Simplified non-linear dynamical equations of circular cylindrical shells

Abstract

Simplified non-linear dynamical equations of circular cylindrical shells are obtained on the basis of asymptotic analysis. The original partial differential equations (PDEs), which have eighth order in the longitudinal coordinate, are replaced by two sets of equations that have fourth order on this coordinate. The first set contains non-linear and dynamic PDEs. They describe the oscillations in the inner region of the shell. For small non-linearities, they coincide with the well-known linear semi-membrane dynamical equations. Ordinary differential equations of the edge effect allow one to satisfy all the boundary conditions. They are linear and quasistatic. An important question about the boundary conditions for the simplified equations is considered. We also discuss the solution of the obtained boundary value problems.