Equivalent linearization modeling and experimental validation of natural frequency and vibration isolation performance in metal braided hoses

Metal braided hoses are widely used in the petroleum industry, marine engineering, aerospace, and other fields for their excellent displacement compensation and vibration damping. Stiffness properties have attracted most of the research so far, while the dynamic behavior of the hose remains comparatively understudied. This paper therefore establishes single-degree-of-freedom axial and bending dynamic models based on the Bouc-Wen hysteresis model and linearizes the nonlinear equations through energy-equivalent linearization, using the energy dissipated by the hysteresis loop. The linearized equations are solved analytically and validated against frequency sweep tests. The model predicts axial natural frequencies of 11.91 Hz and 19.60 Hz for the first two modes and 13.2 Hz for the first bending mode, all close to the measured values, so the equivalent linearized model can be considered reliable for engineering calculation in the low-frequency range. Experiments on hoses with different diameters, lengths, and braiding-layer numbers further show that the bellows size mainly determines the hose stiffness: larger bellows are stiffer but damp less, and adding braiding layers improves damping only until the accompanying increase in stiffness weakens isolation. In the measurements, the two-layer DN25 hose reached the highest axial vibration level difference of 12.83 dB, the longer DN25 hose reached 25.46 dB in bending, and the stiffer DN50 hose isolated much less, at 7.27 dB axially. These quantitative results provide concrete guidance for the design and application of metal braided hoses.