Modal Analysis of the Ice-Structure Interaction Problem

In this paper the authors present a multimode ice-structure interaction model based on the single degree of freedom ice-structure interaction model initially proposed by Matlock et al. (1969, “A Model for the Prediction of Ice-Structure Interaction,” Proceedings of the First Offshore Technology Conference, Houston, TX, Vol. 1, pp. 687–694, Paper No. OTC 1066; 1971, “Analytical Model for Ice Structure Interaction,” ASCE Journal of the Engineering Mechanics Division, EM4, pp. 1083–1092). The model created by Matlock et al. assumed that the primary response of the structure would be in its fundamental mode of vibration. In order to glean a greater physical understanding of the ice-structure interaction phenomena, it was critical that this study set out to develop a multimode forced response for the pier when a moving ice floe makes contact at a specific vertical pier location. Modal analysis is used in this study, in which the response of each mode is superposed to find the complete modal response of the entire length of a pier subject to incremental ice loading. This incremental ice loading includes ice fracture points as well as loss of contact between ice and structure. In the work of Matlock et al., the physical system is a bottom supported pier modeled as a cantilever beam. Realistic conditions such as ice accumulation on the pier modeled as a point mass and uncertainties in the ice characteristics are introduced in order to provide a stochastic response. The impact of number of modes in modeling is studied as well as dynamics due to fluctuations of ice impact height as a result of typical tidal fluctuations. A Poincaré based analysis following on the research of Karr et al. (1992, “Nonlinear Dynamic Response of a Simple Ice-Structure Interaction Model,” Proceedings of the 11th International Conference of Offshore Mechanics and Arctic Engineering, Vol. 4, pp. 231–237) is employed to identify any periodic behavior of the low and high velocity ice system responses. Recurrence plotting is also utilized to further define any existing structure of the ice-structure interaction time series for low and high speed ice floes. While the Matlock model on which this research is based is admittedly simplistic, the intention of this work is to provide a foundation for future work using time series analysis and modal analysis on more sophisticated models coupling multiple piers and connecting structure for a comprehensive ice-wind-structural dynamics model.