An exact solution procedure is presented for solving free vibration pr
oblems for laminated composite noncircular cylindrical shells. Based o
n the classical lamination theory, strain energy and kinetic energy fu
nctionals are first derived for shells having arbitrary layer stacking
sequences. These functionals are useful for a general analysis based
upon energy principles. However, in the present work equations of moti
on and boundary conditions are obtained from the minimum conditions of
the Lagrangian (Hamilton's principle), The equations of motion are so
lved exactly by using a power series expansion for symmetrically lamin
ated, cross-ply shells having both ends freely supported. Frequencies
are presented for a set of elliptical cylindrical shells, and the effe
cts of various parameters upon them are discussed.