Analysis of Coupled Electromechanical Oscillators by a Band-Pass, Reduced Complexity, Volterra Method

Nonlinear analysis of a typical electromechanical coupled oscillator is approached by using Volterra polynomial series representation for nonlinear systems. The problem is formulated in a band-pass framework, allowing the study of transmission of power and information over the same line from the excitation voltage source to the final electromagnetic transducer stage. An input-output, black-box, monochromatic identification technique is applied, in order to obtain a simple, yet nonlinear, small-signal model for the low-pass modulating envelope of the excitation. The small-signal model consists of a low-order static polynomial nonlinearity intermitted between two linear MA filters. The procedure is carried completely in the frequency domain. The most important of the advantages, offered by the proposed methodology, is that identification is performed by employing only the fundamental harmonic component of the response to single sinusoidal inputs of various frequencies and amplitudes that sweep the band and range of interest.

Modelling the Heave Response of Tension Leg Platforms Using the Volterra Series

Tension Leg Platforms (TLPs) are predominately used for deep water oil and gas production. The use of tendons creates a small amplitude, high cyclic response in the vertical plane (heave, roll and pitch). Under these conditions fatigue cracking becomes an important consideration. The amplitude of the vertical motion is minimised by ensuring the natural frequency of the TLP lies above the energetic part of the wave spectrum. However, due to non-linear wave loading effects, it is possible for waves to create an output at their sum-frequency, which may consequently equal the natural frequency of the platform. This phenomenon is more commonly known as ‘springing’. The Volterra method [1] is a technique used to model the behaviour of TLPs under these conditions. This approach quantifies the linear and non-linear (quadratic, cubic, etc) responses separately using transfer functions, which are determined from the input and output of the system. In this paper an orthogonalised Volterra series for use with both Gaussian and non-Gaussian input data is presented. The data used in the Volterra modelling was collected from tests conducted on a model TLP. The wave height and platform motion were measured at wave frequencies around one, a half and a third of the model’s heave natural frequencies. Both regular and irregular wave tests were performed to varying wave heights and frequencies. Using the Volterra method, the transfer functions were calculated up to the third order. Difficulties encountered due to the use of discrete data were identified and where possible their effects minimized. The results demonstrate clear evidence of springing, with dynamic amplification present at sum-frequencies close to the natural frequency of the platform for the non-linear responses.