Theoretical and experimental investigation of bending waves in beams with a periodic structure, by Bart Van Damme (Empa Switzerland) [Jan. 24, 2017]
DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017
Website of DENORMS Action
Programme of the Workshop
Acoustic metamaterials (i.e. subwavelength absorbers), metasurfaces and sonic crystals for audible sound manipulation
Speaker: Bart Van Damme (Empa Switzerland)
Sound transmission through panels is mainly carried by bending or flexural vibrations. Therefore, noise reduction can be achieved by minimizing the vibration amplitude of partition walls or floors. The traditional approach to achieve this is to increase the mass of the structure, but this can be problematic from an economical or structural point of view. Structural metamaterials exhibiting bandgaps - frequency bands in which certain wave types are highly attenuated - offer a practical solution to reduce sound transmission even with lightweight materials.
Low frequency bandgaps can be achieved using resonant metamaterials, in which case wave energy is dissipated via local mechanical or electromagnetic resonators. This approach results in a single, narrow, range of forbidden frequencies. The bandgap can be widened introducing damped resonators, but this also decreases the wave attenuation.
Bending waves in beams are the result of an interaction between longitudinal and shear waves, reflected many times along the thickness of the beam. It is known that introducing a periodic bending stiffness interferes with the flexural vibrations. The bending stiffness can be altered by varying the beam’s geometry or material parameters. We use an analytical combination of Euler’s beam equation with Floquet boundary conditions to show that a first bandgap can be found using a period of the beam 20 times smaller than the longitudinal wavelength. Moreover, due to the existence of an infinite number of flexural modes, more forbidden bands show up at higher frequencies.
The theoretical predictions are validated using 3D printed samples with varying geometries. The frequency response function of the beams is measured along the beam using a scanning laser vibrometer. The dispersion curves are reconstructed using two techniques: multidimensional FFTs and the inhomogeneous wave convolution (IWC) method. The advantage of the latter is that both the real part and complex part of the wavenumber can be identified from measurements.