Transverse vibrations of cantilever beams: Analytical solutions with general steady-state forcing

Abstract

Novel theoretical approach for characterization of transverse vibrations of cantilever beams under continuous spatially distributed load is proposed. Four beam theories (Euler–Bernoulli, Euler–Bernoulli with dissipation, shear and shear with dissipation) are considered. Explicit analytical solutions are obtained for three of them and simplification algorithm for the fourth is proposed. Despite several limitations implied (time-independent loading, homogeneous boundary conditions) the solution developed is general enough and is applicable for a wide class of space-dependent loads. The approach is verified with available experimental data and shown to be applicable in a wide scale range.

Keywords

• Cantilever beams
• Transverse vibrations
• Euler–Bernoulli beams
• Tall buildings
• Cupula