Periodic Reporting for period 1 - METACTIVE (Nonlinear Approaches for the Design of Active Piezoelectric Metamaterials)
Reporting period: 2019-01-03 to 2021-01-02
This project aimed at exploiting nonlinearity, combined with material and geometrical periodicity, to extend existing models of energy harvesters and periodic lattice structures. It showed that the proposed incremental harmonic balance method has great importance in analyzing the periodic response of the nonlinear energy harvester. Moreover, it presented a few new concepts of the energy harvester based on the phenomena such as parametric amplification phenomena, axially moving beam and coupled Duffing oscillators. By considering the axially moving beam's nonlinear geometry, a new energy harvesting application was proposed with broadband frequency response and multiple stable vibration states. On the other hand, the parametric amplification phenomena have been known for almost five decades, but this phenomenon showed great application in energy harvesting design. We proposed a simple model of parametrically amplified energy harvester when parametric resonance conditions are broken. In both cases, we demonstrated significant amplification of the energy harvesting power.
However, analyzing the waves in periodic structures investigates mass embedded and pre-stressed hexagonal lattices and showed significant influence on the determined frequency band gaps, based on the finite element method and Bloch theorem. On the other hand, elastic wave propagation was investigated in periodic beam-chain structures by considering an analytical modelling and Bloch theorem. The parametric uncertainty propagation was investigated by considering the Gaussian process approach and finite element method in two models, elastically periodic beam and hexagonal lattices structures. The decomposition is performed by projecting the response onto the eigenspace and involves a nominal number of actual physics-based function evaluations (the eigenvalue analysis). This allows the stochastic dynamic response evaluation to be solved with a low computational cost. Moreover, time-dependent inerter based-lattices with discrete and structural elements were proposed for unidirectional wave prolongations. By considering the Bloch theorem and plane wave expansion method, it determined the frequency band structure diagrams and asymmetric bandgap. This phenomenon is based on the broken reciprocity principle from the theory of elasticity and acoustics. For numerical validations of the obtained analytical results, we used finite element and finite difference methods.
However, analyzing the waves in periodic structures investigates mass embedded and pre-stressed hexagonal lattices and showed significant influence on the determined frequency band gaps, based on the finite element method and Bloch theorem. On the other hand, elastic wave propagation was investigated in periodic beam-chain structures by considering an analytical modelling and Bloch theorem. The parametric uncertainty propagation was investigated by considering the Gaussian process approach and finite element method in two models, elastically periodic beam and hexagonal lattices structures. The decomposition is performed by projecting the response onto the eigenspace and involves a nominal number of actual physics-based function evaluations (the eigenvalue analysis). This allows the stochastic dynamic response evaluation to be solved with a low computational cost. Moreover, time-dependent inerter based-lattices with discrete and structural elements were proposed for unidirectional wave prolongations. By considering the Bloch theorem and plane wave expansion method, it determined the frequency band structure diagrams and asymmetric bandgap. This phenomenon is based on the broken reciprocity principle from the theory of elasticity and acoustics. For numerical validations of the obtained analytical results, we used finite element and finite difference methods.
- Month 1-6: New works on nonlinear vibration energy harvesting were conducted. The results are reported in publications [1 - 3]
It was shown that the proposed incremental harmonic balance method has great importance in analyzing the periodic response of the nonlinear energy harvester. Moreover, we proposed a few new energy harvester concepts based on the phenomena such as parametric amplification phenomena and coupled Duffing oscillators. We proposed a simple model of parametrically amplified energy harvester when parametric resonance conditions are broken. In both cases, we got great amplification of the energy harvesting power.
- Month 7-12: New works structural models of fractional beams and stochastic dynamics were conducted. The results are reported in publications [4-7]
Fractional damping and nonlocal elasticity play an important role in modelling the future design of the energy harvesters. In this part of the research, we proposed different mathematical modelling approaches of beam-based structures with base excitation with fractional damping characteristics and scale-dependent beams. Moreover, the stochastic response of the coupled beam structures is investigated based on the FEM model and Gaussian process, where the propagation of material uncertainties was investigated.
- Month 13-18: New works on nonlinear phenomena in mechanical models. The results are reported in publications [8-9]
Special calls of the nonlinear mechanical system are based on the axially moving beam with discrete attachments for application in broadband energy harvesting devices. This model shows great dynamic characteristics, especially in the estimation of the harvesting power of the energy harvesting devices. The amplitude-frequency response was shown for the scale-dependent beam placed on the visco-Pasternak foundation based on the incremental harmonic
balance and continuation method. The superharmonic resonance was analyzed and showed the nonlinear hysteresis phenomena in such beam based nonlinear model.
- Month 19-24: New works on Bloch waves and periodic structures was conducted. The results are reported in publications [10-12]
For analyzing the waves in periodic structures, mass embedded and pre-stressed hexagonal lattices are investigated and showed significant influence on the determined frequency band gaps, based on the finite element method and Bloch theorem. On the other hand, elastic wave propagation is investigated in periodic beam chain structures by considering an analytical modelling and Bloch theorem.
It was shown that the proposed incremental harmonic balance method has great importance in analyzing the periodic response of the nonlinear energy harvester. Moreover, we proposed a few new energy harvester concepts based on the phenomena such as parametric amplification phenomena and coupled Duffing oscillators. We proposed a simple model of parametrically amplified energy harvester when parametric resonance conditions are broken. In both cases, we got great amplification of the energy harvesting power.
- Month 7-12: New works structural models of fractional beams and stochastic dynamics were conducted. The results are reported in publications [4-7]
Fractional damping and nonlocal elasticity play an important role in modelling the future design of the energy harvesters. In this part of the research, we proposed different mathematical modelling approaches of beam-based structures with base excitation with fractional damping characteristics and scale-dependent beams. Moreover, the stochastic response of the coupled beam structures is investigated based on the FEM model and Gaussian process, where the propagation of material uncertainties was investigated.
- Month 13-18: New works on nonlinear phenomena in mechanical models. The results are reported in publications [8-9]
Special calls of the nonlinear mechanical system are based on the axially moving beam with discrete attachments for application in broadband energy harvesting devices. This model shows great dynamic characteristics, especially in the estimation of the harvesting power of the energy harvesting devices. The amplitude-frequency response was shown for the scale-dependent beam placed on the visco-Pasternak foundation based on the incremental harmonic
balance and continuation method. The superharmonic resonance was analyzed and showed the nonlinear hysteresis phenomena in such beam based nonlinear model.
- Month 19-24: New works on Bloch waves and periodic structures was conducted. The results are reported in publications [10-12]
For analyzing the waves in periodic structures, mass embedded and pre-stressed hexagonal lattices are investigated and showed significant influence on the determined frequency band gaps, based on the finite element method and Bloch theorem. On the other hand, elastic wave propagation is investigated in periodic beam chain structures by considering an analytical modelling and Bloch theorem.
The key novel scientific aspects of the proposed research, in relation to the current state-of-the art, are: 1) The consideration of geometric nonlinearity in conjunction with piezoelectricity for APM structures 2) The proposition of APM working as mechanical filters and dynamical absorbers with changeable characteristics.3) The proposition of APM by incorporation of multiple internal resonators and working as energy harvesting devices. 4) Physical realisation of proposed devices by using rapid prototyping and experimental validation.
• The address (URL) of the action's public website: None specific
• The address (URL) of the action's public website: None specific