Axisymmetric dynamic response of the multi-layered transversely isotropic medium

• Published in: Soil dynamics and earthquake engineering (1984) Vol. 78; pp. 1 - 18
• Main Authors: Zhang, Pengchong, Liu, Jun, Lin, Gao, Wang, Wenyuan
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2015
• Subjects: Anisotropy; Axisymmetric; Axisymmetric dynamic response; Differential equations; Dynamic response; Hankel integral transform; Mathematical analysis; Mathematical models; Media; Mixed variable formulation; Multi-layered transverse isotropy; Powder injection molding; Precise integration method; Precise integration method; Hankel integral transform; Mixed variable formulation; Axisymmetric dynamic response; Multi-layered transverse isotropy
• DOI: 10.1016/j.soildyn.2015.07.007
• ISSN: 0267-7261

By virtue of the precise integration method (PIM) and the technique of mixed variable formulations, solutions for the dynamic response of the multi-layered transversely isotropic medium subjected to the axisymmetric time-harmonic forces are presented. The planes of cross anisotropy are assumed to be parallel to the horizontal surface of the stratified media. Four kinds of vertically acting axisymmetric loads are prescribed either at the external surface or in the interior of the soil system. Thicknesses and number of the medium strata are not limited. Employing the Hankel integral transform in cylindrical coordinate, the axisymmetric governing equations in terms of displacements of the multi-layered media are uncoupled. Applying mixed variable formulations, more concise first-order ordinary differential matrix equations from the uncoupled motion equations can be obtained. Solutions of the ordinary differential matrix equations in the transformed domain are acquired by utilizing the approach of PIM. Since PIM is highly accurate to solve the sets of first-order ordinary differential equations, any desired accuracy of the solutions can be achieved. All calculations are based on the corresponding algebraic operations and computational efforts can be reduced to a great extent. Comparisons with the existing numerical solutions are made to confirm the accuracy of the present solutions proposed by this procedure. Several examples are illustrated to explore the influences of the type and degree of material anisotropy, the frequency of excitation and loading positions on the dynamic response of the stratified medium. •Axisymmetric dynamic response of isotropic multi-layered soil is firstly obtained by PIM.•Solutions of axisymmetric dynamic response by PIM and mixed variable formulation are derived.•Four kinds of axisymmetric loads acting at different positions are investigated in details.•The solution has higher accuracy and efficient compared to the other methods.•The influences of material parameters and forces on the dynamic response are discussed in details.