The axisymmetric Rayleigh waves in a semi-infinite elastic solid

•Rayleigh wave model in axisymmetric mode and solutions in cylindrical coordinates.•Same velocity as Cartesian coordinates confirming irrelevancy to coordinate systems.•Strength decreases slowly for solution in Bessel functions decaying with radius.•Treated as plane wave in far field with the Bessel approximated by the trigonometric.•Particle trajectory of axisymmetric Rayleigh wave is a straight line, not eclipse. It is well-known that Rayleigh wave, also known as surface acoustic wave (SAW), solutions in semi-infinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.