Dynamic Analysis and Design of Offshore Structures by Srinivasan Chandrasekaran

Author:Srinivasan Chandrasekaran
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(3.94)

Substituting {x} = {X} sin ωt, we get

(3.95)

The above equation is rewritten as

(3.96)

Equation (3.96) is of the following form:

(3.97)

Iterative process is started by assuming a set of displacements for the right column of Eq. (3.97) and then expanding the right-hand side which results in a column of numbers. This is then normalized and compared with the new obtained value of the displacement vector. The procedure is repeated until the new set of displacements converges with that of the previous step of iteration. The iteration process with the use of Eq. (3.97) converges to the lowest value of (1/ω 2) so that the fundamental mode of vibration is obtained. For next higher modes and natural frequencies, Orthogonality principle is applied to obtain a modified matrix that is free from the lower modes.

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