Stochastic response of articulated leg platform in probability domain

The probability density function (PDF) of the nonlinear response of an articulated leg platform (ALP) is obtained using stochastic averaging procedure together with weighted residual error minimization technique. Since stochastic averaging procedure is strictly applicable for weak (small size) excitations and damping functions, the error minimization technique has been employed to take into account the size effect which arises in practical problems like ALP. The application of the method to articulated leg platform also requires relative velocity squared drag force to be expressed in a manner which allows stochastic averaging procedure to be used. The procedure uses random Van-der-Pol transformation, FPK equation and Itoˆs equation of limiting diffusion process assuming the response to be slowly converging to diffusive Markov process. The computation scheme is developed using FFT to obtain the averaged drift and diffusion coefficients of the Itoˆs equation. An articulated tower with variable buoyancy chamber in a water depth of 141 m is analyzed for a random sea state represented by the Pierson–Morkowitz (P–M) spectrum having 16 and 8 m significant wave heights. The tower is idealized as a SDOF system with the rotation ( φ ) of the tower at the base hinge as unknown. The PDF of the angular rotation ( φ ) and the joint PDF ( φ , φ ̇ ) are obtained and compared with those derived from the simulation analysis. A 20 min sea state corresponding to the P–M spectrum is simulated for this purpose. It is shown that the procedure provides results which compare very well with those obtained from the simulation analysis