Some Studies on Parametric Instability and Control of Composite Structures Using Smart Layers. : The present investigation is an attempt towards a comprehensive understanding of the problem of parametric instability of composite and functionally graded beams and plates when subjected to axial periodic pulsating loads. The non-dimensional equations of motion have been derived using the Hamilton’s variational principle coupled with the finite element method. The regions of parametric instability have been established by applying the method of multiple scales. In addition, a control algorithm based on negative velocity feedback law is employed to control the zones of parametric instability. The effects of various system parameters on the regions parametric instability are analyzed critically. Based on the results, qualitative suggestions are made that could lead to better stable systems in the present context.