derived uniquely in closed form.

scholarly journals Curved Nanotube Structures under Mechanical Loading

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Hamidreza Yazdani Sarvestani ◽  
Ali Naghashpour
Keyword(s):  
Carbon Nanotube ◽  
Theoretical Study ◽  
Nonlocal Parameter ◽  
Bending Moment ◽  
Theoretical Development ◽  
Governing Equations ◽  
Nonlocal Continuum ◽  
The Subject ◽  
Displacement Based ◽  
Displacement Approach

Configuration of carbon nanotube (CNT) has been the subject of research to perform theoretical development for analyzing nanocomposites. A new theoretical solution is developed to study curved nanotube structures subjected to mechanical loadings. A curved nanotube structure is considered. A nonlocal displacement-based solution is proposed by using a displacement approach of Toroidal Elasticity based on Eringen’s theory of nonlocal continuum mechanics. The governing equations of curved nanotube structures are developed in toroidal coordinate system. The method of successive approximation is used to discretize the displacement-based governing equations and find the general solution subjected to bending moment. The numerical results show that all displacement components increase with increasing the nonlocal parameter. The present theoretical study highlights the significance of the geometry and nonlocal parameter effects on mechanical behavior of nanotube structures.

ESTIMATION OF DYNAMIC SYSTEM'S EXCITATION FORCES BY THE INDEPENDENT COMPONENT ANALYSIS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250032 ◽  
Author(s):  
ALI AKROUT ◽  
DHOUHA TOUNSI ◽  
MOHAMED TAKTAK ◽  
MOHAMED SLIM ABBÈS ◽  
MOHAMED HADDAR
Keyword(s):  
Independent Component Analysis ◽  
Numerical Procedure ◽  
Component Analysis ◽  
Independent Component ◽  
Dynamic Responses ◽  
Statistical Criterion ◽  
Mass Spring ◽  
Discrete Mass ◽  
Signal Sources ◽  
Good Agreement

This paper deals with a numerical investigation for the estimation of dynamic system's excitation sources using the independent component analysis (ICA). In fact, the ICA concept is an important technique of the blind source separation (BSS) method. In this case, only the dynamic responses of a given mechanical system are supposed to be known. Thus, the main difficulty of such problem resides in the existence of any information about the excitation forces. For this purpose, the ICA concept, which consists on optimizing a fourth-order statistical criterion, can be highlighted. Hence, a numerical procedure based on the signal sources independency in the ICA concept is developed. In this work, the analytical or the finite element (FE) dynamic responses are calculated and exploited in order to identify the excitation forces applied on discrete (mass-spring) and continuous (beam) systems. Then, estimated results obtained by the ICA concept are presented and compared to those achieved analytically or by the FE and the modal recombination methods. Since a good agreement is obtained, this approach can be used when the vibratory responses of a dynamic system are obtained through sensor's measurements.

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