TY - JOUR

T1 - Thin rod under longitudinal dynamic compression

AU - Belyaev, A. K.

AU - Tovstik, P. E.

AU - Tovstik, Tatiana Petrovna

PY - 2017/7/1

Y1 - 2017/7/1

N2 - The paper contains a short survey of the papers on the static and dynamic longitudinal compression of a thin rod initiated by Morozov and and carried out in 2009–2016 with his direct participation. We consider linear and nonlinear problems related to the propagation of longitudinal waves in a rod and the transverse vibrations generated by these waves; parametric resonances; beating due to energy exchange between longitudinal and transverse vibrations; the rod shape evolution as the load exceeds the Euler critical value; the possibility of buckling of the rod rectilinear shape under a load less than the Euler load; and the rod dynamics at the initial stage of motion. The prospects of further investigations related to the complication of the models are considered, in particular, the problem of longitudinal impact by a body on a rod and the transverse vibrations generated by it.

AB - The paper contains a short survey of the papers on the static and dynamic longitudinal compression of a thin rod initiated by Morozov and and carried out in 2009–2016 with his direct participation. We consider linear and nonlinear problems related to the propagation of longitudinal waves in a rod and the transverse vibrations generated by these waves; parametric resonances; beating due to energy exchange between longitudinal and transverse vibrations; the rod shape evolution as the load exceeds the Euler critical value; the possibility of buckling of the rod rectilinear shape under a load less than the Euler load; and the rod dynamics at the initial stage of motion. The prospects of further investigations related to the complication of the models are considered, in particular, the problem of longitudinal impact by a body on a rod and the transverse vibrations generated by it.

KW - beating

KW - Euler elastics

KW - longitudinal impact

KW - parametric resonances

KW - rod

KW - transverse bending

UR - http://www.scopus.com/inward/record.url?scp=85036635030&partnerID=8YFLogxK

U2 - 10.3103/S0025654417040021

DO - 10.3103/S0025654417040021

M3 - Article

AN - SCOPUS:85036635030

VL - 52

SP - 364

EP - 377

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 4

ER -