Dynamic instability of castellated beams subjected to transverse periodic loading

In this study, an analytical solution is developed for the investigation of free vibra-tion, static buckling and dynamic instability of castellated beams subjected to trans-verse periodic loading. Bolotin’s method is used to perform the dynamic instability analysis. By assuming the instability modes, the mass, stiffness, and geometric stiff-ness matrices are derived using the kinetic energy, strain energy and potential of ap-plied loads. Analytical equations for determining the free vibration frequency, critical buckling moment, and excitation frequency of castellated beams are derived. In ad-dition, the influences of the flange width of the castellated beam and the static part of the applied load on the variation of dynamic instability zones are discussed.

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