The asymptotic behaviour of second-order stochastic Volterra series models of slow drift response

The paper presents a detailed study of the structure and asymptotic behaviour of a second-order stochastic Volterra series model of the slow drift response of large volume compliant offshore structures subjected to random seas. A long standing challenge has been to develop efficient and accurate methods for calculating the response statistics of compliant offshore structures to random seas. Recent work has revealed that the statistical properties of the response process, which consist of a linear, first-order component and a nonlinear, second-order component, is surprisingly complex. The goal of the research work presented here is to complement efforts to develop numerical procedures to calculate the statistics of the response process.

[1]  Achintya Haldar,et al.  Uncertainty modeling in vibration, control and fuzzy analysis of structural systems , 1997 .

[2]  Robin S. Langley.  A statistical analysis of low frequency second-order forces and motions , 1987 .

[3]  A. Naess.  STATISTICAL ANALYSIS OF SECOND-ORDER RESPONSE OF MARINE STRUCTURES , 1985 .

[4]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[5]  Pol D. Spanos,et al.  Stochastic response of MDOF wind-excited structures by means of Volterra series approach , 1998 .

[6]  Stewart McWilliam,et al.  A statistical analysis of first and second order vessel motions induced by waves and wind gusts , 1993 .

[7]  M. Kac,et al.  On the Theory of Noise in Radio Receivers with Square Law Detectors , 1947 .

[8]  Hans Christian Karlsen,et al.  Numerical calculation of the level crossing rate of second order stochastic Volterra systems , 2004 .

[9]  T Vinje.  ON THE STATISTICAL DISTRIBUTION OF SECOND-ORDER FORCES AND MOTION , 1983 .

[10]  Arvid Naess,et al.  Numerical methods for calculating the crossing rate of high and extreme response levels of compliant offshore structures subjected to random waves , 2006 .

[11]  Stewart McWilliam,et al.  EXTREME VALUES OF FIRST- AND SECOND-ORDER WAVE-INDUCED VESSEL MOTIONS , 1993 .

[12]  Arvid Naess.  The response statistics of non-linear, second-order transformations to Gaussian loads , 1987 .

[13]  A. Naess,et al.  An Efficient Numerical Method for Calculating the Statistical Distribution of Combined First-Order and Wave-Drift Response , 1992 .

[14]  Ahsan Kareem,et al.  DYNAMICS OF NONLINEAR STOCHASTIC SYSTEMS: A FREQUENCY DOMAIN APPROACH , 1997 .

[15]  A. Naess.  THE STATISTICAL DISTRIBUTION OF SECOND-ORDER SLOWLY VARYING FORCES AND MOTIONS , 1986 .

[16]  G. Karami.  Lecture Notes in Engineering , 1989 .

[17]  A. Naess.  Statistical analysis of nonlinear, second-order forces and motions of offshore structures short-crested random seas , 1990 .