Modeling of the multi-cable supported arch and a novel technique to investigate the natural vibratory characteristics

•Modeling MSA with the idea “dividing whole into parts, assembling parts to whole”.•The global structure is divided into a series of chained cable-arch substructures.•STT isolating technique is novel, unification converts to transferring arch segments.•Vibratory characteristics on sag-to-span ratios and inclined angels are investigated.•Local/global modes and veering phenomena in frequency spectrum are observed.