Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix-中国期刊网

摘要 Inthispaper,howtocomputetheeigenfrequenciesofthestructurescomposedofaseriesofinclinedcablesisshown.Thephysicsofaninclinedcablecanbecomplicated,sosolvingthedifferentialequationsevenapproximatelyisdifficult.However,ratherthansolvingthesystemof4first-orderequationsgoverningthedynamicsofeachcable,thegoverningequationsareinsteadconvertedtoasetofequationsthattheexteriormatrixsatisfies.Therefore,theexteriormatrixmethod(EMM)isusedwithoutsolvingtheoriginalgoverningequations.Eventhoughthisproducesasystemof6first-orderequations,thesimpleasymptotictechniquestofindthefirstthreetermsoftheperturbativesolutioncanbeused.Thesolutionscanthenbeassembledtoproducea6×6exteriormatrixforacablesection.Thematricesforeachcableinthestructurearemultipliedtogether,alongwiththeexteriormatricesforeachjoint.Therootsoftheproductgiveustheeigenfrequenciesofthesystem.

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Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix

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Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix

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