Signatures of the second spectrum of bending modes in beams with variable cross-sections

Motivated by the scarcity of experimental works reporting the spectrum of bending vibration modes in beams with variable cross-sections over a relatively wide range of frequencies, in this work, we report an extensive and accurate experimental and numerical study of the spectrum of aluminium beams with variable cross-sections. Three distinct geometries are analysed: conical rectangular, conical circular, and a locally periodic beam composed of conical rectangular segments. By using proper configurations of electromagnetic acoustic transducers (EMATs), we achieve selective excitation and detection of bending modes in a contactless manner, minimising experimental perturbations. We have found signatures of the so-called second spectrum beyond a cutoff frequency, characterised by the emergence of a pattern of doublets, and we have corroborated the experimental results with Finite element simulations in COMSOL. The excellent agreement between experiment and simulation–characterized by relative frequency errors below 4%–supports the reliability of both the experimental method and numerical models. The present work also aims to serve as a benchmark for studies related to beams with variable cross-sections.