A novel multi-step superposition model for the dispersion analysis of multiaxial prestressed plate-like structures

Abstract

Understanding the dispersion characteristics of multi-axial prestressed plate-like structures is crucial for the engineering application of guided wave non-destructive testing. However, existing analytical and semi-analytical models neglect both constitutive and geometric nonlinearities induced by the prestress and require tedious theoretical derivation and coding, which may not achieve accurate predictions. To address these issues, a convenient model based on the multi-step superposition analysis was proposed to investigate the effects of an arbitrary multiaxial prestress on the dispersion characteristics of plate-like structures. The core idea of this model involves introducing an initial configuration to describe the static pre-deformation between undeformed and final states; then, the dynamic wave motion was superimposed on the initial pre-deformation for the eigenfrequency analysis. Additionally, the strain energy density of the hyperelastic material was implanted and set as the relevant variable between the two steps by the inheritance of the solution. This model significantly improved the accuracy compared to the conventional method, as validated through biaxial acoustoelastic experiments. Subsequently, the acoustoelastic responses of the multiaxial prestressed 6061-T6 aluminum plate were investigated. The results reveal that the non-uniform in-plane prestress leads to the coupling of guided wave modes propagating along non-principal directions. Furthermore, the effects induced by multiaxial prestress in the frequency bands with low dispersion could be decomposed into the sum of the effects induced by three uniaxial prestresses with a very small deviation. This work provides new insights into the acoustoelastic behavior and a theoretical basis to optimize the guided wave mode and frequency.