Sobre o evento:
The resonant frequencies of nanomechanical sensors can be highly sensitive to minute amounts of mass deposited on their surface. This remarkable property makes vibrating nanobeams and nanoplates promising tools for mass detection in chemical and biological applications. Beyond measuring the total added mass, a more challenging question arises: can a few resonant frequency shifts reveal how the unknown mass is distributed across the sensor?
Addressing this question requires an accurate mechanical model, since modelling errors may obscure the frequency shifts induced by the added mass. At the nanoscale, size-dependent effects can become significant, motivating the use of generalized continuum theories, such as strain-gradient elasticity. From a mathematical perspective, reconstructing an unknown mass distribution from a small number of resonant frequency shifts leads to a finite-data inverse eigenvalue problem, posing challenging questions of uniqueness and stability.
In this talk, we present recent results on mass identification using nanoplate resonators. Assuming that the added mass is a small perturbation of the reference mass, we show how resonant frequency shifts provide quantitative information on generalized Fourier coefficients of the unknown mass distribution, thereby revealing aspects of its spatial structure. Numerical experiments illustrate the reconstruction procedure and show that reliable results can be obtained even in the presence of measurement errors, provided these are sufficiently small relative to the mass-induced frequency shifts.
Minibiografia do palestrante:
Antonino Morassi is Full Professor of Structural Mechanics at the University of Udine, Italy. He holds degrees in Civil Engineering and Mathematics, and his research focuses on both theoretical and applied inverse problems in linear elasticity and structural mechanics. His recent research interests include the modelling of complex vibrating systems, such as nanostructures and spider webs, and the identification of their mechanical properties using dynamic methods.
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