Periodic Reporting for period 1 - METASINK (Nonlinear Energy Sink Metamaterial Approaches for Flow-Induced Vibration Attenuation)
Reporting period: 2020-10-01 to 2022-09-30
This project aimed at exploiting the nonlinearity, damping, material/geometrical periodicity, and topological phenomena in mechanical lattice structures for simultaneous fluid-flow-induced vibration attenuation and energy harvesting purposes. The main focus was on metamaterials and phononic-like structures in their mechanical setup having periodic architecture such that they possess unique wave propagation and topological properties. A mathematical model based on cubic nonlinear stiffness and fractional-order damping were suggested to study wave propagation in a periodic lattice chain. The proposed approach enabled a study of the effects of nonlinearity and fractional damping on dispersion characteristics and band gaps capable of stopping the waves at certain frequency ranges.
Exotic topological phenomena can be also found in mechanical metamaterials inducing localized edge/interface states that are robust to defects and disorders in the lattice. In this project, we proposed one such phononic-like lattice based on elastically coupled beam elements having multiple existing interface modes. Properties of conventional lattices were extended through the application of inerter elements. The project develops computational analytical models to better understand the behavior and tunability of topological properties of such enhanced mechanical lattices. A step forward in this direction was the introduction of periodic and quasi-periodic inerter-based locally resonant lattices with emerging interface modes in the sub-wavelength range. The inerter elements were shown to be capable of tuning interface modes frequencies without changing their main topological properties. The effect of viscous damping was examined showing a significant effect on the amplitude of the localized interface mode. Moreover, uncertainty quantification of inerter-based locally resonant quasi-periodic lattices demonstrated the existence of multiple robust edge modes that can be utilized for energy harvesting.
Remarkable wave propagation properties were discovered in the suggested novel design of two-dimensional lattices with curved beam elements. The Bloch wave analysis based on equivalent unit cell architecture revealed the newly emerged band gaps for increasing curvature angle when compared to the conventional hexagonal- and auxetic-like lattices. Directional wave propagation was also identified showing the high potential for the appearance of the phenomena such as lensing and wave beaming.
Exotic topological phenomena can be also found in mechanical metamaterials inducing localized edge/interface states that are robust to defects and disorders in the lattice. In this project, we proposed one such phononic-like lattice based on elastically coupled beam elements having multiple existing interface modes. Properties of conventional lattices were extended through the application of inerter elements. The project develops computational analytical models to better understand the behavior and tunability of topological properties of such enhanced mechanical lattices. A step forward in this direction was the introduction of periodic and quasi-periodic inerter-based locally resonant lattices with emerging interface modes in the sub-wavelength range. The inerter elements were shown to be capable of tuning interface modes frequencies without changing their main topological properties. The effect of viscous damping was examined showing a significant effect on the amplitude of the localized interface mode. Moreover, uncertainty quantification of inerter-based locally resonant quasi-periodic lattices demonstrated the existence of multiple robust edge modes that can be utilized for energy harvesting.
Remarkable wave propagation properties were discovered in the suggested novel design of two-dimensional lattices with curved beam elements. The Bloch wave analysis based on equivalent unit cell architecture revealed the newly emerged band gaps for increasing curvature angle when compared to the conventional hexagonal- and auxetic-like lattices. Directional wave propagation was also identified showing the high potential for the appearance of the phenomena such as lensing and wave beaming.
Month 1-5: The research started with the investigation of a novel type of phononic-like discrete-continuous system constituted of multiple slender beam structures couped through elastic layers made of springs with alternating stiffnesses. Interesting topological interface modes immune to defects and disorders in the lattice were detected based on the dispersion and eigenfrequency analysis of the proposed lattice system. We also proposed the integration of discrete inerter elements into the beam array system capable of tuning the interface mode frequencies through the inertia amplification effect. The system is shown to be suitable for both attenuations of waves within the band gap frequency range and energy harvesting from localized interface modes. One journal paper was prepared from this part of the research and published in a peer-reviewed journal.
Month 6-12: We have proposed a locally resonant lattice system that exhibits multiple topologically protected interface modes in lower and higher frequency band gaps. The topological invariant Zak phase was calculated for each of the band gaps. The eigenfrequencies and frequency response function were determined for the finite lattice system to confirm the existence of interface modes. Further, we investigated the effects of nonlinear spring and fractional-order damping on wave propagation in the discrete monoatomic types of periodic lattices. Multiple-scales perturbation method was modified to solve fractional-order differential equations and obtain dispersion characteristics of the nonlinear lattice. The effects of nonlinearity and fractional damping parameters on dispersion curves were investigated. These results were published in conference proceedings.
Month 13-18: Part of the research plan was to continue the work in the field of topological lattices with local resonators by extending the model to achieve better tunability and consideration of damping and a corresponding analysis of wave propagation and topological properties. The main results towards improved tunability were obtained by introducing the inerter elements into the lattice capable of shifting the interface mode frequencies to lower values only by increasing the inertance. It was revealed that inerters are not affecting the topological properties of the lattice. Based on the finite lattice model, we have shown that arbitrary viscous damping is reducing the interface mode amplitude where this effect is even more pronounced for a larger number of unit cells in the lattice and higher values of damping. Part of the obtained results was presented in one conference while another part was published as a peer-reviewed research article.
Month 19-24: In this period, part of the research was devoted to the uncertainty quantification of inerter-based quasiperiodic discrete lattice systems. Here, quasiperiodic modulation of stiffness and inertia properties of the lattice was proposed to achieve unique band gaps crossed with a number of edge modes. Both deterministic and stochastic Hofstadter butterfly and bulk spectra were mapped to demonstrate the existence of band gaps and edge modes for different levels of uncertainty. The Gaussian process model was developed and compared against Monte Carlo simulations in order to achieve faster computation of the stochastic model. This lattice design is shown to be promising from the viewpoint of future applications in mitigating fluid-flow-induced vibration containing multiple frequencies and vibration modes. The full research paper prepared from this part of the research is currently under review. Another part of the research included the investigation of the band structure and directional wave propagation in two-dimensional hexagonal- and auxetic-like lattices with curved beam elements. This research was published in a peer-reviewed journal.
Month 6-12: We have proposed a locally resonant lattice system that exhibits multiple topologically protected interface modes in lower and higher frequency band gaps. The topological invariant Zak phase was calculated for each of the band gaps. The eigenfrequencies and frequency response function were determined for the finite lattice system to confirm the existence of interface modes. Further, we investigated the effects of nonlinear spring and fractional-order damping on wave propagation in the discrete monoatomic types of periodic lattices. Multiple-scales perturbation method was modified to solve fractional-order differential equations and obtain dispersion characteristics of the nonlinear lattice. The effects of nonlinearity and fractional damping parameters on dispersion curves were investigated. These results were published in conference proceedings.
Month 13-18: Part of the research plan was to continue the work in the field of topological lattices with local resonators by extending the model to achieve better tunability and consideration of damping and a corresponding analysis of wave propagation and topological properties. The main results towards improved tunability were obtained by introducing the inerter elements into the lattice capable of shifting the interface mode frequencies to lower values only by increasing the inertance. It was revealed that inerters are not affecting the topological properties of the lattice. Based on the finite lattice model, we have shown that arbitrary viscous damping is reducing the interface mode amplitude where this effect is even more pronounced for a larger number of unit cells in the lattice and higher values of damping. Part of the obtained results was presented in one conference while another part was published as a peer-reviewed research article.
Month 19-24: In this period, part of the research was devoted to the uncertainty quantification of inerter-based quasiperiodic discrete lattice systems. Here, quasiperiodic modulation of stiffness and inertia properties of the lattice was proposed to achieve unique band gaps crossed with a number of edge modes. Both deterministic and stochastic Hofstadter butterfly and bulk spectra were mapped to demonstrate the existence of band gaps and edge modes for different levels of uncertainty. The Gaussian process model was developed and compared against Monte Carlo simulations in order to achieve faster computation of the stochastic model. This lattice design is shown to be promising from the viewpoint of future applications in mitigating fluid-flow-induced vibration containing multiple frequencies and vibration modes. The full research paper prepared from this part of the research is currently under review. Another part of the research included the investigation of the band structure and directional wave propagation in two-dimensional hexagonal- and auxetic-like lattices with curved beam elements. This research was published in a peer-reviewed journal.
The important novel scientific aspects of the performed research are 1) The simultaneous consideration of cubic nonlinearity and fractional-order damping in models of periodic lattice systems; 2) The introduction of inerter elements in beam-based phononic-like lattices to tune interface modes frequencies; 3) The proposition of inerter-based periodic and quasi-periodic locally resonant lattices capable of mitigating fluid-flow-induced vibrations and working as energy harvesters; 4) Introduction of curved beam elements in two-dimensional hexagonal- and auxetic-like lattices to induce new band gaps in lower and higher frequency ranges. The METASINK project is expected to have a wider socio-economic impact evidenced by the proposed novel mechanical metamaterial-based approach for fluid-flow vibration attenuation.