Higher harmonic guided waves in isotropic weakly non-linear elastic plates

Open Access
Chillara, Vamshi Krishna
Graduate Program:
Engineering Mechanics
Master of Science
Document Type:
Master Thesis
Date of Defense:
February 27, 2012
Committee Members:
  • Clifford Jesse Lissenden Iii, Thesis Advisor
  • Higher harmonics
  • non-linear elastic
  • guided waves
Use of non-linear ultrasonic waves for material characterization is a topic of significant interest in many applications. Use of guided waves for this purpose is a promising option but appropriate selection of guided wave modes for the generation of cumulative higher harmonics is of critical importance due to the multi-mode nature of ultrasonic guided waves. This thesis deals with the problem of generating non-linear guided waves in plates from a theoretical perspective. A theoretical framework to predict the higher harmonic guided wave generation in plates has been developed. Geometric and material non-linearities are incorporated by using the Lagrangian strain (non-linearized strain) and higher order terms in the strain energy function. A new formulation in terms of the displacement gradient has been developed for the present problem. A perturbation technique and normal mode expansion have been used to solve the problem and arrive at the conditions of “internal resonance” which are sufficient for the generation of cumulative second harmonics. A comprehensive analysis as to which guided wave modes have the capability to generate cumulative second harmonic guided waves has been performed. This is extended to predict the non-linear interaction of guided waves in plates that can be used to predict any higher harmonic generation in plate. The analysis led to the conclusion that Shear Horizontal and Rayleigh Lamb modes can generate only Rayleigh Lamb symmetric modes as second harmonics with single primary mode excitation. Specific modes that satisfy the condition of internal resonance have been identified. The analysis on generalized interaction of guided wave modes led to a more complete understanding of the higher harmonic guided waves in plates.