1. Inverse load identification in vibrating nanoplates.
- Author
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Kawano, Alexandre, Morassi, Antonino, and Zaera, Ramón
- Subjects
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STRAINS & stresses (Mechanics) , *INVERSE problems , *DYNAMIC loads , *ELASTICITY , *COMPUTER simulation , *RECTANGLES , *ELECTRON field emission - 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 ∑m=1Mgm(t)fm(x)$$ {\sum}_{m=1}^M{g}_m(t){f}_m(x) $$, where M≥1$$ M\ge 1 $$ and {gm(t)}m=1M$$ {\left\{{g}_m(t)\right\}}_{m=1}^M $$ 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 {fm(x)}m=1M$$ {\left\{{f}_m(x)\right\}}_{m=1}^M $$ 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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