To achieve the desired research objectives, four work packages were performed,
Work package 1: design of negative stiffness inclusions and nonperiodic rainbow oscillators in composite metamaterial structures: Composite metamaterial structures with negative and positive stiffness oscillators were designed in this work package. A multilayered sandwich structure was proposed with negative stiffness nonlinear inclusions constituted of two buckled Euler beams and an oscillating mass to improve their structural vibration absorption performance. Such negative stiffness element has been investigated as single degree of freedom isolation mechanisms for mechanical systems with grounding, it was for the first time implemented in multilayered structures. Besides, most of the existing metamaterials are periodic structures, although the periodic metamaterials can obtain good vibration attenuation within bandgap regions, the width of bandgaps is still narrow for practical applications. Nonperiodic metamaterial beams and lattice structures were therefore developed in this project for the purpose of achieving broader energy stop bands. The metamaterial beams were composed of Π-shaped beams partitioned into substructures by plates insertions and nonperiodic cantilever-mass resonators, and 2D/3D nonperiodic metamaterial lattice were designed based on cuboid blocks with varying masses connected by curved beams.
Work package 2: modelling the dynamic properties of the proposed composite metamaterials: The multilayered sandwich structures with negative stiffness resonators was modelled through solid, linear brick finite elements (FEs) with nonlinear spring-mass dampers being implemented to simulate the behavior of the negative stiffness nonlinear oscillators within each unit cell. The structural response was computed through an explicit time domain solution employing the ANSYS platform. With regard to the metamaterial beams with nonperiodic rainbow resonators, an analytical model was set up on the basis of the transfer matrix method to determine the structural dynamics. The Frequency response functions of the 2D/3D metamaterial lattices were also calculated by the FE approach, linear hexahedra elements were employed for modelling the geometry of the structures.
Work Package 3: Optimal design of structures having negative stiffness and positive nonperiodic resonators: An optimization scheme was developed by virtue of the Genetic Algorithm to optimize the oscillator distributions in the metamaterial structures. For the purpose of improving the vibration attenuation at frequencies of interest, two optimization strategies were proposed that invoked two objective functions respectively. The objective functions were defined based on maximum receptance function value or average receptance function value within the prescribed frequency ranges. Receptance function values within the prescribed frequency range were expected to be small when their maximum value or average values remain low. Both the optimal strategies were found effective to enhance the vibration attenuation and broaden the bandgaps at frequencies of interest.
Work Package 4: Manufacturing and testing of the optimal design: The designed metamaterial structures were manufactured by Sintered laser sintering technology with Nylon-12 powder. The printed metamaterial beams and lattice structures were tested with an experimental system which consisted of a mechanical shaker employed to excite the structures, an impedance head to measure the excitation forces and a Doppler vibrometer to measure the vibrational displacements at sampling points. The measured results were found to have good agreement with the numeral modelling results.
Dissemination: To attract significant attention from the ‘Composite lightweight Structures’, ‘Metamaterials’ and the‘Wave Propagation’ scientific communities, the project results were disseminated via:
- International Conferences: participation in high-calibre international conferences to deliver the results to the industrial and academic sectors
- Publications in top-ranked (according to their SNIP index) international journals such as “Scientific reports”, ‘Mechanical Systems and Signal Processing’, ‘Journal of Sound and Vibration’, etc. All produced journal publications as well as conference proceedings provide green open access to the public through the UNOTT website repository (https://nottingham- repository.worktribe.com/).
- The open-source Ansys files of simulation models and computation method of the rainbow metamaterials were submitted along with the article as supplementary files (
https://doi.org/10.1016/j.dib.2019.104772(opens in new window)) which hence were easily shared and reused by other researchers.
- The research outcomes were also directly communicated to the Supervisor’s and the Researcher’s collaborators.
