Effects of Quadratic Nonlinearities on the Response of Individual Modes of Towed Cable Systems Under Tow Point Excitation

Underwater towed systems are very important to many marine applications. To date, many methods of analysis have been developed to simulate the dynamic behavior of these systems. The models that result from these methods can be separated into two categories - linear and nonlinear models. Linear models provide insight into the underlying system dynamics but only near steady- state configurations. Fully nonlinear models can simulate the dynamics of these systems undergoing arbitrary motions but produce equations of motion EOM that are very complex. This paper presents a methodology for understanding the first- order effects of the quadratic nonlinearities present in the DOM of nonlinear models. Specifically, the EOM produced by DYNTOCABS a computer program in use at the Coastal Systems Station are numerically reduced to form a set of equations that govern the modal response of the system to tow point excitation. The method of multiple scales is then used to analyze the effects of these nonlinearities on the response of individual modes. Results are given for two modes of a simple towed system. They suggest that out-of-plane modes respond linearly to out-of-plane excitations, while in-plane modes can respond in a relatively strong nonlinear fashion to in-plane excitations.