Considering the mixed boundary-value conditions,the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established.

Then the dual integral equations of the venical vibration of a rigid circular plate on a fluid-saturated poroelastic half space are established according to the mixed boundary permeability condit.

Based on the equivalent settlements of rigid circular plate,the continuity and smooth contact conditions between subsoil surface and rigid circular plate,the dual integral equation of the interaction stresses between the rigid circular plate and multi-layered soil,was deduced after introducing Hankel transform.

Torsional vibrations of a rigid disk on single-layered saturated soil;

Therefore, the proposal above, implemented with neuro-muscle-skeleton model and optimal control tool, could derives stiffness ellipses which are consistent with experimental results and avoid monotonous changes in the ellipses simulated from the original model.

Dynamic response analysis of rigid-plastic circular plate under underwater blast loading;