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Propagation of plane harmonic waves in homogeneous anisotropic generalized thermoelastic materials was studied after deriving the secular equation. It was found that four dispersive wave modes are possible. Three modes called quasi-elastic (E) are the usual modes of coupled thermoelasticity. The fourth mode, called quasi-thermal (T), which is diffusive in coupled thermoelasticity, now becomes wave-like with finite velocity of propagation. High and low-frequency approximations have been obtained for all the modes.
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