On the Parametric Resonance of Columns Carrying Concentrated Masses

The effect of various parameters upon the region of dynamic instability of a uniform simply supported column carrying n concentrated masses and subjected to an axial periodic force at one end is presented. The effect of axial inertia of the mass per unit length of the column is also included. This problem is reduced to a coupled system of two homogeneous partial differential equations of second order with periodic coefficients which can be written in the form of a matric differential equation of the Mathieu-Hill type. A solution methodology is developed and successfully demonstrated through numerical examples.