Identification of general added mass distribution in nanorods from two-spectra finite data Articles uri icon

publication date

  • December 2019

start page

  • 106286(1)

end page

  • 106286(18)


  • 134

International Standard Serial Number (ISSN)

  • 0888-3270

Electronic International Standard Serial Number (EISSN)

  • 1096-1216


  • Nanomechanical resonators consisting in one-dimensional vibrating structures have remarkable performance in detecting small adherent masses. The mass sensing principle is based on the use of the resonant
    frequency shifts caused by unknown attached masses. In spite of its
    importance in applications, few studies are available on this inverse
    problem. Dilena et al. (2019) presented a method for reconstructing a
    small mass distribution by using the first N resonant
    frequencies of the free axial vibration of a nanorod under clamped end
    conditions. In order to avoid trivial non-uniqueness when spectral data
    belonging to a single spectrum are used, the mass variation was supposed
    to be supported in half of the axis interval. In this paper, we remove
    this a priori assumption on the mass support, and we show how to extend
    the method to reconstruct a general mass distribution by adding to the input data the first N
    lower eigenvalues of the nanorod under clamped-free end conditions. The
    nanobeam is modelled using the modified strain gradient theory to
    account for the microstructure and size effects. The reconstruction is
    based on an iterative procedure which takes advantage of the closed-form
    solution available when the mass change is small, and turns out to be
    convergent under this assumption. The results of an extended series of
    numerical simulations support the theoretical results.


  • axial vibration; inverse problems; mass identification; nanorods; nanosensors; strain gradient theory