Determination of Dynamic Characteristics of Offshore Platforms From Random Variables
Authors: Earle E.N. 
Published: December 2007

Earle, E.N., Member SPE-AIME, Shell Development Co., Houston, Tex.

Abstract
The dynamic response characteristics of three offshore production platforms have been determined. The technique used involves curve fitting to match a theoretical spectral-density function to the spectral-density function computed from measured random vibration. Results in the form of natural frequencies and damping are presented for the three structures. These results show that the damping in offshore platforms is about 3.5 percent of critical.

Introduction
Structures of all sizes and shapes are usually subjected to time-varying loads. These loads can be created by wind, waves, earthquakes, or machinery. The effect on the structure, its dynamic response, is of utmost importance to the design engineer since the dynamic response of a structure can exceed the static response by a significant factor. If a structure were to be loaded such that the frequency of the load was about equal to the natural frequency of the structure, the stresses in the members caused by the dynamic load would far exceed the stresses caused by the static load applied to the structure. The size of the dynamic stresses within the structure depends not only on the size of the external load, but also on the amount of damping of the structure. Theoretical methods are available for computing the natural frequencies and the dynamic response of various types of structures. These methods usually require that an estimate of the amount of damping be made to complete computations. For the typical deep-water offshore drilling platform, which is anchored to the ocean floor by piling, it would be desirable to know the actual damping in the structure and the structure's natural frequencies to compare with theoretical predictions or estimates. The approach used here to determine the actual damping and natural frequencies of an offshore platform involved acquiring random vibrations data platform involved acquiring random vibrations data from an offshore platform and developing a method to analyze these data.

DATA ACQUISITION
The data gathering system is shown in Fig. 1. Three three-dimensional geophones sensed the vibrations. The signals from these geophones were sent to an amplifier that amplified the signals. These signals were then fed to a tape recorder and were monitored on an oscilloscope during recording. Each of these elements are discussed in more detail below.

GEOPHONES
The geophones used were Geospace Corp. Model No. HS-10-1 LP-3D units. Each contains three separate one-dimensional units mounted along mutually orthogonal axes inside a pressure-tight case that keeps out moisture. Each unit consists of a heavy electrical coil that is spring mounted to the case in such a way that the coil tends to remain at rest when the case moves. The output of the coil is proportional to the velocity of the case at frequencies above the natural frequency of the spring mass system that consists of the coil and its mounting. Below this frequency, the output decreases with decreasing frequency. The natural frequency of the units used here is 1.0 Hz.
SPEJ
p. 502