Beating in the problem of longitudinal impact on a thin rod

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Beating in the problem of longitudinal impact on a thin rod. / Belyaev, A.K.; Morozov, N.F.; Tovstik, P.E.; Tovstik, T.P.

In: Mechanics of Solids, No. 4, 2015, p. 451-462.

Research output: Contribution to journal › Article

BibTeX

@article{25f7d53cd78d49c182fc7e1f619c239f,

title = "Beating in the problem of longitudinal impact on a thin rod",

abstract = "{\textcopyright} 2015, Allerton Press, Inc.The longitudinal impact on an elastic rod generating a periodic system of longitudinal waves in the rod, is considered. For certain values of the problem parameters in the linear approximation, these waves generate parametric resonances accompanied by an infinite increase in the transverse vibrations amplitude. To obtain the finite values of the amplitudes, a quasilinear system where the influence of transverse vibrations on the longitudinal ones is taken into account was considered. Earlier, this system was solved numerically by the Bubnov—Galerkin method and the beatings accompanied by energy exchange between the longitudinal and transverse vibrations were obtained. Here an approximate analytic solution of this system based on two-scale expansions is constructed. A qualitative analysis is performed. The maximum transverse deflection depending on the loading method is estimated.",

author = "A.K. Belyaev and N.F. Morozov and P.E. Tovstik and T.P. Tovstik",

year = "2015",

doi = "10.3103/S0025654415040111",

language = "English",

pages = "451--462",

journal = "Mechanics of Solids",

issn = "0025-6544",

publisher = "Allerton Press, Inc.",

number = "4",

}

RIS

TY - JOUR

T1 - Beating in the problem of longitudinal impact on a thin rod

AU - Belyaev, A.K.

AU - Morozov, N.F.

AU - Tovstik, P.E.

AU - Tovstik, T.P.

PY - 2015

Y1 - 2015

N2 - © 2015, Allerton Press, Inc.The longitudinal impact on an elastic rod generating a periodic system of longitudinal waves in the rod, is considered. For certain values of the problem parameters in the linear approximation, these waves generate parametric resonances accompanied by an infinite increase in the transverse vibrations amplitude. To obtain the finite values of the amplitudes, a quasilinear system where the influence of transverse vibrations on the longitudinal ones is taken into account was considered. Earlier, this system was solved numerically by the Bubnov—Galerkin method and the beatings accompanied by energy exchange between the longitudinal and transverse vibrations were obtained. Here an approximate analytic solution of this system based on two-scale expansions is constructed. A qualitative analysis is performed. The maximum transverse deflection depending on the loading method is estimated.

AB - © 2015, Allerton Press, Inc.The longitudinal impact on an elastic rod generating a periodic system of longitudinal waves in the rod, is considered. For certain values of the problem parameters in the linear approximation, these waves generate parametric resonances accompanied by an infinite increase in the transverse vibrations amplitude. To obtain the finite values of the amplitudes, a quasilinear system where the influence of transverse vibrations on the longitudinal ones is taken into account was considered. Earlier, this system was solved numerically by the Bubnov—Galerkin method and the beatings accompanied by energy exchange between the longitudinal and transverse vibrations were obtained. Here an approximate analytic solution of this system based on two-scale expansions is constructed. A qualitative analysis is performed. The maximum transverse deflection depending on the loading method is estimated.

U2 - 10.3103/S0025654415040111

DO - 10.3103/S0025654415040111

M3 - Article

SP - 451

EP - 462

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 4

ER -

ID: 4010954