©2012 Civil-Comp Ltd
Dipartimento di Ingegneria Meccanica e Civile, Universita di Modena e Reggio Emilia, Italy
Keywords: shells, nonlinear dynamics.
full paper (pdf) -
Several commercial software codes enable static, stability and vibration analyses to be carried out; however regarding shell dynamics, such kind of analyses are only generally reliable in the linear field, i.e. for very small deformations. Problems such as global stability, post-critical behaviour and nonlinear vibrations cannot yet be accurately analysed with commercial software; in such fields there is need of further development of computational models.
The present paper is focused on the experimental and theoretical analysis of circular cylindrical shells subject to base excitation. The shell axis is vertical, it is clamped at the base and connected to a rigid body on the top; the base provides a vertical seismic-like excitation. The goal is to investigate the shell response when a resonant harmonic forcing is applied: the first axisymmetric mode is excited around the resonance at relatively low frequency and low amplitude of excitation. A violent resonant phenomenon is experimentally observed as well as an interesting saturation phenomenon close to the previously mentioned resonance. A theoretical model is developed to reproduce the experimental evidence and provide an explanation of the complex dynamics observed experimentally; the model takes into account geometric shell nonlinearities, electro-dynamic shaker equations and the shell shaker interaction.
In this paper an experimental investigation of the nonlinear dynamics of circular cylindrical shells excited by a base excitation is presented. A nonlinear model of the shell considering also the shell shaker interaction is developed. The experiments clearly show a strong nonlinear phenomenon appearing when the first axisymmetric mode is excited: the phenomenon leads to large amplitude vibrations in a wide range of frequencies, it appears extremely dangerous as it can lead to the collapse of the shell; moreover, it appears to suddenly both increase and decrease the excitation frequency and is extremely violent. By observing experimentally a strong transfer of energy from low to high frequency a conjecture can be made about the nonlinear interaction among axisymmetric (directly excited) and asymmetric modes. A saturation phenomenon regarding the vibration of the top disk is observed, this is associated with the violent shell vibration; the shell behaves like an energy sink, absorbing part of the disk energy.
The theoretical model shows satisfactory agreement with experiments and clarifies the energy transfer mechanism from low frequency axisymmetric modes and high frequency asymmetric modes, confirming the conjecture arising by the experimental data analysis.
It is now clear that, in order to safely predict the response of a thin walled shell carrying a mass on the top, i.e. the typical aerospace problem for launchers, a nonlinear shell model is required, but it is not enough: further modelling regarding the shell mass interaction and the interaction between the shell and the excitation source is required.