Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

Abstract In this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations problem based on von Kármán plate theory Kirchhoff–Love hypothesis. small-size effect is taken into account due nonlocal elasticity theory. formulation mixed employs Airy stress function. two-mode approximation deflection application Bubnov–Galerkin method reduces system ordinary differential equations. Varying load parameters parameter, bifurcation analysis performed. bifurcations diagrams, maximum Lyapunov exponents, phase portraits as well Poincare maps constructed numerical simulations. It shown that for some conditions chaotic motion may occur in system. Also, small-scale effects character vibrating regimes illustrated discussed.