This paper presents a study on the tuning of vibration absorbers and Helmholtz resonators
used to control at target resonance frequencies respectively the flexural response of lightly
damped distributed structures and the acoustic response of lightly damped cavities subject
to broadband stochastic excitations. The vibration and acoustic control effects of these two
devices are assessed considering the broadband flexural response and acoustic response of
typical structures and enclosures encountered in practical applications, that is: beam, thin
plate and thin walled cylinder structures and one-dimensional duct, two-dimensional
slender volume, three-dimensional volume enclosures. The herein proposed multi-mode
tuning approaches are based on the H2 cost functions of the total flexural kinetic energy
of the three structures and of the total acoustic potential energy of the three enclosures.
The H2 cost functions are defined within finite frequency bands centred at the target
structural or acoustic resonance frequencies respectively. A comprehensive overview of the
modal density and modal overlap functions for the flexural response of the three structures
and for the acoustic response of the three enclosures is also presented to provide
physical interpretations and practical guidelines on the performance and applicability of
classical single-mode and the proposed multi-mode tuning approaches. The study shows
that classical tuning laws can be straightforwardly employed to control the response at low
resonance frequencies such that the modal overlap is not greater than one, whereas to
control the response at higher resonance frequencies, where the modal overlap is significantly
greater than one, the proposed multi-mode tuning approach should be adopted.
