Tunable Mechanical Topological Insulators Based On Persistent Homology Deep Transfer Learning

The magnetorheological elastomer material is applied to mechanical topological insulators,and firstly,the energy band structures of different metastables of periodic mechanical topological insulators with magnetorheological elastomer as the base material and three-legged rod metallic material as the scatterer and periodic mechanical Topological insulators with magnetorheological elastomer as the scatterer material and silicone rubber as the base material are investigated.Secondly,the topological phase transition is achieved by simulating the quantum valley Hall effect,which reverses the energy bands between different valley pseudo-spins during the change of the inevitable simplicial Dirac point at the k point.Then,through the calculation of the supercell energy band structure,the topological boundary states existing in the structure are discovered,and the topological boundary states are used to design the elastic wave topological transmission channel to realize the precise guidance of the elastic wave,and the noncontact active regulation of the transmission frequency of the topological transmission channel is realized by controlling the frequency range of the applied magnetic field to change the topological transmission channel.The research results can provide a corresponding reference for the intelligent control of noise and vibration,etc.A nonperiodic mechanical topological insulator was constructed by changing the distance between the scatterers of the periodic mechanical topological insulator with magnetorheological elastomer as the scatterer material and silicone rubber as the substrate material.The study of its energy band and elastic wave topological transmission path transmission was carried out to prove that it has the backscattering suppression property of topological transmission;it provides theoretical reference for the loss and processing and manufacturing errors in the application of mechanical topological insulator in practice.The relationship between the scatterer shape and the forbidden band range of a mechanical topological insulator is investigated using a deep transfer learning method based on persistent homology.The effect of scatterer shape on the forbidden band is analyzed by changing the scatterer shape while keeping the filling rate constant.The scatterer shape and the upper and lower boundaries of the forbidden band are discretized and the topological features are represented in barcode form based on the persistent homodyne theory.Combining image topological feature recognition and deep transfer learning to train the topological barcode of the forbidden band with scatterer shape labels,the neural network will predict the scatterer shape with similar forbidden band features when the topological features of the expected design are input,thus realizing the reverse design of mechanical topological insulator structure and providing a new idea for the forward and reverse design of mechanical topological insulator structure.