Vibration of thick prismatic structures with three-dimensional flexibilities

This paper presents an investigation on free vibration of thick prismatic structures (thick-walled open sections of L, T, C, and I shapes). The derivation of a linear frequency equation based on an exact three-dimensional small-strain linearly elastic principle is presented. This formulation uses one and two-dimensional polynomial series to approximate the spatial displacements of the thick-walled open sections in three dimension. The proposed technique is applicable to vibration of thick-walled open sections 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. The perturbation of frequency responses due to the variations of cross-sectional geometries and wall thicknesses is investigated. First-known frequency parameters and three-dimensional deformed mode shapes of these thick-walled open sections are presented in vivid graphical forms. The new results may serve as a benchmark reference to future research into the refined beam and plate theories and also for checking t7he accuracy of new numerical techniques.