Introduction

The first step in planning response analysis is whether the analysis can be accomplished as a static one or whether a dynamic model must be used. Dynamic analyses are generally necessary in connection with transient loads; otherwise, the results may be significantly conservative or nonconservative. For load processes consisting of several harmonic components, the main criterion is whether the load process contains energy in the range of eigenfrequencies of the system. Figure 14.1 shows an overview of the largest eigenperiod (natural period) of vibration or motion of offshore structures, as well as the relevant range of periods of dynamic loads associated with waves.

Solution of Equations of Motion

General

The equations of motion for a linear structural system (Section 4.10)

may be solved in the time or frequency domain. The choice of formulation especially depends on:

• The nature of the loading; i.e., whether it is steady state or transient (which often involves response in a wide frequency band).

• Frequency dependence of the dynamic properties (mass, damping,

• Nonlinear features of the loading or dynamic properties.

In Chapter 2, solutions of the equation of motion for SDOF systems with different load conditions are described. If the solution method either in time or frequency domain is formulated for the coupled system of equations in Eq. (14.1), the method is denoted as direct.