Investigation of Free Vibrations of Three-Layered Circular Shell Supported by Annular Ribs of Rigidity

The construction of a mathematical model and the development of an algorithm of free vibrations investigation in the three-layered circular shell with a light-weight aggregate supported by annular rigidity ribs are considered in paper. The hypotheses of Kirchoff-Lyav are accepted for external bearing layers of shell and for aggregate there is accepted the linear law of tangential displacements change by thickness. The boundary conditions of a shell region closed between the ribs are established. Using the boundary transition, conditions along the lines of the ribs, taking into account and without deformations of displacement in the ribs, but without taking into account the torsional rigidity in the ribs are determined. The equation of motion of supported three-layered shell is obtained. The frequencies of free vibrations were investigated and values of parameter of the first frequency of free vibrations for a shell, supported by one and three rigidity ribs, were calculated. There are given values depending on the physical and mechanical properties of materials and geometric dimensions of the shell, the curvature parameter, and the rigidity parameter of an aggregate.

Elastic-Plastic Dynamic Response of the Tube with Free Boundary Condition Subjected to Impact

Some experimental results of the free-free tubes laterally impacted by the missile were given and the finite element program LS-DYNA was used to simulate this dynamic response process. The instantaneous deformation of the circular shell given by experiments and computer simulation were compared and discussed. It can be seen that when the impact occur the local dents firstly appear at the beginning of impact. With time increase, the depth of the dents increase, the scope of the deformation of the tube wall is enlarged; the total stiffness of the cross-section of the tube is weaken and decreases at the impact point, the beam-like bending deformation take place and the rigid-body translations occur. Through the computer simulation the exchanged energy between the missile and the tube were acquired. The impact energy of the missile is transferred to internal energy and kinetic energy of the tube. The ratio of the internal energy with the kinetic energy of the tube is great for the weakness rigidity of the tube wall, which is opposite to that of a free-free beam. This research made us deeply understand the character of the response when studying the elastic-plastic behavior of the free circular shell under intense dynamic loading.