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However, the design process for these complex high-dimensional coupled nonlinear systems remains poorly developed, particularly when applied for ocean-going vessels that experience rolling and pitching motions. The present work addresses this issue by establishing a six-degree-of-freedom HSLDS vibration isolation model for FRVISs composed of eight isolators, and the model is applied to fully analyze the swing stability and multidimensional vibration isolation performance of these systems. The influence of nonlinearity on the mechanical properties of the vibration isolators is analyzed more clearly by assuming that each vibration isolator realizes nonlinear HSLDS characteristics in the <jats:italic>z<\/jats:italic> direction and linear characteristics in the <jats:italic>x<\/jats:italic> and <jats:italic>y<\/jats:italic> directions. The results demonstrate that the swing displacement responses of the system are greatly reduced under weak nonlinearity, which reflects the high static stiffness and high static stability characteristics of an HSLDS system. The multidimensional vibration isolation performance of the system is evaluated according to the impacts of nonlinearity, the installation height <jats:italic>H<\/jats:italic><jats:sub><jats:italic>z<\/jats:italic><\/jats:sub> of the isolators, and the relative position <jats:italic>D<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub> of the two middle isolators. The results of analysis demonstrate that applying a value of <jats:italic>H<\/jats:italic><jats:sub><jats:italic>z<\/jats:italic><\/jats:sub>\u2009=\u20090 produces the best vibration isolation performance overall under strong nonlinearity by avoiding unnecessary secondary peaks in the force transmission rate under harmonic mechanical excitation and ensuring a maximum high-frequency vibration isolation effect. However, applying a weak nonlinearity is better than a strong nonlinearity if <jats:italic>H<\/jats:italic><jats:sub><jats:italic>z<\/jats:italic><\/jats:sub> is not zero. In contrast, <jats:italic>D<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub> has little effect on the vibration isolation effect of the raft in the <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic>, and <jats:italic>z<\/jats:italic> directions. Therefore, an equidistant installation with <jats:italic>D<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>\u2009=\u20090.5 would be considered ideal from the standpoint of installation stability.<\/jats:p>","DOI":"10.1038\/s41598-024-58469-x","type":"journal-article","created":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T12:02:47Z","timestamp":1712577767000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Mechanical characteristics analysis of high dimensional vibration isolation systems based on high-static-low-dynamic stiffness technology"],"prefix":"10.1038","volume":"14","author":[{"given":"Bu-yun","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang-geng","family":"Shuai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian-guo","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,8]]},"reference":[{"key":"58469_CR1","unstructured":"Howard, C. 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