Flexural wave propagation in anisotropic laminates and inversion algorithms to recover elastic constants

Abstract

Knowledge of the elastic properties of composite materials can be an invaluable tool for both the quality assurance of manufacturing techniques and design verification. Recent advancements in ultrasonic velocity measurements have demonstrated the ability to recover elastic properties in anisotropic laminates. A simplified experimental setup was investigated to recover the elastic properties based on the flexural wave propagation in anisotropic laminates. The initial objective of this thesis was to verify flexural wave propagation in composite laminates through the comparison of experimental and theoretical phase velocities. In the second part of this thesis, the experimental phase velocities were used to calculate the elastic properties of the material by inverting the governing equations. The initial method used to recover elastic constants was successful in the recovery of a partial set of the bending and extensional stiffnesses. The inability to recover all bending stiffnesses dictated the investigation of a second method. This method used an iterative method based on a nonlinear Newton's method to recover the bending stiffnesses. This method did not converge due to ill conditioning of the solution matrix. Although this method did not converge, it is believed that other more robust methods suggested herein would converge to the proper solution.