Summary. The Rayleigh wave is dispersive in a stratified half-space. The modes of Rayleigh waves in a stratified half-space are usually defined by the order of

The space elevator system is a space tether system used to solve low-cost space transportation. Its high efficiency, large load, reusability and other characteristics have broad application prospects in the aerospace field. Most of the existing mechanical models are based on “chain-bar” and a lumped mass tether model, which cannot effectively reflect the flexible behaviour of the rope of space elevator system. To establish an accurate mechanical model, the gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) are used to build the mechanical model of the space elevator system. The universal gravitation and centrifugal force in the model are derived. The calculation results of the ANCF model are compared with the results of the finite element method (FEM) and lumped mass (LM) models. The results show that the calculation results of the ANCF method are not very different from the results of the FEM and LM models in the case of axial loading. In the case of lateral loading, the calculation results of the ANCF method are basically the same as the results of the FEM and LM models, but can better reflect the local flexible deformation of the space elevator rope, and have a better calculation stability than FEM. Under the same calculation accuracy, the ANCF method can use fewer elements, and the speed of convergence is faster than the FEM and LM models.

The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM.

To study the fundamental dynamics of the nonequatorial space elevator, a universal modeling strategy is presented that applies to any anchored latitude. The equations of motion are established on the basis of the lumped mass model of the tether coupled with an interactional elevator. The relationship between the maximum anchored latitude and the design stress is studied by solving the equilibrium equations. The linearized equations of motion are formulated on the basis of the static equilibrium positions to analyze the modal of the tether. Numerical simulation is performed to analyze the properties of the system with a moving elevator. The results show that a positive correlation arises between the maximum anchored latitudes and the design stress. The fundamental modal and the fifth-order modal are associated with the latitudes considering the frequency and modal shape, respectively. Further, the asymptotically stable characteristics are verified. The amplitude of the residual oscillation is magnified with an increase in the anchored latitude or the elevator speed.