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.
