| In recent years,the upsurge in topological insulators and topological phases in condensed matter physics,characterized by internal insulation and defect-immune robust edge state at the boundary,has brought innovative ideas for the design of classical wave systems with novel characteristics.The elastic wave structure of mechanical system has become a powerful and universal platform for exploring topological physics and detecting related peculiar phenomena due to its advantages of macroscopic easy realization and high controllability.The extension of topological physics to mechanical structures brings innovative ideas for elastic wave control,waveguide design,vibration energy harvesting,and energy flow transmission guidance.The study of topological states in mechanical systems has achieved fruitful results.However,most of these studies are focused on idealized mass-spring systems,which are difficult to translate into practical macroscopic models.In addition,the majority of topological states implemented in continuous structures are confined to a single frequency band,and it is difficult to tune and reconstruct the structures once they are designed.Therefore,this dissertation takes some fundamental mechanical elements commonly used in engineering applications as objects to extend the discrete mass-spring system and broaden the scope of topological mechanical structure design.By means of theoretical analysis and simulation,this dissertation presents a design scheme of elastic wave topological states with excellent properties such as multiple working bands,purity and tunability.The details are as follows:(1)The mass-spring system is extended by using the common mechanical elements such as beam and rod in engineering applications,and a kind of beam-rod coupling elastic system with multi-band topologically protected states based on quantum valley Hall effect is presented,which combines the advantages of discrete lattice(no other mixed modes in the band gap)and continuous system(wide frequency range)to a certain extent.A set of theoretical analysis framework based on the beam-spring coupling model is developed,and the results are verified by the solid finite element model.The band structure and the corresponding modal analysis show that the symmetry of the underlying honeycomb lattice and the multi-order natural modal properties of the beam structure guarantee the existence of Dirac degeneracy points at multiple frequency points,which creates conditions for the construction of multi-band topological states.(2)A new method is proposed to trigger the topological phase transition by adjusting the nut spacing on the beam,and a strategy to realize the elastic structure with multi-band pure topological states and tunable in situ is given.It is found that by simply adjusting the nut spacing on the beam,two kinds of valley Hall phases can be produced,which are characterized by the opposite valley Chern number.Dispersion analysis of supercells composed of unit cells of different topological phases and numerical simulation of finite size structures show that domain walls formed by two-phase structures support pure topologically protected interface states in the dual frequency range.At the same time,the feasibility of in situ tuning of structure by adjusting nut spacing is demonstrated.(3)An aperiodic elastic lattice structure modulated by artificial Kekule distortion is designed to support Majorana-like elastic wave topologically bound states in multiple frequency ranges simultaneously.Through systematic theoretical analysis and finite element simulation,we show that these Majorana-like bound states in different frequency ranges are all bound to vortex core formed by Kekule modulation,and show highly selfreplicating properties.Numerical simulation results show that the multi-band topologically bound states have excellent mechanical energy focusing characteristics and strong robustness to structural defects.(4)A theoretical model of periodic beam array is proposed to realize the multi-band and reconfigurable elastic wave topological pumping effect in a spatially modulated mechanical structure.The virtual momentum space is synthesized through modulating the height of movable nut on the beam along the extended space dimension.The results show that this modulation scheme,by simply adjusting the nut height,not only makes the topological edge state transfer from edge to edge exist in multiple frequency ranges,but also makes it possible to reconfigure and tune the structure in situ. |
