Modeling of the Lamb wave asymmetric modes with an improved two-dimensional thin plate theory

Abstract

For the modeling of Lamb wave propagation, the accuracy of some two-dimensional (2D) plate theories like the first order shear deformation theory (FSDT) may decline at a high frequency, since their displacement fields cannot match those complicated Lamb wave structures. To address this issue, this paper proposes an improved 2D thin plate theory which has a more accurate high frequency modeling ability of Lamb wave than the FSDT. This is done by designing the displacement field according to the high frequency Lamb wave structure. Since the shear stress curves of the Lamb wave are complicated and would vary with the frequency, the initial displacement field takes a combination of polynomial and trigonometric forms, which has two coefficients that need to be determined by fitting the shear stress curve at a certain frequency. Then, a strategy is applied to determine the eventual displacement field by searching the high frequency range for the optimum coefficients that enable a best modeling accuracy. The relative error of its modeling result of A0 mode can be controlled within 0.03 % below 800 kHz·2 mm, and keeps the highest error of 1.43 % up to 2500 kHz·2 mm. To verify its high frequency modeling performance, a finite element method program is finally built. Results show that both the wavefields of A0 and A1 can be accurately simulated with the improved two-dimensional thin plate theory.