In the early years of numerical simulation methods, Fermi, Pasta, Ulam and Tsingou (FPUT) discovered that an undamped, weakly nonlinear equation describing the motion of a chain of masses and springs could show complex dynamics. Integration of these equations froma n initial displacement in the formof the fundamental mode resulted in significant mode coupling: energy was transferred from the fundamental mode to several other modes, before the energy would return to the initial condition. To date, very little observations of such behavior in mechanical vibrations have been reported. Recent developments in fabrication of high stress Silicon-Nitride (Si3N4) string resonators have shown that it is possible to generate resonators with extremely high Q-factors, proving a potential testbed for these mechanics. This research shows, through modal conversionof the FPUT potential, that one may observe significant FPUT behavior in systems with non-integer frequency ratios and certain coupling coefficients. In addition, it is shown that for the default FPUT beta-model, the effect of damping is negligible for fundamental mode Q-factors higher than 10,000. Simulations of the experimental
frequency response of a high-Q Si3N4 string resonator show that the nonlinear dynamics of these resonators may be approximated by an analytical model that does not possess the required frequency ratios and coupling coefficients for FPUT behavior. Another string model, for which no mechanical equivalent
has (yet) been found, may potentially show FPUT behavior. Several string-like resonator designs are tested using a numerical tool which can extract the modal coefficients. These resonators are modelled using simplified
deformation models, which account only for axial deformation of the structure. The results for various string-like designs show that the eigenfrequencies and nonlinearity may be engineered easily, but these do
not generate the required coupling coefficient for FPUT behavior. ... Read more

Elastic guided waves are carriers of information of the (change in) condition of plate-like structures like wind-turbine blades, airplane wings and road surfaces on bridges. To measure these guided waves we do not have to use piezos. Other sensors offer interesting benefits like contactless sensing, embedding, or measuring without electricity. However, quantitively comparing them is not trivial: the sensors all have different geometries, operating principles and are sensitive to different mode shapes of guided waves. We designed and performed an experiment to quantitatively compare the performance of five state of the art sensors (piezo, in-fiber interferometer, FBG, free-space interferometer, and ring resonator sensors) to measure So and Ao guided elastic waves. The measurements were performed on guided waves in an 8 mm steel plate, in the 60-150 kHz range. The dimensions of the plate and the positioning of the sources and sensors was chosen such that the So and Ao waves arrived in separate time windows. The in-fiber interferometer was the sensor that came closest to the piezo, that was used as reference sensor (-11 dB difference in SNR), the other optical based sensors have SNR values below -30 dB compared to the piezo. The measurements and simulations show that it is important to have two quantitative SNR measures for the performance to measure guided waves: one for the So and one for the Ao wave. For one sensor we found a difference of 22 dB between these two SNR measures. ... Read more