Comparative study of higher modes of vibration in cantilever beams: Exact analytical analysis versus FEM analysis for accordion free reed acoustics

This study delves into the critical role of higher vibration modes in cantilever beams, focusing on their significance for the acoustics of accordion free reeds. Through a comparative analysis, we explore exact analytical methods versus Finite Element Method (FEM) simulations to understand the vibrations not only parallel to the airflow direction but also perpendicular and torsional modes. Previous research has underscored the importance of these higher modes in shaping the timbre and influencing attack transients. Our findings reveal that while analytical solutions provide precise insights into fundamental vibrations, FEM offers comprehensive data on complex mode interactions. This dual approach enhances the understanding of reed dynamics, offering valuable insights for musical instrument design and acoustic optimization. By bridging analytical rigor with computational flexibility, this paper contributes to the nuanced study of musical timbre and transient behaviors, laying the groundwork for future innovations in reed instrument engineering.