A method for adapting existing earthquake response spectrum techniques to the analysis and design of offshore structures is presented. The offshore structure is modeled as a lumped parameter system and a nonlinear fluid resistance law is assumed. The nonlinear hydrodynamic drag effects are approximated satisfactorily by a linearizing technique except for the high frequency portion of the response spectrum where a special relation is shown. Rules are given for the construction of approximate earthquake response spectra using design estimates for the maximum values of ground displacement, velocity, and acceleration and certain characteristics of the structure. With the procedures set forth in this paper, earthquake response spectra that include fluid inertia and drag effects can be developed and used for offshore structures, and much of the information already available on response spectrum techniques for land-based structures can easily be adapted for use by designers of ocean structures. Examples are given of the application of the method to offshore structures.
Earthquake response spectra are used extensively in the design of land-based structures to resist lateral forces associated with earthquake motions. However, the use of response spectra directly in the design of offshore structures is hindered by the effects of fluid-structure interaction. If the effects of fluid-structure interaction can be satisfactorily accounted for in such a manner that response pectra techniques can be extended to the design of offshore structures, then the wealth ofresponse spectrum information that is presently available for land-based structures can be used by designers of ocean structures.
In this paper, an offshore structure is modeled as a lumped-parameter multi degree of freedom system as shown in Fig. 1. The hydrodynamic forces acting at each node as the system moves through the surrounding fluid are considered to be those computed from Morison's equation and include nonlinear hydrodynamic drag forces. It is noted that the energy dissipated by waves created at the surface as the structure moves through the water is not included in this formulation. These nonlinear forces will be linearized in such a manner as to ensure the existence of classical normal modes 2 in the linearized equations of motion and each resulting modal equation will contain an equivalent linear hydraulic damping coefficient. Procedures will then be given for the construction of an approximate earthquake elastic displacement response spectrum (which includes the effects of fluid-structure interaction) for each mode of vibration in the system.
The procedures presented in this paper were developed by comparing computer solutions of the nonlinear equations of motion with computer solutions of the linearized equations of motion using actual earthquake records. 3
