Immersed cylinder piles are usually modelled as immersed cantilever cylinder columns carrying a tip mass and rotary moment of inertia.In this paper,the equations of motion of an immersed cylinder pile along transversal modes of vibration are developed.Compressibility of water and structural damping are included in the formulation.Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses.The proposed method is applied to numerical examples,and the results obtained are shown satisfactory when compared to other numerical solutions in the literature,or to finite element solutions and experimental data.
Kai WeiWancheng YuanNajib BouaananiChih-Chen Chang
For the dynamic demand assessment of bridge structures under ship impact loading,it may be prudent to adopt analytical models which permit rapid analysis with reasonable accuracy.Herein,a nonlinear dynamic macro-element is proposed and implemented to quantify the demand of bridge substructures subjected to ship collisions.In the proposed nonlinear macro-element,a combination of an elastic-plastic spring and a dashpot in parallel is employed to describe the mechanical behavior of ship-bows with strain rate effects.Based on the analytical model using the proposed macro-element,a typical substructure under 5000 deadweight tonnage(DWT) ship collision is discussed.Our analyses indicate that the responses of the structure using the nonlinear macro-element agree with the results from the high resolution model,but the efficiency and feasibility of the proposed method increase significantly in practical applications.Furthermore,comparisons between some current design codes(AASHTO,JTGD60-2004,and TB10002.1-2005) and the developed dynamic analysis method suggest that these design codes may be improved,at least to consider the effect of dynamic amplification on structural demand.
