  In this paper we present the study of the mathematical model of a real life
joint used in an underwater robotic fish. Fluid-structure interaction is
utterly simplified and the motion of the joint is approximated by D\"uffing's
equation. We compare the quality of analytical harmonic solutions previously
reported, with the input-output relation obtained via truncated Volterra series
expansion. Comparisons show a trade-off between accuracy and flexibility of the
methods. The methods are discussed in detail in order to facilitate
reproduction of our results. The approach presented herein can be used to
verify results in nonlinear resonance applications and in the design of
bio-inspired compliant robots that exploit passive properties of their
dynamics. We focus on the potential use of this type of joint for energy
extraction from environmental sources, in this case a K\'arm\'an vortex street
shed by an obstacle in a flow. Open challenges and questions are mentioned
throughout the document.
