Synthesis of multi-input Volterra systems by a topological assemblage scheme

The Volterra series expansion is widely employed to represent the input-output relationship of nonlinear dynamical systems. Such a representation is based on the Volterra frequency-response functions (VFRF), which can be calculated from the equation governing the system by the so-called harmonic probing method. This operation is straightforward for simple systems, may reach a prohibitive level of complexity for multiple-input systems when the calculation of a high-order VFRF is required. An alternative technique for the evaluation of the VFRFs of multiple-input systems is here presented generalizing an existing technique originally limited to the scalar case. A 2-dof mechanical example is used to illustrate the application of the technique.