Band Gap Simulation And Analysis Of Piezoelectric Phononic Crystal Based On Node Integration Algorithm

With the development and progress of automobile industry,the vibration and noise have been widely concerned by automobile developers.Excessive vibration and noise will not only reduce the service life of auto parts and auto safety,but also cause personal injury.Because the phononic crystal has band gap characteristics,that is,there is a strong attenuation band gap range when elastic wave propagates in the phononic crystal,so it plays a significant role in vibration reduction and noise reduction.With the rapid development of CAE technology,numerical algorithms play an important role in band gap simulation of phononic crystals.However,the existing numerical methods have some defects,such as poor applicability and low accuracy.In view of this,based on the gradient smoothing technology,this paper constructs a set of node integration algorithm with unstructured mesh(2D Triangular Mesh;3D tetrahedral mesh)as the true background,and applies it to the simulation of conventional phononic crystal,piezoelectric material and piezoelectric phononic crystal.The main research contents are as follows:(1)The node integration algorithm for the analysis of band structure and transmission characteristics of conventional phononic crystals is constructed.Due to the periodic arrangement of phononic crystal structure,the protocell is divided into a series of triangular or tetrahedral meshes.Based on the background grid nodes,the smooth domain is constructed,and the strain in the integral domain is reconstructed by using the gradient smoothing technique.Finally,the band structure equation is obtained by combining with Bloch theorem,and the transmission characteristics of finite period phononic crystals are further constructed.Through the analysis of a series of related examples,the advantages of the node integration method in calculation accuracy,convergence and grid distortion resistance are verified.(2)The nodal integration algorithm for the static and modal analysis of piezoelectric materials is proposed.Based on the unstructured mesh problem domain is discreted,the electric potential is introduced into the discrete model as a field variable,and the smooth domain is constructed by grid nodes.The mechanical strain and electric field are treated by using the gradient smooth technology,and the nodal integral equations of piezoelectric materials statics and modal analysis are obtained.The analysis results of two or three-dimensional piezoelectric examples show that the method can effectively reduce the calculation error,improve the simulation accuracy and improve the convergence speed.(3)By combining piezoelectric materials and phononic crystals,the node integration method for band gap simulation of piezoelectric phononic crystals is constructed.In the background of unstructured grid,the smooth domain is constructed according to the nodes.Based on the smooth gradient technique and Bloch theorem,the node integration method for band gap simulation of piezoelectric phononic crystal is constructed.Through the analysis of two or three-dimensional piezoelectric phononic crystal examples,it is verified that the nodal integration method has the advantages of high calculation accuracy and wide adaptability.Furthermore,the band structure of piezoelectric phononic crystal under different boundaries is studied,which lays the foundation for the active control of piezoelectric phononic crystal.