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Melnikov analysis of the nonlocal nanobeam resting on fractional-order softening nonlinear viscoelastic foundations. (English) Zbl 1484.37100

Summary: In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that the distance between chaotic region and non-chaotic region in this kind of structure depends strongly on the fractional order parameter.

MSC:

37N15 Dynamical systems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
26A33 Fractional derivatives and integrals
74D10 Nonlinear constitutive equations for materials with memory
74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
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