Vibrational behavior of sandwich structures overloaded by fractal distribution of masses

Jérémie Derré (1) , Frank Simon (1)

1 ONERA - The French Aerospace Lab [Toulouse]

This paper presents the modeling and numerical simulations of the vibrational behavior of sandwich panels locally overloaded by a fractal distribution of masses. The structural model hypotheses consist in a homogenized material, which is overloaded by small masses distributed following a fractal pattern. The flat panel is then uniformly discretized and the spatial derivatives operators are approximated using finite differences. The time-harmonic equation is recast into an eigenvalue problem and solved to find natural frequencies and mode shapes. The panel is simply-supported on all of its edges. Simulations of a non-overloaded panel are compared to analytic results in term of wavenumbers and mode shapes. Simulations of fractally overloaded panels exhibit localization phenomena when the inter-mass distance is comparable to half the structural wavelength. The influence of the fractal distribution is investigated through the fractal order, the modal frequencies, and the evolution of the modal density. The material is designed to reduce the structural vibration but also the acoustic radiation generated by the structure. The finite differences model can be used to compute the acoustic radiation of such a structure.

Mots clés: ACOUSTICS; VIBRATION; SANDWICH PANEL; FRACTAL; ACOUSTIC PHENOMENA; AUDITORY SYSTEM; FINITE DIFFERENCE METHODS; COMPOSITE MATERIALS; OSCILLATORS

Domaines: Vibrations [physics.class-ph]; Modélisation et simulation

Jérémie Derré, Frank Simon. Vibrational behavior of sandwich structures overloaded by fractal distribution of masses. Proceedings of meetings on acoustics, 2017, Acoustics `17 Boston 173rd Meeting of Acoustical Society of America and 8th Forum Acusticum, 30, pp.065012. ⟨10.1121/2.0000602⟩. ⟨hal-01716272⟩