Low Dimensional Models of Shell Vibrations. Parametrically Excited Vibrations of Cylinder Shells

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

“…The instability was identi"ed from "nite-element computations of the time response of the shell using a criterion due to Budianski and Roth. Popov et al [104] and McRobie et al [105] presented two studies; one on the vibrations of cylindrical shells, parametrically exited by axial forcing, and another on the internal auto-parametric instabilities in the non-linear free vibrations of a cylindrical shell, using geometric averaging. A Rayleigh}Ritz discretization of the von Karman}Donnel equations was used, and led to the Hamiltonian and transformation into action-angle co-ordinates, followed by averaging, which provided readily a geometric description of the modal interaction.…”

Addendum to “Nonlinear Vibrations of Simply Supported, Circular Cylindrical Shells, Coupled to Quiescent Fluid”

“…Only the trend of the nonlinearity (backbone curve) is obtained; the frequency-response relationship is not investigated. Popov et al (1998) and Foale et al (1998) investigate di!erent methods to obtain a low-dimensional system from the nonlinear equations of motion of a shallow cylindrical shell panel under periodic axial forcing.…”

Multimode interaction in axially excited cylindrical shells

“…Although there are many papers on modal coupling and interaction in the presence of static loads, little is known on their influence on the dynamic stability of thin-walled cylindrical shells. So, when considering the effect of nonlinearity, there is the possibility of interaction between the different non-linear vibration modes, which can cause significant changes in the stability boundaries and bifurcation diagrams [1,2]. However, no consistent modal solution taking into account the simultaneous effect of modal coupling plus modal interaction is found in literature [3,4].…”