TY - JOUR

T1 - Dynamics of a rod undergoing a longitudinal impact by a body

AU - Belyaev, A. K.

AU - Ma, C. C.

AU - Morozov, N. F.

AU - Tovstik, P. E.

AU - Tovstik, Tatiana Petrovna

AU - Shurpatov, A. O.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - A longitudinal elastic impact caused by a body on a thin rod is considered. The results of theoretical, finite element, and experimental approaches to solving the problem are compared. The theoretical approach takes into account both the propagation of longitudinal waves in the rod and the local deformations described in the Hertz model. This approach leads to a differential equation with a delayed argument. The three-dimensional dynamic problem is considered in terms of the finite element approach in which the wave propagation and local deformation are automatically taken into account. A benchmark test of these two approaches showed a complete qualitative and satisfactory quantitative agreement of the results concerning the contact force and the impact time. In the experiments, only the impact time was determined. The comparison of the measured impact time with the theoretical and finite element method’s results was satisfactory. Owing to the fact that the tested rod was relatively short, the approximate model with two degrees of freedom was also developed to calculate the force and the impact time. The problem of excitation of transverse oscillation after the rebound of the impactor off the rod is solved. For the parametric resonance, the motion has a character of beats at which the energy of longitudinal oscillation is transferred into the energy of transverse oscillation and vice versa. The estimate for the maximum possible amplitude of transverse oscillation is obtained.

AB - A longitudinal elastic impact caused by a body on a thin rod is considered. The results of theoretical, finite element, and experimental approaches to solving the problem are compared. The theoretical approach takes into account both the propagation of longitudinal waves in the rod and the local deformations described in the Hertz model. This approach leads to a differential equation with a delayed argument. The three-dimensional dynamic problem is considered in terms of the finite element approach in which the wave propagation and local deformation are automatically taken into account. A benchmark test of these two approaches showed a complete qualitative and satisfactory quantitative agreement of the results concerning the contact force and the impact time. In the experiments, only the impact time was determined. The comparison of the measured impact time with the theoretical and finite element method’s results was satisfactory. Owing to the fact that the tested rod was relatively short, the approximate model with two degrees of freedom was also developed to calculate the force and the impact time. The problem of excitation of transverse oscillation after the rebound of the impactor off the rod is solved. For the parametric resonance, the motion has a character of beats at which the energy of longitudinal oscillation is transferred into the energy of transverse oscillation and vice versa. The estimate for the maximum possible amplitude of transverse oscillation is obtained.

KW - Hertz theory

KW - impact

KW - impact impulse

KW - impact time

KW - parametric resonance

KW - rod

KW - Saint-Venant theory

KW - Sears theory

UR - http://www.scopus.com/inward/record.url?scp=85029169466&partnerID=8YFLogxK

U2 - 10.3103/S1063454117030050

DO - 10.3103/S1063454117030050

M3 - Article

AN - SCOPUS:85029169466

VL - 50

SP - 310

EP - 317

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -