Research On Aperiodic Mechanical Topological Insulators Based On Persistent Homology Deep Learning

Mechanical topological insulators have some characteristics that conventional mechanical metamaterials do not have,such as the nondestructive transmission of elastic or mechanical waves and the robustness of their conduction.However,for the periodic mechanical topological insulators,there are still defects such as too small band gap of topological edge states and unfrequently-modulated.Moreover,structurally,it is difficult to construct arbitrary conduction path with the periodic mechanical topological insulators.Moreover,there are many changes in the structural form of mechanical topological insulators,and each change can change the band characteristics of a single cell.Therefore,how to establish the relationship between the geometric characteristics of mechanical topological insulators and the band gap characteristics has become an important topic.Based on this,this paper carries out the following aspects of research:(1)the magnetorheological elastomer materials as substrates of mechanical topological insulators,utilize the elastic modulus of magnetorheological elastomers adjustable characteristics,makes the band gap and its absolute value of constructed mechanical topological insulators adjustable by regulating magnetic field.After applying magnetorheological elastomer to mechanical topological insulators,the frequency band gap of topological edge states increases from 16.5Hz to 90.1Hz,which greatly improves the tunability of mechanical topological insulators.(2)The constructed mechanical topological insulator can adapt to the wave propagation of multiple paths through the amorphous construction of the single cell.The uniform conduction of mechanical waves in each position of the channel is realized by the aperiodic position of the periodic topological insulator scatterer,and the waveguide properties of the three aperiodic channels are all good.(3)The influence of the shape of the model and the size of the matrix on the band structure of the single cell is analyzed geometrically,so that the band gap characteristics of the single cell can be represented by the algebraic topological characteristics.Through analysis,it is found that the length of the second longest barcode code in 0 dimension Betty number is equal to the size of the band gap of the single cell band structure in the persistent homology barcode graph which reveals the topological characteristics.(4)Through deep transfer learning Goog Le Net algorithm,the relationship between mechanical topological insulators and bandgap features is established from four aspects,which are:(1)Geometric features based on the geometric model of mechanical topological insulators;(2)Geometric characteristics of band structure based on mechanical topological insulators;(3)Algebraic topological characteristics of mechanical topological insulators based on geometric model;(4)Algebraic topological characteristics of band structure based on mechanical topological insulators.Through the deep transfer learning algorithm,this paper established the relationship between the geometric characteristics of the mechanical topological insulator cell and its band gap characteristics,and the recognition rate could reach 100% in the sample set.(5)After the Goog Le Net algorithm model is obtained,three kinds of new examples are constructed to verify its stability,so as to obtain the best method of establishing feature relation.Through the verification of a new example,it is found that the relationship between the geometric features based on the band structure of the mechanical topological insulators and the algebraic topological features based on the band structure of the mechanical topological insulators has good robustness,and the recognition of new examples can also achieve 100% accuracy.It can be concluded that the above two methods are the best methods to establish the relationship between the geometric characteristics of a single cell and the band gap characteristics.The research in this paper provides a reference for the forward and reverse design of aperiodic mechanical topological insulators.