Efficient modeling and simulations of Lamb wave propagation in thin plates by using a new spectral plate element

A new spectral plate element is presented for modeling selectively or simultaneously the symmetric and/or anti-symmetric modes of Lamb waves propagating in thin plate structures. The Legendre polynomials and the extended form of the displacement field are used in the formulation. The diagonal mass matrix is obtained by using a simple method with less computational effort. Detailed derivations are provided. Comparisons with existing results are performed to validate the formulations as well as the written programs. Numerical calculations have been carried out for thin aluminum plates with and without damages by using the proposed spectral plate element. Comparisons reveal that the proposed spectral plate element is more effective than the spectral plate element based on Chebyshev polynomials and the 3-D spectral finite elements with the same order of Legendre polynomials as the shape functions.