Multi-material additive manufacturing for the design and production of acoustic black holes

Abstract

Acoustic Black Holes (ABHs) are a passive vibration control treatment, which induce a reduction in wavespeed along the direction of wave travel through a reduction in mechanical impedance. This is most commonly implemented as a geometric taper, where the thickness of the host structure is reduced to induce the required impedance change. This realisation approach, however, leaves the ABH susceptible to high stresses due to the low thickness and high displacements, and subsequently leaves the system prone to damage. Functionally graded ABHs have also been proposed which instead vary the material properties along the direction of wave travel. Typically, a continuous grading of material properties is used to realise the ABH in a consistent way to the conventional geometric ABH taper. This work, however, investigates the potential of using a discretised gradient, which allows a multi-material ABH design to be produced using currently available multi-material inkjet printing techniques. 

The work presented in this thesis first investigates the viscoelastic behaviour of the inkjet printed materials that will be used in the production of the subsequent ABH designs. Additively manufactured materials are a relatively new class of material and so their behaviour is not as well studied as traditional engineering materials. Additionally, since the majority of prior applications have been focused on the static or low frequency behaviour of these materials, characterisation of the dynamic behaviour at higher frequencies is required. This thesis establishes a method of studying the response of additively manufactured polymers to varying excitation frequency and temperature conditions and performs an analysis of the Stratasys inkjet printed polymers to be used in the remainder of the thesis. The Stratasys polymers can be split into two families: flexible and rigid. The flexible family of materials are
found to exhibit viscoelastic behaviour and a parametrised model of this behaviour is obtained. The rigid family of materials is found to exhibit only linear elastic behaviour.

The characterised materials are subsequently used in the design and manufacture of inkjet printed ABHs. In the first instance, a study is carried out to evaluate the performance of inkjet printed geometric ABHs in a beam termination application. The
reflection coefficient, commonly used as a performance metric in the study of metal ABHs, is found to be unsuitable due to the high intrinsic loss of the materials, and the kinetic energy is found to be a more appropriate performance metric for the study of
vibration reduction in polymer ABHs. A study into the optimal ABH tip height and damping layer configuration is then performed on a polymer ABH through finite element modelling, considering both the kinetic energy of the host beam and the stress in the ABH taper. The kinetic energy modelling is validated experimentally.

The design and performance of a discretised multi-material ABH is also studied. Two methods of multi-material ABH design are investigated and compared; material property mapping to a continuous geometric ABH equivalent Young’s modulus profile, and optimisation of the material section lengths via an optimisation routine. These designs are investigated through finite element modelling before being validated experimentally. Their performance is also compared to the previously studied geometric ABHs, considering both the structural kinetic energy and stress. The multi-material ABHs are found to exhibit comparable kinetic energy reduction to the geometric ABHs discussed whilst experiencing significantly lower maximum stresses, suggesting a potentially much longer working life. Additionally, the material mapping method of designing the multi-material ABH provides kinetic energy reduction close to that achieved by the optimised multi-material ABH at a comparatively negligible computational cost.

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Identifiers

ORCID for Beth Austin: orcid.org/0000-0002-8995-8391

ORCID for Jordan Cheer: orcid.org/0000-0002-0552-5506

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