title: Amplitude-dependent Lamb wave dispersion in nonlinear plates.
abstract: The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching.
authors: Department of Robotics and Mechatronics, AGH - University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Krakow, Poland.
authors: Pawel
authors: P
authors: Packo
authors: Department of Robotics and Mechatronics, AGH - University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Krakow, Poland.
authors: Tadeusz
authors: T
authors: Uhl
authors: Department of Robotics and Mechatronics, AGH - University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Krakow, Poland.
authors: Wieslaw J
authors: WJ
authors: Staszewski
authors: School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, Georgia, 30332-0405, USA.
authors: Michael J
authors: MJ
authors: Leamy