Coupled in- and out-of-plane bending, axial, and torsional vibrations exist in a built-up space frame, which greatly challenges the conventional modal approach. A wave-based exact analytical method is applied to study vibrations in built-up multistory space frames. From the wave vibration standpoint, vibrations are described as waves propagating along uniform structural elements and being reflected and transmitted at structural discontinuities. Free vibration responses are studied based on classical vibration theories. Numerical examples are given with comparison to results available in the literature. Good agreements have been reached. This study not only provides an exact analytical approach to complex vibration problems in built-up multistory space frames that have mostly been studied numerically but also provides a benchmark to existing numerical tools.

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