Tuned mass absorber on a flexible structure

Balanced calibration of resonant piezoelectric RL shunts with quasi-static background flexibility correction

“…The inclusion of the influence from residual vibration modes by a quasi-static representation has previously been suggested for calibration of resonant active control strategies [32], and used for damping of edgewise vibrations of wind turbine blades [33] and rotors [34]. A more rigorous procedure for including the effect of the non-resonant modes as a local flexibility between the absorber and the structure was recently developed by Krenk and Høgsberg [35].…”

Resonant passive–active vibration absorber with integrated force feedback control

“…As demonstrated in [25,26] the influence of spill-over from nonresonant modes can be represented by the extended modal representation…”

“…This explicit parameter calibration is also directly applicable for the tuned inerter damper considered in [6], with optimal absorber location being the only difference to the tuned mass damper [25]. For the pure passive absorber the inertia in H q (ω) = −ω 2 m q is realized by a mechanical inerter element, while for the active realization the control equation G q (ω) = −ω 2 m q contains a double integration of the measured absorber force, which might be sensible to actuator saturation from low-frequency sensor input [29].…”

Explicit solution for the natural frequency of structures with partial viscoelastic treatment

“…With respect to design considerations it is therefore reasonable to extend this property to general relaxation models, whereby optimality is only determined by the first term in Eq. (19) (20) where the latter approximation is again based on the assumption that the real part of the generalized parameter η r is negligible. The accuracy of this condition is demonstrated in the numerical example, considered next.…”

“…This type of correction term is commonly applied in numerical analysis for effective truncation of series expansions [17][18][19]. But recently this approach has also been used in [20,21] to derive accurate calibration formulae for resonant vibration damping of flexible structures. A compact solution format for the complex-valued natural frequency of the resonant vibration mode is derived from the scalar equations of motion, and an optimality condition is finally formulated for maximum damping of the flexible structure.…”