Authors' Reply

Non-Linear Vibrations of Shell-Type Structures: A Review With Bibliography

“…A reliable discussion and interesting comment have been made about this subject between Raju and Rao [165,166], and Evensen [167], and between Prathab [168] and Evensen [169]. It is interesting to note that these comments caused Ganapathy and Varadan [82] [173] and Moussaoui et al [92] on the hardening strong non-linearity observed in reference [41] for moderately thin, in"nite circular cylindrical shells. This set of discussions testify that the topic of circular cylindrical shells behaviour still presents open questions, which should be clari"ed through experiments on non-linear vibrations of moderately thin and thick shells.…”

“…However, he concluded that in contrast to the linear case in which the chessboard de#ection pattern is a natural choice, its selection in the non-linear problem must be more carefully assessed [75]. It may be worth noticing here that the question of the choice of the de#ection shape has been rediscussed recently in reference [92]. Using Donnell's shallow-shell theory, Reissner isolated a single half-wave (lobe) of the vibration mode, and analyzed it for simply supported shells, and found that the non-linearity could be either of the hardening or softening type, depending upon the geometry of the lobe.…”

Nonlinear transverse steady-state periodic forced vibration of 2-dof discrete systems with cubic nonlinearities

“…-Different geometries : rectangular and circular plates, finite and infinite shells, rings (see for instence the just cited referenceses and also (Rougui et al, 2003;Haterbouch et al, 2003;Moussaoui et al, 2001)).…”