Open AccessNatural vibrations of nanostrips with cracks
Author(s) -
Md. Mamun Hossain,
Jaan Lellep
Publication year - 2021
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2021.25.06
Subject(s) - vibration , piecewise , strips , inertia , elasticity (physics) , materials science , natural frequency , rotary inertia , nonlinear system , structural engineering , composite material , mechanics , mathematical analysis , physics , mathematics , classical mechanics , acoustics , engineering , quantum mechanics
Employing the main equations of the theory of plates accounting for the rotational inertia the transverse vibrations of nanobeams and nanostrips are investigated. The nano strips under consideration have piecewise constant dimensions of cross sections. The nanosheets are weakened by cracks at re-entrant corners of steps. While the material behavior corresponds to the Eringen’s nonlocal theory of elasticity it is assumed that the cracks produce additional local compliance, which can be evaluated with the aid of the stress intensity factor at the cracktip. A numerical algorithm for determination of natural frequencies of nanosheets is developed.