Saratov, Saratov, Russian Federation
Saratov, Saratov, Russian Federation
Russian Federation
GRNTI 50.07 Теоретические основы вычислительной техники
BBK 3297 Вычислительная техника
The paper presents a visualization of the contact interaction of two Bernoulli-Euler nanobeams connected through boundary conditions. Mathematical models of beams are based on the gradient deformation theory and the theory of contact interaction of B. Y. Cantor. The visualization is based on Fourier transform and wavelet transform, phase portrait.
Bernoulli-Euler nanobeam, gradient deformation theory, contact problem, Fourier transform, wavelet
1. Fu, Y., Zhang, J. Electromechanical dynamic bucklingphenomenon in symmetric electric fields actuated microbeamsconsidering material damping. Acta Mech. 212, (2010), 29-42.
2. M. Moghimi Zand, and M. T. Ahmadian, “Static pull-inanalysis of electrostatically actuated microbeams usinghomotopy perturbation method”, Appl. Math. Model. 34(2010), 1032-1041.
3. Jia, X.L., Yang, J., Kitipornchai, S.: Pull-in instability ofgeometrically nonlinear micro-switches under electrostatic andCasimir forces. Acta Mech. 218, (2011), 161-174.
4. Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.,1994. Strain gradient plasticity: theory and experiments. ActaMetall. Mater. 42, 475-487.
5. Nix, W.D. Mechanical properties of thin films. Metall.Trans. A 20, (1989), 2217-2245.
6. E. Mazza, S. Abel,J. Dual, Experimental determination ofmechanical properties of Ni and Ni-Fe microbars, MicrosystemTechnologies 2 (4) (1996), 197-202
7. Lam DCC, Yang F, Chong ACM, Wang J, Tong PExperiments and theory in strain gradient elasticity. J MechPhys Solids 51: (2003) 1477-1508
8. Q. Ma,D. R. Clarke, Size dependent hardness of silversingle crystals, Journal of Materials Research 10 (4) (1995)853-863.
9. Dell’Isola F, Della Corte A, Esposito R, Russo L. Somecases of unrecognized transmission of scientific knowledge:From antiquity to Gabrio Piola’s peridynamics and generalizedcontinuum theories. Generalized Continua as Models forClassical and Advanced Materials: Springer; (2016). p. 77-128.
10. Cosserat E, Cosserat F. Théorie des corps déformables:Paris: Hermann et Fils, 1909.
11. Mindlin RD. Second gradient of strain and surface-tensionin linear elasticity. Int J Solids Struct. (1965);1:417-38.
12. Yang F, Chong ACM, Lam DCC, Tong P. Couple stressbased strain gradient theory for elasticity. Int J Solids Struct.(2002) ;39:2731-43.
13. Kantor B. Ya/, Bogatyrenko T. L. A method for solvingcontact problems in the nonlinear theory of shells. Dokl.Ukrain Academy of Sciences. Ser A 1; (1986). pp 18-21.
14. Krysko V.A., Koch M.I., Zhigalov M.V., Krysko A.V.“Chaotic Phase Synchronization of Vibrations of MultilayerBeam Structures” Journal of Applied Mechanics and TechnicalPhysics. 2012. T. 53. № 3. S. 451-459.
15. J. Awrejcewicz, M.V. Zhigalov, V.A. Krysko-jr., U.Nackenhorst, I.V. Papkova, A.V. Krysko, 'Nonlinear dynamicsand chaotic synchronization of contact interactions of multilayer beams', in: 'Dynamical Systems - Theory', Eds. J.Awrejcewicz, M. Kaźmierczak, P. Olejnik, J. Mrozowski, TUof Lodz Press, 2013, 283-292 (ISBN 978-83-7283-588-8)
16. Osipov G.V., Pikovsky A.S., Rosenblum M.G., Kurths J.Phys.rev. Lett. 1997. V. 55. P.2353.
17. Pikovsky A.S., Rosenblum M.G., Kurths J.Synhronization: a Universal Cocept in Nonlinear Sciences.Cambridge University Press, 2001.
