ABSTRACT
In this chapter, the response evolution of a marine riser is solved by path integration. First, the random vibration of the marine riser is studied by analyzing the environment around the riser, and its equation of motion is established by the Galerkin method, leading to a differential equation. Next, based on the differential equation, the path integration method is employed to study the evolution of the response of the probability density function (PDF). In the path integration procedure, the transition PDF is approximated by a short-time Gaussian PDF. The integration is conducted by the Gauss-Legendre scheme. A further parametric analysis is conducted on the effects of different parameters on the marine riser. The PDF evolution of the response is discussed in detail for the marine riser. When geometric nonlinearity is slight, the PDFs are roughly Gaussian, but displacement and velocity both have softening behaviors on their tail PDF region, compared to the PDF distribution of equivalent linearization (EQL). When geometric nonlinearity becomes strong, displacement has a hardening PDF distribution, whereas velocity has a softening PDF distribution. Furthermore, their PDF distributions are not symmetrical, and velocity has a more significantly non-symmetrical distribution.
