Finite element large amplitude free flexural vibration analysis of isotropic plates

Abstract

Structural components are generally subjected to dynamic loadings in their working life. Very often these components may have to perform in severe dynamic environment wherein the maximum damage results from the resonant vibration. Susceptibility to fracture of materials due to vibration is determined from stress and frequency. Maximum amplitude of the vibration must be in the limited for the safety of the structure. Hence vibration analysis has become very important in designing a structure to know in advance its response and to take necessary steps to control the structural vibrations and its amplitudes.The non-linear or large amplitude flexural vibration of plates has received considerable attention in recent years because of the great importance and interest attached to the structures of low flexural rigidity. These easily deformable structures vibrate at large amplitudes. The solution obtained based on the lineage models provide no more than a first approximation to the actual solutions. The increasing demand for more realistic models to predict the responses of elastic bodies combined with the availability of super computational facilities have enabled researchers to abandon the linear theories in favor of non-linear methods of solutions.