Design And Research Of Negative Thermal Expansion And Band Gap Structure Based On Hoberman Sphere

Negative thermal expansion?NTE?structure is a kind of functional structure with the characteristics of thermal contraction and expansion.NTE structures exhibit unusual mechanical properties compared with traditional structures,leading to huge application potentials in various fields,such as precision instruments,Micro thermal actuators.Similarly,the new functional structures and devices based on Band gap?BG?structures have potential application prospects in various fields,such as vibration or sound minimization,acoustic superlens,and frequency filter.Herein,a novel NTE structure and a new BG structure are proposed,inspired by the scissor-like geodesic circle of Hoberman sphere.The main work are summarized as follows:?1?A novel NTE annular structure by integrating novel scissor-like units and SMA springs was proposed.By combining theoretical and experimental methods,we reveal that the proposed structure can achieve large expansion-shrinkage ratio,i.e.from-0.14 to 0.12?using outer diameter,D_o to quantify?and from-0.38 to 0.28?utilizing inter diameter,D_i to quantify?when the temperature fluctuates between 20-70?.We further show that the expansion-shrinkage ratio can be easily adjusted by altering the geometric parameters.The number of scissor-like units,N,connecting rod,l₁,and connecting rod,l₃ have largest and least effects on expansion-shrinkage ratio,respectively.It is worth emphasizing that the novel idea to propose the novel structure is not restricted to the topological geometry presented in this study,other topological shapes,e.g.,square and sphericity,can be also employed.Additionally,the thermal sensitive material that integrated in the novel structure can be also replaced by other materials,e.g.,shape memory polymers.These novel NTE structures provide more potential applications for some specific fields.?2?A new two-dimensional?2D?BG structure constituted by the periodic hexagonal lattices is presented.The band structures,transmission spectrum as well as displacement field of the proposed PC are analyzed by employing the finite element method?FEM?with the Bloch theorem.Results show that the first BG of the Model A can be achieved in the range of 244.6 Hz to 1490.0 Hz with a BG width of 1245.4 Hz and a gap-mid gap ratio?BG%?of 143.6%.Also,a BG span from 244.6 Hz to 2543.9Hz with a BG width of 2299.3 Hz and a BG%of 164.9%is obtained when an approximate flat band between the first and second BGs is neglected.The BG of the Model B can be produced between 85.6 Hz and 156.9 Hz with a BG width of 71.3 Hz and a BG%of 58.8%,showing an ultra-wide BG in the low-mid frequency range.The attenuation frequency ranges of the transmission spectrum and band structure show good agreement,and the attenuation capacity of elastic wave or sound wave increases with the number of periods of the structure.The formation mechanism of the BGs is investigated according to the eigenmodes at the BG edges analysis,revealing that the BGs are primarily generated by the localized resonance modes.We further show that the position and width of the BGs can be adjusted within a broad frequency range by altering the key geometric parameters.