Investigation on piezoelectrically induced Lamb wave generation and propagation

Abstract

An analytical solution for transient Lamb wave generation with piezoelectric wafers is presented. The time harmonic problem is solved in the wavenumber domain after Fourier transformation and subsequent inverse transformation by the residue theorem. To evaluate the solution for transient loading the Fourier transform is used again, this time with respect to the time variable. A standard numerical algorithm is utilized to evaluate the necessary integrals as well as the discrete Fourier transform. The solution is valid for the whole waveguide continuum and satisfies the underlying partial differential equations as well as the transient boundary conditions. A numerical example shows that the analytical solution coincides with the finite element result of the problem. The results of the analytical model are also confirmed by experimental investigations.