The study of various celestial bodies is of great interest at the present time. Soil studies are being conducted. Vibrating robots could be possible tools for implementing the missions involving moving on the surface of celestial bodies. At the same time, such missions must be safe and sustainable. Such missions are very expensive. And they require high-quality modeling. The dynamics of a vibrating robot is investigated in this work. These structures can move on the surface of various celestial bodies, such as Mars, the Moon or asteroids. Various models can be used as a model of the contact interaction of bodies with a surface, in particular the AmontonCoulomb law of friction. This paper is aimed at studying a mechanical system consisting of a rigid body (outer body) placed on a horizontal rough plane and of an internal moving mass moving inside the outer body in a circle lying in a vertical plane, so that the radius vector of the point has a constant angular velocity. Based on the general properties of the solutions, possible periodic modes and their features depending on the parameters of the problem are considered. All qualitatively different solutions in this case are described.

Traditional geotechnical engineering is challenged in terms of sustainability, resilience, reliability and resources availability in the context of climate change and urbanization expansion. Abstracting inspiration from nature and adopting to geotechnical engineering, bio-inspired geotechnics can provide innovative solutions to address these challenges. This paper reviews the underlying mechanics of bio-inspired geotechnical engineering from three perspectives, i.e., bio-inspired burrowing strategies and mechanisms, bio-inspired surfaces with textures and bio-inspired underground structures. The results highlight that the bio-inspired burrowing strategies (i.e., particle removal, chiseling/grabbing-pushing, peristalsis, dual-anchor, pivot burrowing, undulatory propulsion, reciprocating, rotation and root growth) differ in their application scopes and burrowing efficacy, and the auxiliary burrowing, the principle of least impendence, as well as the multi-functional root growth presents promising solutions to burrowing challenges. Bio-inspired textured surfaces exhibit performance enhancement with regard to anisotropic friction, wear resistance and actuator initiation. In bio-inspired underground structures, snakeskin- and root-inspired geotechnical elements provide superior performance due to the frictional anisotropy and branching effects, respectively, and the potential implementation techniques are challenging current geotechnical engineering. Finally, transferring issues, potential research trends and future prospects are presented, and the significance of collaborative engagement of both engineers and scientists for promotion in bio-inspired geotechnics is emphasized. (c) 2024 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.