NONLINEAR FREE-VIBRATIONS OF COMPOSITES PLATES

The evolution of the Natural Mode Method (NMM) for finite element anal ysis 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 tra nslational and rotational inertia are included in the mass matrix whic h 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 e lement solutions. Subsequently the large-amplitude nonlinear undamped free vibration of composite plates is investigated. A computational sc heme is conceived, whereby the structure is initially displaced by con ducting a full geometrically nonlinear static analysis, and subsequent ly set to transient nonlinear free oscillations by removing the static loading. In this regard, we discuss the two structured Eulerian (conv ective) computational schemes employed namely, the ARIBAN scheme (accu mulation of rigid-body and natural modes) for static nonlinear analysi s, and the cubic Hermitian scheme (CUHERM) for large-displacement tran sient deformation. Numerical examples demonstrate the efficiency of th e formulation and the potential of the Natural Mode Method to deal vig orously with intricate nonlinear time-dependent phenomena, as well as its potential to provide answers for larger and more complex structure s. The study also indicates the efficiency and tailoring flexibility o ffered by advanced composite structural systems.