Interactions between nonlinear resonators represented in Volterra series

• Published in: Journal of sound and vibration Vol. 520; p. 116590
• Main Author: Roze, David
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 03.03.2022; Elsevier Science Ltd; Elsevier
• Subjects: Acoustics; Bowing; Chemical synthesis; Constraint modelling; Engineering Sciences; Inverse problems; Inverse volterra kernels; Kernels; Mechanics; Nonlinear interactions; Nonlinear resonators; Nonlinear systems; Numerical analysis; Physics; Resonators; Signal and Image processing; Simulation; Strings; Velocity; Vibrations; Volterra series; Nonlinear resonators; Volterra series; Inverse volterra kernels; Nonlinear interactions
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2021.116590

This paper aims at introducing nonlinear interactions in the sound synthesis of nonlinear resonators. Sound synthesis is performed using the formalism of Volterra series which is used to describe and simulate weakly nonlinear models using their Volterra kernels. Interactions are constraints imposed to the considered models and are used to excite (e.g. bowing a string or striking a plate) or connect resonators together (such as connecting a string to a bridge). This requires to resolve an inverse problem giving the interaction force as a function of a given velocity. In the case of Volterra series, kernels of the inverse problem have been defined by Schetzen. Using this definition, a structure of simulation of the direct and inverse problems at each time step will be defined. Application to the case of a Kirchhoff-Carrier string connected to a Berger plate will be presented including computation of the kernels (direct and inverse), structure of simulation and numerical results.