NONLINEAR FREE-VIBRATIONS OF COMPOSITES PLATES

The evolution of the Natural Mode Method (NMM) for finite element analysis of complex composite structures continues in the present study by applying its principles and formulating the kinematically consistent matrix of a model three-node multilayered triangular element. Both translational and rotational inertia are included in the mass matrix which is conceived using kinematical and geometrical arguments consistent with the assumed natural rigid-body and straining modes of the element. Linear eigenfrequencies are validated with experimental and finite element solutions. Subsequently the large-amplitude nonlinear undamped free vibration of composite plates is investigated. A computational scheme is conceived, whereby the structure is initially displaced by conducting a full geometrically nonlinear static analysis, and subsequently set to transient nonlinear free oscillations by removing the static loading. In this regard, we discuss the two structured Eulerian (convective) computational schemes employed namely, the ARIBAN scheme (accumulation of rigid-body and natural modes) for static nonlinear analysis, and the cubic Hermitian scheme (CUHERM) for large-displacement transient deformation. Numerical examples demonstrate the efficiency of the formulation and the potential of the Natural Mode Method to deal vigorously with intricate nonlinear time-dependent phenomena, as well as its potential to provide answers for larger and more complex structures. The study also indicates the efficiency and tailoring flexibility offered by advanced composite structural systems.