Numerical Simulation Of Lamb Wave Propagation In Plate-like Structures With Defects

With the development of advanced transducers and signal processing technologies, structural health monitoring(SHM) is gradually coming into application in reality. Lamb wave approaches have shown potential in early researches as a solution to SHM for damage prognosis due to their inherent traits, such as small attenuation in long-distance propagation and high sensitivity to tiny damages. A novel high order finite element, called the spectral finite element, is used to investigate the propagation of Lamb waves in plate-like structures, and key algorithms in numerical calculation are presented and discussed.The thesis starts with an introduction to a PZT‐structure shear layer coupling model in order to better understand the complex behavior of Lamb wave motion, which is excited and sensed by piezoelectric transducers. It shows that for a certain range of excitation frequencies the displacements are linear across the thickness of plates. This lays a foundation for establishing a two dimensional(2D) spectral element. Next, the characteristics of spectral finite element including shape function, condition number of element matrices and critical time step are discussed and studied in details. For the case when the element nodes are different from the integration points, a simple but general method is proposed to compute the derivatives at the integration points explicitly by using the differential quadrature rule. Based on the first-order shear deformation theory with considering the effects of the lateral contraction in the thickness direction, a simple way is proposed to avoid the thickness locking and a 2D piezoelectric spectral finite element is developed. At the end, numerical models with damages are established with the help of spectral finite elements, and a damage detection strategy is introduced to localize the damages. Furthermore, a contact algorithm is also used to investigate the influence of crack contact on the scatter signals from crack surface during wave propagations.The research was partially supported by the National Natural Science Foundation of China(50830201) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The thesis was completed in the Sate Key Laboratory of Mechanics and Control of Mechanical Structures.