The nonlinear dynamic behaviour in an alongside berth mooring arrangement

  • Pedro W. F. BarrosEmail author
  • Carlos E. N. Mazzilli
Technical Paper


Determining the forces acting upon wharf structures due to moored ships requires the analysis of a dynamic nonlinear system. Such system owes its complexity to the body–fluid (ship and water) interaction and to the discontinuity in stiffness caused by the impact with the fenders. As a means of simplification, these mooring forces are usually calculated in static models that consider only three modes of movement (surge, sway and yaw), and in order to account for the dynamic behaviour of the system, the active forces applied in the static analysis are multiplied by amplification factors. Nevertheless, information that provides adequate values of these amplification factors is scarce, and further studies on the behaviour of such dynamic system are necessary. In this paper, a nonlinear static model of an oil tanker in an alongside berth mooring arrangement is adapted to a one-degree-of-freedom dynamic model depicting the sway mode, by using Bathe’s numerical time integration algorithms. The analysis of this system is carried out, and its results are compared with analytical models of bi-linear oscillators and impact oscillators as a means of validation. Non-unique solutions are seen to be possible, which pose relevant questions regarding the state of the art of wharf structure design.


Ship mooring Bi-linear oscillator Impact oscillator 



The second author acknowledges the support of the Brazilian National Council of Research (CNPq) under Grant 32757/2013-9.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Escola Politécnica da Universidade de São PauloSão PauloBrazil

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