TY - JOUR

T1 - Dynamic approach to the Ishlinsky-Lavrent’ev problem

AU - Belyaev, A.K.

AU - Il'in, D.N.

AU - Morozov, N.F.

PY - 2013

Y1 - 2013

N2 - The problem of the dynamic stability of the rod subjected to a jump longitudinal load is solved with the help of method of series expansion of displacements in terms of longitudinal and bending vibration modes. Longitudinal oscillations are manifested in the form of longitudinal periodic forces that cause a parametric resonance. The approach is demonstrated by the example of simply supported rod, whose end is subjected to an axial jump force. The instability regions are shown to have the form depending upon the spectral properties of the longitudinal and bending vibrations, damping values and axial force. An expression for the critical dynamic load jump leading to a parametric resonance is derived.

AB - The problem of the dynamic stability of the rod subjected to a jump longitudinal load is solved with the help of method of series expansion of displacements in terms of longitudinal and bending vibration modes. Longitudinal oscillations are manifested in the form of longitudinal periodic forces that cause a parametric resonance. The approach is demonstrated by the example of simply supported rod, whose end is subjected to an axial jump force. The instability regions are shown to have the form depending upon the spectral properties of the longitudinal and bending vibrations, damping values and axial force. An expression for the critical dynamic load jump leading to a parametric resonance is derived.

U2 - 10.3103/S002565441305004X

DO - 10.3103/S002565441305004X

M3 - Article

VL - 48

SP - 504

EP - 508

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 0025-6544

IS - 5

ER -