Some new aspects in a classic problem of axial rod compression are presented. For short-term impact the influence of longitudinal waves propagation on the rod instability is investigated. For the long-term compression which considerably exceeds the Euler load, the generalization of the overcritical deformations in the rod from investigated by M.A. Lavrentiev and A.Yu. Ishlinsky in the linear statement to the nonlinear Euler elastics is studied.
Topics
Wave mechanics
REFERENCES
1.
L.
Euler
, Foundation method of curves with maximal or minimal property
. Moscow
. GTTL
. 1934
. (in Russian
)2.
M. A.
Lavrent’ev
, A. Ju.
Ishlinsky
, Dynamical modes of stability loss of elastic systems
. Dorlady Physics
. 1949
. 64
(6
). P. 776
–782
. (in Russian
)3.
N. F.
Morozov
, P. E.
Tovstik
, Dynamics of rod at a longitudinal impact
. Vestnik St.Petersburg Univ. Ser. 1
. 2009
. No 2
. P. 105
–111
. (in Russian
)4.
A. K.
Belyaev
, D. N.
Il’in
, N. F.
Morozov
, Dynamical approach to the Ishlinsky–Lavrent’ev problem
. Mech. of Solids
. 2013
. No 5
. P. 28
–33
. (in Russian
)5.
N. F.
Morozov
, P. E.
Tovstik
, The rod dynamics under a short-term longitudinal impact
. Vestnik St.Petersburg Univ. Ser. 1
. 2013
. No 3
. P. 131
–141
. (in Russian
)6.
N. F.
Morozov
, P. E.
Tovstik
, Transverse rod vibrations under a short-term longitudinal impact
. Doklady Physics
. 2013
. 58
(9
). P. 387
–391
.7.
N. F.
Morozov
, P. E.
Tovstik
, T. P.
Tovstik
, Again on the Ishlinskii-Lavrentyev problem
. Doklady Physics
. 2014
. 59
(4
). P. 189
–192
.8.
A. M.
Lyapunov
, General problem of a motion stability
. Moscow
. Leningrad. Gostekhizdat
. 1950
. (in Russian
)
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