Nonlinear vibration and characteristics of flexible plate-strips with non-symmetric boundary conditions

Regular and chaotic vibrations together with bifurcations of flexible plate-strips with non-symmetric boundary conditions, are investigated through the Bubnov–Galerkin method and a finite difference method of error O(h4). Particular attention is paid to non-symmetric boundary conditions. Lyapunov exponents are estimated via Bennetin’s method. Some new examples of routes from regular to chaotic dynamics, and within chaotic dynamics are illustrated and discussed. The phase transitions from chaos to hyperchaos, and a novel phenomenon of a shift from hyperchaos to hyperhyper chaos is also reported.