In this paper, based on the theoretical research of structural modal analysis, different types of phonon crystal modal structures are designed for the first time, and the characteristics and the generation mechanism of the bandgap were studied through theoretical calculations and experiments. According to the phenomenon in the experimental results, we can find that the vibration transmission characteristics of phonon crystal structure α3 are the best, and it is also superior to that of phonon crystal structure α10 (full period structure). Therefore, the comparison of theoretical analysis with experimental phenomena shows that the bandgap generation mechanism should be modal resonance instead of local resonance in the finite periodic structure. The profound reason lies in there is no separate Z direction local vibration mode of periodic structure in the vibration mode of finite structure, and the bandgap of finite structure is the mode superposition torsional resonance mechanism between scatterer and substrate mode.

To address the challenge of suppressing low-frequency vibrations in offshore wind turbine towers under complex environmental loads, this paper innovatively proposes a pendulum-tuned particle damper (PTPD). This design combines the high space utilization efficiency of pendulum structures with the broadband energy dissipation advantages of particle damping. A four-degree-of-freedom coupled tower-PTPD model and its Lagrangian equations of motion were established. Using the Finite Element-Discrete Element (FEM-DEM) coupling method, the effects of pendulum length and particle diameter on vibration suppression performance were systematically studied under three wind load conditions. Simulation results show that under Condition 1, a PTPD with a 3.50 m pendulum length filled with 200 mm iron-based particles achieves a peak vibration reduction rate of 58.1%, significantly reducing the tower's vibration acceleration amplitude. A 1:65 scaled model was designed and tested, demonstrating that a combination of 625 mm pendulum length and 10 mm particles achieved a 58.0% vibration reduction rate. This validates the parameter optimization principles derived from simulations and provides an effective solution for anti-fatigue design of offshore wind turbines.

Monitoring and early warning systems for cross-fault buried pipelines are critical measures to ensure the safe operation of oil and gas pipelines. Accurately acquiring pipeline strain response serves as the fundamental basis for achieving this objective. This study proposes a comprehensive analytical methodology combining finite element analysis (FEA) and experimental verification to investigate strain responses in cross-fault buried pipelines. Firstly, a finite element modeling approach with equivalent-spring boundaries was established for cross-fault pipeline systems. Secondly, based on the similarity ratio theory, an experimental platform was designed using Φ89 mm X42 steel pipes and in situ soil materials. Subsequently, the finite element model of the experimental conditions was constructed using the proposed FEA. Guided by simulation results, strain sensors were strategically deployed on test pipelines to capture strain response data under mechanical loading. Finally, prototype-scale strain responses were obtained through similarity ratio inverse modeling, and a comparative analysis with full-scale FEA results was performed. The results demonstrate that strike-slip fault displacement induces characteristic “S”-shaped antisymmetric deformation in pipelines, with maximum strain concentrations occurring near the fault plane. Both the magnitude and location of maximum strain derived from similarity ratio inverse modeling show close agreement with FEA predictions, with relative discrepancies within 18%. This consistency validates the reliability of the experimental design and confirms the accuracy of the finite element model. The proposed methodology provides valuable technical guidance for implementing strain-based monitoring and early warning systems in cross-fault buried pipeline applications.