應用Volterra模式分析高速船舶波中非線性反應之研究

Abstract

船舶高速航行於波浪中，其運動及壓力反應皆呈現非線性的行為，同時線性統計理論亦不足以對不規則波中的統計特性一窺全貌；另一方面，Volterra模式已被應用於船舶非線性運動時的統計特性分析。因此本文重點在探討高速船在波中運動時水壓所呈現的非線性特性，特別是在乾濕變換的水線附近及承受衝擊壓的艏底位置。為確立Volterra模式對水壓分析的有效性，進而規劃一系列以RD200船型為對象之曳航試驗，量測包含起伏及俯仰二個運動、加速度及船殼25點的水壓等項目，同時本文亦提出該模式所需之頻率響應函數的計算方式，並以三階及五階Volterra模式進行討論分析，其結果確立三階Volterra模式可充份掌握水壓在規則波中變化的非線性特性。此外更進一步的藉由非線性截片法在規則波中所建構之理論基礎，經由非線性Volterra模式所架構之平台，來評估該理論來預測不規則波統計特性之可行性。透過時域及分散譜比較，累進分布機率及機率密度函數等統計分析，驗證了該模式可掌握非線性及非高斯水壓變化的特性。

It is well known that the hydrodynamic responses of a high-speed vessel traveling in regular head waves even of moderate wave height can show significant nonlinear behavior, and so linear statistical techniques become insufficient for predicting the statistics of responses in irregular waves. On the other hand, it has been shown that an approximate third-order Volterra model is applicable to handling the statistics of some nonlinear seakeeping problems, such as motions and vertical hull girder loads. In the present study, the focus is on the nonlinear behavior of the pressure acting on the hull surface of a high-speed vessel in waves, especially on the pressure responses of alternately wet and dry areas near waterline and on the bow zone with high deadrise angles that may be subject to slight impact and water pile-up effects. To clarify the validity of applying Volterra modeling to this problem, a series of experiments in regular and irregular head waves are carried out, and approximate third-order and fifth-order Volterra models with proposed algorithm for finding frequency response functions (FRFs) were applied as a means of validation. It was confirmed that the approximate third-order Volterra model has adequate accuracy to simulate deterministically the variation of pressure responses in regular waves of different wave steepness up to a wave amplitude to wavelength ratio of 0.01 even for the highly nonlinear pressures acting on the above-mentioned areas of the hull surface. In additions, further validation was performed using experimental data and theoretical calculation in irregular waves. The frequency response functions (FRFs) obtained both from the experimental data or theoretical calculation in regular waves were applied to the approximate third-order Volterra model combining with the input of irregular waves to simulate deterministically the responses in irregular waves of sea state five, and then the spectra and statistics were analyzed. Through the comparisons of the simulated time histories, variance spectra, and statistics such as cumulative distributions of peak values, probability density functions with the experimental results of motions, accelerations and pressure responses in irregular waves, it was confirmed that the approximate third-order Volterra model has adequate accuracy to simulate deterministically and statistically the pressure responses in irregular head waves up to a sea state of five even for highly nonlinear and non-Gaussian pressures acting on the above-mentioned areas of the hull surface.