Dynamic equations for an orthotropic cylindrical shell
Journal article, 2018
A hierarchy of dynamic shell equations is derived for an orthotropic cylindrical shell. The displacement components are expanded into power series in the thickness coordinate and the three-dimensional elastodynamic equations then yield a set of recursion relations among the expansion functions that can be used to eliminate all but the six lowest-order functions. Applying the boundary conditions on the surfaces of the shell and eliminating all but the six lowest-order expansion functions give the shell equations as a power series in the shell thickness. In principle, these six differential equations can be truncated to any order. Numerical examples showing eigenfrequencies for a ring and for a simply supported shell show the convergence of the method to the 3D solution, and a comparison with previous investigations is also made. Finally, the exact 3D solution is given for a simply supported transversely isotropic shell of arbitrary thickness.