In analogy to the development of the potential equations of motion of linear elastodynamics, the governing potential equations for linear wave motions of hydrodynamics and thermoelastodynamics are systematically exploited. As a result of these developments, problems of linear wave motions of homogeneous, isotropic, thermally conducting multi-layered elastic solids and viscous fluids can be systematically solved for the media whose boundaries are described by rectangular, circular, parabolic, and elliptic cylindrical coordinates, as well as by spherical and conical coordinates. Five practical examples are analytically solved to illustrate how the use of the potential equations of motion leads to more systematic solution procedures; these examples can be used for the modeling studies of aero and hydrospace vehicles, geological wave problems, and macroscopic biomechanics.

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