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Inverse load identification in vibrating nanoplates

Kawano A.
•
Morassi A.
•
Zaera R.
2022
  • journal article

Periodico
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Abstract
In this paper, we consider the uniqueness issue for the inverse problem of load identification in a nanoplate by dynamic measurements. Working in the framework of the strain gradient linear elasticity theory, we first deduce a Kirchhoff-Love nanoplate model, and we analyze the well-posedness of the equilibrium problem, clarifying the correct Neumann conditions on curved portions of the boundary. Our uniqueness result states that, given a transverse dynamic load (Formula presented.), where (Formula presented.) and (Formula presented.) are known time-dependent functions, if the transverse displacement of the nanoplate is known in an open subset of its domain for any interval of time, then the spatial components (Formula presented.) can be determined uniquely from the data. The proof is based on the spherical means method. The uniqueness result suggests a reconstruction technique to approximate the loads, as confirmed by a series of numerical simulations performed on a rectangular clamped nanoplate.
DOI
10.1002/mma.8565
Archivio
http://hdl.handle.net/11390/1229613
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85134251725
https://ricerca.unityfvg.it/handle/11390/1229613
Diritti
metadata only access
Soggetti
  • eigenvalue

  • identification of mas...

  • inverse problem

  • microplate

  • strain-gradient elast...

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