On the natural frequencies of simply supported beams curved in mode shapes

Slender beams present interesting dynamic characteristics when they are curved according to a given shape. When the beam is curved according to one of its mode shapes, the natural frequency associated to that mode tends to increase significantly without affecting the other natural frequencies. It has also been noticed that such effect can only occur if the axial displacements of the beam are constrained. The question is why such phenomenon occur? What is the physics behind these effects? This work tackles these questions by the analytical analysis of the in-plane vibrations of the beam curved in different mode shapes. (C) 2020 Elsevier Ltd. All rights reserved.