Feedforward control of bending waves in frequency domain at structural junctions using an impedance formulation

This paper presents an active impedance-matching technique for vibrating structures described by Euler–Bernoulli theory. Full 2 × 2 impedance matrices are included in the derivation of the reflection matrix of an arbitrary structural junction. This implies that the effects of both bending waves and bending near-fields are included. An active impedance load is introduced in order to match a discontinuity at the junction, i.e. to force the reflection matrix to zero. The impedance-matching technique is applied to two theoretical examples. First, maximum power transfer at a free end is investigated under the condition of incident bending wave and bending near-field; second, the approach is used to match the junction between an Euler–Bernoulli beam and a sandwich composite for an incident bending wave. The latter example proposes an active–passive damping configuration which employs active control to enclose all incident wave power in a dissipative sandwich-type structure. Results show that for this configuration, the active impedance load is responsible for the main part of the power absorption over a broad frequency range.