## 3aSAa5. Investigation of wave processes in a Timoshenko thin-walled beam of open section caused by the shock subjection of an elastic sphere upon its surface.

### Session: Wednesday Morning, May 15

### Time: 9:00

**Author: Yuriy A. Rossikhin**

**Location: Dept. of Theoret. Mech., Voronezh State Acad. of Construction and Architecture, ul. Kirova 3-75, Voronezh 394018, Russia**

**Abstract:**

The problem on the normal impact of an elastic sphere upon an elastic
Timoshenko beam of thin-walled monosymmetrical open section is considered. The
process of impact is accompanied by the dynamic flexure and torsion of the beam,
resulting in the propagation of plane flexural, shear, and torsional waves of
strong discontinuity along the beam axis. Behind the wavefronts the solution is
constructed in terms of one-term ray expansions. During the impact the sphere
moves under the action of the contact force which is determined due to the
Hertz's theory, but the contact region moves under the action of the contact
force, and the bending-torsional moment and transverse forces, which are
subjected to the lateral surfaces of the contact region and are determined using
one-term ray expansions. The joint consideration of the equations of sphere and
the contact region motion leads to the Abel equation of second kind in the rate
of change of the value of the sphere and beam drawing together. The solution to
the Abel equation written in the form of a series in terms of this value allows
one to determine all characteristics of the sphere and beam shock interaction.

from ASA 131st Meeting, Indianapolis, May 1996