Modeling tip displacement in double reeds using dual beam frameworks

While much work has been done towards investigating reed tip displacement for single reeds, few models exist for double reeds. Such a gap in literature has prompted the need for developing coupled multiphysics frameworks to help musicians understand how factors such as age, material stiffness and blade thickness affect tip displacement and sound production. As a first-order approximation, this study proposes two models: a dual Eulerian beam model and a dual Timoshenko beam model, where time-dependent forcing terms are fitted from experimental data collected in an anechoic chamber. This model is solved using a 4th order central finite difference scheme that accounts for variable cross-sectional area and reed stiffness. Bending modes for an Arundo Donax, bio-composite, and Légère reed are compared under the assumption of symmetric forcing as a first-order approximation. Grid refinement studies and L2-error norms comparing the two beam models are reported.