<p class="MsoNormal" style="text-align: justify">Point attachments on a beam cause incident flexural waves to be scattered and/or absorbed. Clusters of such scatterers produce non-symmetric, that is, different depending on the side of incidence, reflection and absorption but will have symmetric transmission, as reciprocity imposes, provided that those attachments are linear. The scattering properties of such linear systems can be analyzed exactly by solving an appropriate system of linear equations. When nonlinear attachments are considered, the multiple scattering problem will in general not be analytically solvable. Instead, approximate perturbation techniques, providing analytical solutions of different orders of approximation, can be applied. For such a cluster of nonlinear scatterers, the transmission of flexural waves through the cluster may also be non-symmetric, thus breaking the transmission symmetry, i.e. reciprocity. Another consequence of the nonlinear elements is the generation of higher-order waves. Depending on the type of nonlinearity, the higher-order waves may arise at different multiples of the frequency of the incident wave. Consequently, the higher-order waves will undergo complex multiple scattering interactions at these harmonic frequencies and may display different amplitudes towards either side of the cluster, also depending on the side of incidence. Utilizing some of these exotic properties of clusters of nonlinear scatterers, we design and present two acoustical devices. First, a cluster of two scatterers where one is nonlinear is shown, whose response properties resemble those of a narrowband stop filter whose filtering properties depend on the amplitude of the incident wave. At a specific frequency and for a particular value of the incident amplitude the wave is fully absorbed, whereas the device transmits waves of slightly different incident amplitude at the same frequency. Using an additional matched control wave of small amplitude and turning this on or off, the cluster can function as a switch for an incident wave at the frequency and amplitude tuned to give total absorption. The second device presented consists of a cluster of three scatterers where one has a cubically nonlinear stiffness, and prohibits the transmission of waves at the fundamental frequency while generating third-harmonic waves only towards the direction of transmission. Thus, this system acts as a frequency converter, where a portion of the incoming energy is converted from the fundamental frequency to the third harmonic and only the third-harmonic wave is transmitted. Such scatterer clusters that present tunability or perform energy conversion may form components of systems that perform logic operations in the regime of elastic waves.</p>

Tunability and Energy Conversion in Nonlinear Multiple Scattering Systems

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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