Investigations of chaotic dynamics of multi-layer beams taking into account rotational inertial effects

• A novel mathematical model of a vibrating Timoshenko-type beam is proposed.
• Rotational internal effects are taken into account.
• Finite Difference and Element Methods are applied validating numerical results.
• Chaotic behavior of beam layers vs. parameters and boundary conditions is studied.
• Novel scenarios into chaos of studied systems are detected and discussed.

We propose a novel mathematical model of a vibrating multi-layer Timoshenko-type beam. We show that the introduced model essentially changes the type of partial differential equations allowing inclusion of rotational inertial effects. We illustrate and discuss the influence of boundary conditions, the beam layers and parameters of the external load on the non-linear dynamics of this composite beam including a study of its regular, bifurcation and chaotic behavior.The originally derived infinite problem is reduced to the finite one using either Finite Difference Method (FDM) or Finite Element Method (FEM) which guarantees validity and reliability of the obtained numerical results. In addition, a comparative study is carried out aiming at a proper choice of the efficient wavelet transform. In particular, scenarios of transition into chaos are studied putting emphasis on novel phenomena. Charts of the system dynamical regimes are also constructed with respect to the control parameters regarding thickness and composition of the beam layers.