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Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds

Rayleigh waves are considered for crystals possessing at least one plane of symmetry. The secular equation is established explicitly for surface waves propagating in any direction of the plane of symmetry, using two different methods. This equation is a quartic for the squared wave speed in general, and a biquadratic for certain directions in certain crystals, where it may itself be solved explicitly. Examples of such materials and directions are found in the case of monoclinic crystals with the plane of symmetry at $x_3=0$. The cases of orthorhombic materials and of incompressible materials are also treated.