Response of Variable Cross‐Sectional Members to Waves

Abstract

A method is described for solving transient responses of structural members of variable cross‐section subjected to wave forces. The member is divided into small segments andsthe transfer matrix and the Laplace transform method are applied to the equation of motion of the segments including fluid inertias. Since it is difficult to perform the Laplace transformation when the wave force is a complicated function of the time, the analysis utilizes the Fourier series expansion procedure to obtain the result for general dynamic loads, Then the transformed solution becomes a function of the coordinate of the position. The transfer matrix method derives the solution of the member by the combination of the solution of each segment which is expressed in terms of the Laplace transform parameter. The Laplace transform inversion integral transforms the solution in the image domain into the time domain when the residue theorem is applied. As an example, numerical calculations are carried out for the response of a circular variable cross‐section pipe in a fluid subjected to conoidal wave forces.