Correlation between the properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with torque connections

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Correlation between the properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with torque connections. / Indeitsev, D. A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 50, No. 2, 01.04.2017, p. 166-172.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{8ce2de66f96e4fef82bbd7d734f55317,

title = "Correlation between the properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with torque connections",

abstract = "A chain of N rigid bodies with elastic connections transmitting a torque interaction is considered. Similar individual inertial elements of the chain have one degree of freedom. An exact analytical solution of the problem of oscillation eigenfrequencies and eigenmodes is constructed for an arbitrary value of N. The properties of frequencies and modes of such a chain are compared with those of a canonical Newton chain. It is established that the correlation between eigenfrequencies and the properties of the corresponding eigenmodes fundamentally differs from that for a canonical Newton chain. Lower eigenfrequencies of a chain of rigid bodies with inertialess torque connections correspond to modes with a larger number of nodes, while higher eigenfrequencies correspond to the smoother modes. The nontypical correlation between the oscillation eigenfrequencies and eigenmodes discovered based on the exact analytical solution to the problem of free oscillations of a chain of N rotating rigid bodies contradicts the ideas underlying theoretical studies in the field of solid state physics devoted to simulation of mechanical and thermal dynamic processes in crystalline lattices.",

keywords = "chains of rigid bodies, modes of oscillations",

author = "Indeitsev, {D. A.}",

year = "2017",

month = apr,

day = "1",

doi = "10.3103/S1063454117020066",

language = "English",

volume = "50",

pages = "166--172",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Correlation between the properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with torque connections

AU - Indeitsev, D. A.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - A chain of N rigid bodies with elastic connections transmitting a torque interaction is considered. Similar individual inertial elements of the chain have one degree of freedom. An exact analytical solution of the problem of oscillation eigenfrequencies and eigenmodes is constructed for an arbitrary value of N. The properties of frequencies and modes of such a chain are compared with those of a canonical Newton chain. It is established that the correlation between eigenfrequencies and the properties of the corresponding eigenmodes fundamentally differs from that for a canonical Newton chain. Lower eigenfrequencies of a chain of rigid bodies with inertialess torque connections correspond to modes with a larger number of nodes, while higher eigenfrequencies correspond to the smoother modes. The nontypical correlation between the oscillation eigenfrequencies and eigenmodes discovered based on the exact analytical solution to the problem of free oscillations of a chain of N rotating rigid bodies contradicts the ideas underlying theoretical studies in the field of solid state physics devoted to simulation of mechanical and thermal dynamic processes in crystalline lattices.

AB - A chain of N rigid bodies with elastic connections transmitting a torque interaction is considered. Similar individual inertial elements of the chain have one degree of freedom. An exact analytical solution of the problem of oscillation eigenfrequencies and eigenmodes is constructed for an arbitrary value of N. The properties of frequencies and modes of such a chain are compared with those of a canonical Newton chain. It is established that the correlation between eigenfrequencies and the properties of the corresponding eigenmodes fundamentally differs from that for a canonical Newton chain. Lower eigenfrequencies of a chain of rigid bodies with inertialess torque connections correspond to modes with a larger number of nodes, while higher eigenfrequencies correspond to the smoother modes. The nontypical correlation between the oscillation eigenfrequencies and eigenmodes discovered based on the exact analytical solution to the problem of free oscillations of a chain of N rotating rigid bodies contradicts the ideas underlying theoretical studies in the field of solid state physics devoted to simulation of mechanical and thermal dynamic processes in crystalline lattices.

KW - chains of rigid bodies

KW - modes of oscillations

UR - http://www.scopus.com/inward/record.url?scp=85022029829&partnerID=8YFLogxK

U2 - 10.3103/S1063454117020066

DO - 10.3103/S1063454117020066

M3 - Article

AN - SCOPUS:85022029829

VL - 50

SP - 166

EP - 172

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 75069557