Simulation of Rayleigh waves in cracked plates

• Published in: Mathematical methods in the applied sciences Vol. 30; no. 1; pp. 15 - 42
• Main Authors: Cao, M. T., Moreno, C., Quintela, P.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.01.2007; Wiley; Teubner
• Subjects: contact; cracked plates; elastodynamic; Exact sciences and technology; finite element methods; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematics; Newmark methods; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Physics; Rayleigh waves; Sciences and techniques of general use; Signorini's conditions; Solid mechanics; Structural and continuum mechanics; Cracked plate; Newmark method; Rayleigh waves; Thin plate; cracked plates; Iterative method; Contact problems; Newmark methods; Signorini's conditions; Boundary condition; Elastic plate; Finite element method; Applied mathematics; Signorini's condition; finite element methods; contact; elastodynamic; Nonlinearity; Rayleigh wave; Numerical simulation; Elastodynamics; Approximate solution
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.774

The aim of this paper is to develop new numerical procedures to detect micro cracks, or superficial imperfections, in thin plates using excitation by Rayleigh waves. We shall consider a unilateral contact problem between the two sides of the crack in an elastic plate subjected to suitable boundary conditions in order to reproduce a single Rayleigh wave cycle. An approximate solution of this problem will be calculated by using one of the Newmark methods for time discretization and a finite element method for space discretization. To deal with the nonlinearity due to the contact condition, an iterative algorithm involving one multiplier will be used; this multiplier will be approximated by using Newton's techniques. Finally, we will show numerical simulations for both cracked and non‐cracked plates. Copyright © 2006 John Wiley & Sons, Ltd.