Based on our direct shear creep experiment and the direct shear rheological constitutive model, a semi-empirical time-dependent parameter of the shear strength is obtained by Mohr–Coulomb shear strength theory, and different time-dependent traction force calculations between deep-sea sediment and a tracked miner are conducted by the work-energy principle. The time-dependent traction force calculation under its influencing factors, including the time, track shoe number, and grounding pressure, are analyzed and proved to be valid by the traction force experiment of a single-track shoe. The results show that the time-dependent cohesion force obtained by a semi-empirical way can be easily used to deduce the time-dependent traction force models under the different grounding pressure distributions and applied into deep-sea engineering application conveniently; the verified traction force models by the traction force experiment of a single-track shoe illustrate that traction force under the decrement grounding pressure distribution is the worst among the four kinds of grounding pressure distributions and suggested for evaluating the most unfavorable traction force and calculating the trafficability and stability of the deep-sea tracked miner.

Nonlinear systems affected by non-smooth factors are widely used in mathematical modeling and the description of dynamic behaviors, where the selection of system parameters plays a crucial role in solving practical problems. Whereas the theoretical analysis of the effects of system parameters on global bifurcations and chaotic motions has been thoroughly established in smooth systems, the parametric influence on chaotic thresholds in non-smooth systems remains unresolved. In this paper, a class of single-degree-of-freedom nonlinear dry friction systems with nonlinear damping, subjected to periodic excitation, is considered. Through in-depth analysis of the Melnikov function, it is discovered that the ratio of linear to nonlinear damping alters the morphology of the chaos threshold in non-smooth systems. Under specific conditions, this ratio takes 12/35 as the critical value that transforms the dominant factor of the system’s chaos threshold. Simultaneously, analytical chaos thresholds corresponding to three distinct damping ratios are derived. Based on these thresholds, further demonstrate the bell-shaped variation of the threshold with external excitation frequency and its monotonic dependence on conveyor belt speed and friction force. Finally, combining the theoretical analysis with numerical simulations, the effect of these parameter sets on the homoclinic orbits and chaos thresholds are verified. The research demonstrates that the dynamic behavior of the system is highly sensitive to parameter variations, with both theoretical and numerical results being consistent. This provides strong theoretical support for further optimizing the dynamic performance of nonlinear conveyor belt systems and improving their stability and reliability.

The dynamic behavior of fluid-conveying pipes can lead to significant safety hazards when subjected to impact vibrations, influenced by complex operational environments such as base excitations, distributed follower forces, and support looseness. A model for the impact vibration of a simply supported, rigidly constrained fluid-conveying pipe is established based on Hamilton’s principle under the combined effects of base excitations and distributed follower forces. The Galerkin method and the NDFs (variable-order numerical differentiation formulas) algorithm are employed for discretizing and solving the equation, respectively. The influences of parameters on the model are discussed under the actions of the base excitation frequency, magnitude of distributed follower forces, and fluid velocity. The evolutionary pathways within the model the periodic motions, quasi-periodic motions, chaos are captured by the analysis of bifurcation diagrams, phase diagrams, Poincaré maps, and time-history curves. So are unique behaviors to rigid impacts such as chatter vibrations and wiping contacts, and the stable focus on the Poincaré map mutates into an attractor with a shape resembling a plum blossom under multi-source excitation. The research reveals that Plum blossom attractors provide critical transition markers for analyzing vibration evolution from stable focus to attracting circles. Low base excitation frequencies trigger chatter-impact vibrations. The findings of this study provide a theoretical basis for the engineering parameter settings or safe operation of fluid-conveying pipes under multi-source excitation.