This paper presents an investigation on free vibration of thick prismatic structures (thick-walled opensections of L, T C, and I shapes). The derivation of a linear frequency equation based on an exactthree-dimensional small-strain linearly elastic principle is presented. This formulation uses one andtwo-dimensional polynomial series to approximate the spatial displacements of the thick-walled opensections in three dimension. The proposed technique is applicable to vibration of thick-walled opensections of different cross-sectional geometries and end support conditions. In this study, however;we focus primarily on the cantilevered case which has high value in practical applications. Theperturbation of frequency responses due to the variations of cross-sectional geometries and wallthicknesses is investigated. First-known frequency parameters and three-dimensional deformedmode shapes of these thick-walled open sections are presented in vivid graphical forms. The newresults may serve as a benchmark reference to future research into the refined beam and plate theoriesand also for checking the accuracy of new numerical techniques.
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