Solution of nonlinear Lamb waves in plates with discontinuous thickness

Nonlinear Lamb waves can propagate over long distances in plate and shell structures and are sensitive to the early fatigue damage of materials. Therefore, they offer unique advantages in the fields of nondestructive testing and material health monitoring. Plate and shell structures with discontinuous thicknesses (e.g., ribs, stiffeners, or joints) will cause nonlinear Lamb wave scattering, and it is necessary to study the scattering processes of nonlinear Lamb waves at discontinuities and how these processes impact the resulting signal characteristics. Thus, nonlinear Lamb waves can be used to identify the structural characteristics and defect characteristics of signals in practical applications. In this paper, the propagating and scattering processes of the second harmonic of a Lamb wave in a discontinuous plate are studied, including the contributions of the evanescent Lamb modes near the discontinuity and the nonlinear boundary effect at the discontinuity. The scattering characteristics of the second harmonics with respect to the frequency and geometry of the plate are analyzed. In addition, the integral formula is adjusted to improve the computational stability under different numbers of Lamb wave modes. Transient finite element simulation is used to validate the proposed method.