Chaotic vibrations of size-dependent flexible rectangular plates

摘要: A mathematical model describing nonlinear vibrations of size-dependent rectangular plates is proposed. The are treated as the Cosserat continuum with bounded rotations their particles (pseudo-continuum). governing partial differential equations (PDEs) and boundary/initial conditions obtained using von Karman geometric relations, they yielded by energetic Hamilton principle. derived mixed-form PDEs reduced to ordinary algebraic (AEs) (i) Galerkin–Krylov–Bogoliubov method (GKBM) in higher approximations, then solved help a combination Runge–Kutta methods second fourth order, (ii) finite difference (FDM), (iii) Newmark method. convergence FDM vs interval space coordinate grids GKBM number employed terms approximating function investigated. latter approach allows for achieving reliable results taking account almost infinite-degree-of-freedom approximation regular chaotic dynamics studied plates. problem stability loss under harmonic load also tackled.