A structural escape from Dr Hydroelastic Chen
As an opening, Chen showed to everyone two short videos, comparing the motion of a rigid body in sinusoidal waves and the deflection of an elastic one. Bearing those images in mind, we saw him walked to the whiteboard, continuing his presentation. The main features for a submerged elastic body are slenderness (i.e. L/D>30) and uneven loading, as Chen pointed out. Then, he turned to the structure’s motion of equation, assuming small deflection, from which we can calculate mode shape and natural frequency. From a physics point of view, the deflection of an elastic body can be seen as the superposition of various factored mode shape. The question is how to impose fluid force into this equation? The presumption is that the water particular is non-rotational, incompressible, non-cohesive, and the amplitude of wave height is small (airy wave). In old age, when the computer was less-capable, mathematician(s) further discretised the potential field of water into radiation, diffraction, and incident. Besides, a force-matrix representing the static water restored force is needed. Incorporating those four equations and the boundary conditions into the equation of motion of structure in respect to a specific natural frequency yields the generalised equation of motion of a structural system of one mode shape, analogous to an equation of motion with a single degree of freedom (DOF). Dr Chen noted that the extra efforts for solving a hydroelastic problem than a rigid body problem are the force due to the elastic restoration of structure and structure’s boundary condition. He presented two states of art research concerning the simulation of the boundary between the fluid and the deformed structure. Chen mentioned two case examples; one is Yumeshima-Maishima floating bridge. The comparison showed that the elastic model revealed a twist DOF which the rigid body model cannot observe. The calculation of a bulk carrier showed a similar tendency.
During the presentation, I turned my head to the left where SDJT members sat. I cannot help notice the glowing faces lined in red, asking questions and received satisfied answers from Chen. The scenery refreshes the memory of——if recalled correctly——Kuhn’s writing the structure of science where “paradigm shifts” was used for the first time. The same thing occurred in this short twenty minutes presentation again as Chen managed to guide our eight structural engineer researchers to look at another direction, i.e. no longer structural centred view. That is no doubt good, and particularly true for the submerged “submerged floating tunnel”.