Semi-analytical peridynamic method for modal analysis of acoustoelastic Lamb waves

• The connection between biot's and hyperelastic acoustoelasticity theories is clarified. • A semi-analytical peridynamic method for modeling wave propagation is developed. • Convergence of grid spacing and approximated order of accuracy is examined. • Effects of material heterogeneity, applied stress and residual stress are studied. Lamb wave has been widely used as a non-destructive testing tool for inspecting the defects or damage in the plate system. A comprehensive understanding and correct prediction of the modal characteristics of Lamb waves are of high importance for ensuring successful practical applications. In this paper, a new method called the semi-analytical peridynamic (SAPD) method for analyzing wave propagation is developed. This method, within the framework of the general acoustoelasticity theory, uses the peridynamic differential operator to transform the equations of motion for guided waves in prestressed anisotropic media and the boundary conditions from local differential forms to nonlocal integral forms. By introducing meshfree discretization and Lagrange multipliers, these governing equations can be reorganized into a standard generalized eigenvalue formalism and solved. The effectiveness and accuracy of the SAPD method are first verified through comparison with the exact solutions. Phase and group velocity dispersion curves and displacement distributions of Lamb waves in three typical cases are then calculated to study the effects of material heterogeneity, applied stress and residual stress on the propagation of Lamb waves. Since complex grid generation algorithms are avoided, the SAPD method exhibits the advantages in terms of simplicity and implementation.