Abstract
This paper deals with free vibrations of horizontally curved beams built with a constant volume of beam material. The cross section of each beam is a solid regular polygon whose depth is varied in a functional fashion. Three shapes of beam (circular, parabolic, and sinusoidal) and three kinds of taper type (circular, parabolic, and sinusoidal) are considered. Differential equations governing free vibrations of such tapered beams are derived; these equations are numerically solved to calculate the natural frequencies and mode shapes. The results are presented in tables and figures that relate the frequency curves to beam parameters. Typical mode shapes of the deformations are presented in figures. Laboratory scale experiments were conducted to measure the natural frequencies.
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Lee, B.K., Park, K.K., Lee, T.E. et al. Free vibrations of horizontally curved beams with constant volume. KSCE J Civ Eng 18, 199–212 (2014). https://doi.org/10.1007/s12205-014-0356-y
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DOI: https://doi.org/10.1007/s12205-014-0356-y