Modal Analysis of the Ice-Structure Interaction Problem
In the present study, the author builds upon the single degree of freedom ice-structure interaction model initially proposed by Matlock, et al. (1969, 1971). The model created by Matlock, et al. (1969, 1971), 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 ice-structure interaction phenomena, it was critical that this study set out to develop a multi-mode forced response for the pier when a moving ice floe makes contact at a specific vertical pier location. Modal analysis is used in which the response of each mode is superposed to find the full 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 this model, the physical system is a bottom supported pier modeled as a cantilever beam. The frequencies at which vibration naturally occurs, and the mode shapes which the vibrating pier assumes, are properties which can be determined analytically and thus a more precise picture of pier vibration under ice loading is presented. 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 PoincarÃ© based analysis following on the research of Karr, et al. (1992) is employed to identify any periodic behavior of the system response. Recurrence plotting is also utilized to further define any existing structure of the ice-structure interaction time series for low and high speed floes. The intention of this work is to provide a foundation for future research coupling multiple piers and connecting structure for a comprehensive ice-wind-structural dynamics model.