Dynamic analysis of a rigid circular foundation on a transversely isotropic half-space under a buried inclined time-harmonic load

• Dynamic analysis of a disk on a TI half-space under a buried time-harmonic load.
• Static results pertinent to both frictionless and bonded contacts are discussed.
• Both normal and rotational compliances are depicted for some TI materials.
• Neglecting the anisotropic behavior of the medium can alter the results.
• G′/GG′/G is the dominant term on both normal and rotational compliances.

The dynamic analysis of a surface rigid foundation in smooth contact with a transversely isotropic half-space under a buried inclined time-harmonic load is addressed. By virtue of the superposition technique, appropriate Green׳s functions, and employing further mathematical techniques, solution of the mixed-boundary-value problem is expressed in terms of two well-known Fredholm integral equations. Two limiting cases of the problem corresponding to the static loading and isotropic medium are considered and the available results in the literature are fully recovered. For the static case, the results pertinent to both frictionless and bonded contacts are obtained and compared. With the aid of the residue theorem and asymptotic decomposition method, an effective and robust approach is proposed for the numerical evaluation of the obtained semi-infinite integrals. For a wide range of the excitation frequency, both normal and rotational compliances are depicted in dimensionless plots for different transversely isotropic materials. Based on the obtained results, the effects of anisotropy are highlighted and discussed.