A New Numerical Scheme with B-Spine Wavelet on the Interval for Transverse Vibration Problem of the Tethered Deep-Sea Robot

Abstract

This research is focused on the accurate modeling of a tethered deep-sea robot system with variable-length. Since the flexible umbilical cable is influenced by the surface vessel motion, the ocean current and sea states, etc., its transient response will reduce the deep-sea robot’s stability. Thus, dynamic modeling of the elastic umbilical cable is a crucial issue. In this paper, transverse vibration of the tethered deep-sea robot system can be modelled as a one-dimensional distributed parameter system, a class of partial differential equations with nonhomogeneous boundary conditions theoretically. A new numerical scheme with B-spine wavelet on the interval (BSWI) is used to discretize and transform inhomogeneous partial differential equations into a set of ordinary differential equations and to obtain the dynamic response of the tethered deep-sea robot system with different ocean currents. Compared with conventional methods, BSWI finite element with multiresolution analysis principle can approximate the transverse vibration of the flexible umbilical cable better, and handle boundary conditions more easily. Numerical examples of different cases are analyzed in detail by the discussion of an ADAMS model, and simulation results of the ADAMS model also verify that BSWI finite element method has a desirable performance than other methods.