Normal Mode Expansion Method for Generalized Thermoelastic Lamb Waves in Transversely Isotropic Thin Plates

A quantitative theory for modeling the generalized thermoelastic Lamb waves, which propagates in transversely isotropic plates with thermal relaxation, is presented by employing normal mode expansion method of generalized Lamb wave modes. The displacement and temperature fields are expressed by a summation of the symmetric and antisymmetric thermoelastic modes in the surface thermal stresses and thermal gradient free transversely isotropic plate, and therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin plates. The transient waveforms excited by the thermoelastic expansion are analyzed for a transversely isotropic thin plate. The results show that the theory provides a quantitative analysis to characterize anisotropic elastic stiffness properties of transversely isotropic plates by Lamb wave detection. Numerical calculations have been presented for a zinc plate. However, the methods can be used for other materials as well.