Development of a Dynamic Directional Amplification (DDA) Mechanism

by Antonios Mantakas and Moris Kalderon

Antonis Mantakas (ESR07) is working in collaboration with Moris Kalderon (ESR15) in the development of a simple dynamic directional amplifier (DDA) which is introduced as a means to increase the effective mass of an MCK oscillator. The DDA mechanism is realized without additional masses or complex geometries since the amplification can be achieved by coupling the kinematic DoFs of the resonating mass with a rigid link, improving inertia and damping on the desired direction of motion. The main aim of the study is to illustrate, via the use of a formal mathematical framework, numerical modelling as well as physical testing that we can enhance the performance of LR structures while retaining or even improving the practical constraints such as having compact, lightweight, and buildable unit-cells. The mechanism may be incorporated in applications such as sound and vibration isolators, or acoustic panels, as well as in phononic and locally resonant metamaterials as a way to improve their filtering properties. The concept along with the experimental setup is illustrated in Fig 1.

Figure 1: (a) Schematic representation of the dynamic directional amplification (DDA) mechanism, where the motion v of mass m is kinematically constrained to the motion u, at deformed state, and (b) physical model of the mechanism at the Dynamics & Structures Laboratory of NTUA.

The mechanism is subsequently implemented as a means to increase the resonating mass of an LRM structure artificially. Towards this goal, a mass-in-mass model is adopted, and a preliminary parametric analysis is performed using both Bloch’s theory on two-dimensional infinite lattices and conventional vibration theory on finite lattices. A numerical example is studied as a seismic mitigation application in order to highlight the advantages of the proposed arrangement. To this end, a conceptual design of a seismic metamaterial in the form of a metabarrier is proposed and an investigation of its response under seismic excitation is analyzed. Results indicate the beneficial role of the device and DDA mechanism, hence placing the concept as a compelling alternative to existing seismic protection technologies. The proposed DDA metabarrier along with its frequency response is illustrated in Fig 2.

Figure 2: (a) Application of a DDA enhanced LRM metabarrier a seismic mitigation measure, and (b) comparison of the FRF between a conventional LRM metabarrier and a DDA-LRM metabarrier.

It is demonstrated that using dynamic amplification and a moderate number of unit-cells, relatively deep bandgaps at low frequencies can be obtained. By exploiting the dynamic mass of the proposed mass-in-mass periodic structure, it is illustrated that better dispersion properties are obtained compared to the conventional locally resonant metamaterials of equivalent structure. Thus, significant filtering characteristics are achieved while reducing the large parasitic resonating masses.

Currently, Moris and Antonis are working together to finalize the experimental design of a simple DDA mechanism that will validate the numerical and analytical results of the study. The concept will be subsequently tested in phononic and locally resonant metamaterial structures.

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