Analysis of the Effects of the Viscous Thermal Losses in the Flute Musical Instruments

• Main Authors: Gaby Abou Haidar, Xavier Moreau, Roy Abi Zeid Daou
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Fractal and Fractional
• Subjects: wind musical instrument; system approach; viscous thermal losses; artificial mouth; CRONE (Commande Robuste d’Ordre Non-Entier) system design methodology
• Online Access: https://www.mdpi.com/2504-3110/5/1/11

This article presents the third part of a larger project whose final objective is to study and analyse the effects of viscous thermal losses in a flute wind musical instrument. After implementing the test bench in the first phase and modelling and validating the dynamic behaviour of the simulator, based on the previously implemented test bench (without considering the losses in the system) in the second phase, this third phase deals with the study of the viscous thermal losses that will be generated within the resonator of the flute. These losses are mainly due to the friction of the air inside the resonator with its boundaries and the changes of the temperature within this medium. They are mainly affected by the flute geometry and the materials used in the fabrication of this instrument. After modelling these losses in the frequency domain, they will be represented using a system approach where the fractional order part is separated from the system’s transfer function. Thus, this representation allows us to study, in a precise way, the influence of the fractional order behaviour on the overall system. Effectively, the fractional behavior only appears much below the 20 Hz audible frequencies, but it explains the influence of this order on the frequency response over the range [²⁰,²⁰,⁰⁰⁰] Hz. Some simulations will be proposed to show the effects of the fractional order on the system response.