Free vibration to a system of cantilever nanobeams

• Autorzy: Ciekot A. , Kukla S.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a solution to the free vibration problem of a system of two cantilever nanobeams. The nanobeams of the system are axially loaded and coupled by discrete translational springs. The solution of the problem by using the Green’s function method has been obtained. A numerical example shows the effect of the small scale on free vibration frequencies of the nanobeam system considered.

Słowa kluczowe

EN

cantilever nanobeams; free vibration; Green's function method

PL

drgania swobodne; metoda funkcji Greena

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 3
• Strony: 29--36
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Ciekot A.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

autor

Kukla S.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Eringen A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface-waves, Journal of Applied Physics 1983, 54, 4703-4710.
• [2] Reddy J.N., Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 2007, 45, 228-307.
• [3] Aydogdu M., A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E 2009, 41, 1651-1655.
• [4] Thai H.T., A nonlocal beam theory for bending, buckling and vibration of nanobeams, International Journal of Engineering Science 2012, 52, 56-64.
• [5] Eltaher M.A., Alshorbagy A.E., Mahmoud F.F., Vibration analysis of Euler-Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling 2013, 3(7), 4787-4797.
• [6] Peddieson J., Buchanan G.R., McNitt R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 2003, 41, 305-312.
• [7] Lim C.W., Li C., Lu J.L., The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams, Interaction and Multiscale Mech. 2009, 2(3), 223-233.
• [8] Murmu T., Adhikari S., Axial instability of double-nanobeam-system, Physics Letters A 2011, 375, 601-608.
• [9] Ciekot A., Kukla S., Frequency analysis of a double-nanobeam system, Journal of Applied Mathematics and Computational Mechanics 2014, 13(1), 23-31.
• [10] Richards D., Advanced Mathematical Methods with Maple, Cambridge University Press, 2009.