Stochastic analysis of the nonlinear dynamics of oscillating water columns: A frequency domain approach

Abstract

This paper investigates the first and second-order stochastic responses of oscillating water columns (OWCs) under random waves. The OWCs’ nonlinear dynamics are computed in the frequency domain, where sources of nonlinearities are replaced by equivalent polynomial terms up to second order by minimising their difference in a mean-square sense. This procedure is known as the statistical quadratisation (SQ) technique. In such an approach, the linear and quadratic coefficients are obtained using an iterative procedure and non-Gaussian distributions based on Gram–Charlier expansions, and the dynamics are solved using the Volterra theory. The results are compared against a statistical linearisation model (SL), and nonlinear time-domain simulations (TD) to illustrate the capabilities of the method. The result demonstrated an excellent agreement for the first and second-order motions of the water column obtained using statistical quadratisation compared to nonlinear time-domain simulations in terms of spectral response and probability distribution. Along with the good accuracy, the statistical quadratisation has the advantage of being approximately two orders of magnitude faster than nonlinear time-domain simulations. For the proposed systems, the nonlinearity from the variable mass system (inertial type) is shown to be the most important source of second-order effects driving the oscillating water column dynamics based on the environmental conditions and drafts investigated in this work.