Negative Stiffness Produced by Rotation of Non-Spherical Particles and Its Effect on Frictional Sliding

Iuliia Karachevtseva, Elena Pasternak, Arcady V. Dyskin

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Abstract

Previous research shows that the rotation of non-spherical particles under compression might lead to the effect of apparent negative stiffness. The effect of a rotating non-spherical particle is modeled and it is shown that under displacement-controlled loading its dynamics is equivalent to the dynamics of inverted pendulum. Analytically and experimentally, the eigenfrequency and the stability of the inverted pendulum under changing mass is investigated. It is demonstrated that the increase of total mass leads to the decrease of eigenfrequency of the system beyond that of an ordinary pendulum. Furthermore, there exists a value of the mass when the eigen frequency becomes zero. At this point the system loses its stability. This corresponds to the results obtained for a pair of coupled linear oscillators with one negative stiffness spring. Thus the concept of negative stiffness allows formulation of a simple and accurate model of inverted pendulum and rotating non-spherical particles. It is shown that a set of randomly sized rotating non-spherical particles create fluctuations in the friction force, which can form a mechanism of experimentally observed friction force fluctuations.

Original languageEnglish
Article number1800003
Number of pages7
JournalPHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS
Volume256
Issue number1
DOIs
Publication statusPublished - Jan 2019

Cite this

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title = "Negative Stiffness Produced by Rotation of Non-Spherical Particles and Its Effect on Frictional Sliding",
abstract = "Previous research shows that the rotation of non-spherical particles under compression might lead to the effect of apparent negative stiffness. The effect of a rotating non-spherical particle is modeled and it is shown that under displacement-controlled loading its dynamics is equivalent to the dynamics of inverted pendulum. Analytically and experimentally, the eigenfrequency and the stability of the inverted pendulum under changing mass is investigated. It is demonstrated that the increase of total mass leads to the decrease of eigenfrequency of the system beyond that of an ordinary pendulum. Furthermore, there exists a value of the mass when the eigen frequency becomes zero. At this point the system loses its stability. This corresponds to the results obtained for a pair of coupled linear oscillators with one negative stiffness spring. Thus the concept of negative stiffness allows formulation of a simple and accurate model of inverted pendulum and rotating non-spherical particles. It is shown that a set of randomly sized rotating non-spherical particles create fluctuations in the friction force, which can form a mechanism of experimentally observed friction force fluctuations.",
keywords = "inverted pendulum, negative stiffness, non-spherical particles, particle rotation, stability, SEISMIC PROTECTION, STABILITY, COMPOSITES, OSCILLATORS, DEFORMATION, SYSTEMS, DEVICE, DESIGN, CHAINS, JOINT",
author = "Iuliia Karachevtseva and Elena Pasternak and Dyskin, {Arcady V.}",
year = "2019",
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doi = "10.1002/pssb.201800003",
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journal = "Physica Status Solidi. B: Basic Solid State Physics",
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publisher = "Wiley-VCH Verlag GmbH & Co. KGaA",
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TY - JOUR

T1 - Negative Stiffness Produced by Rotation of Non-Spherical Particles and Its Effect on Frictional Sliding

AU - Karachevtseva, Iuliia

AU - Pasternak, Elena

AU - Dyskin, Arcady V.

PY - 2019/1

Y1 - 2019/1

N2 - Previous research shows that the rotation of non-spherical particles under compression might lead to the effect of apparent negative stiffness. The effect of a rotating non-spherical particle is modeled and it is shown that under displacement-controlled loading its dynamics is equivalent to the dynamics of inverted pendulum. Analytically and experimentally, the eigenfrequency and the stability of the inverted pendulum under changing mass is investigated. It is demonstrated that the increase of total mass leads to the decrease of eigenfrequency of the system beyond that of an ordinary pendulum. Furthermore, there exists a value of the mass when the eigen frequency becomes zero. At this point the system loses its stability. This corresponds to the results obtained for a pair of coupled linear oscillators with one negative stiffness spring. Thus the concept of negative stiffness allows formulation of a simple and accurate model of inverted pendulum and rotating non-spherical particles. It is shown that a set of randomly sized rotating non-spherical particles create fluctuations in the friction force, which can form a mechanism of experimentally observed friction force fluctuations.

AB - Previous research shows that the rotation of non-spherical particles under compression might lead to the effect of apparent negative stiffness. The effect of a rotating non-spherical particle is modeled and it is shown that under displacement-controlled loading its dynamics is equivalent to the dynamics of inverted pendulum. Analytically and experimentally, the eigenfrequency and the stability of the inverted pendulum under changing mass is investigated. It is demonstrated that the increase of total mass leads to the decrease of eigenfrequency of the system beyond that of an ordinary pendulum. Furthermore, there exists a value of the mass when the eigen frequency becomes zero. At this point the system loses its stability. This corresponds to the results obtained for a pair of coupled linear oscillators with one negative stiffness spring. Thus the concept of negative stiffness allows formulation of a simple and accurate model of inverted pendulum and rotating non-spherical particles. It is shown that a set of randomly sized rotating non-spherical particles create fluctuations in the friction force, which can form a mechanism of experimentally observed friction force fluctuations.

KW - inverted pendulum

KW - negative stiffness

KW - non-spherical particles

KW - particle rotation

KW - stability

KW - SEISMIC PROTECTION

KW - STABILITY

KW - COMPOSITES

KW - OSCILLATORS

KW - DEFORMATION

KW - SYSTEMS

KW - DEVICE

KW - DESIGN

KW - CHAINS

KW - JOINT

U2 - 10.1002/pssb.201800003

DO - 10.1002/pssb.201800003

M3 - Article

VL - 256

JO - Physica Status Solidi. B: Basic Solid State Physics

JF - Physica Status Solidi. B: Basic Solid State Physics

SN - 0370-1972

IS - 1

M1 - 1800003

ER -