PARAMETRICALLY INDUCED VIBRATION IN CONCRETE COLUMNS

A mathematical model is developed for simply supported plain concrete columns, accounting for their nonlinear material characteristic. The a xial and transverse motions of concrete columns are found to be second - and fourth-order nonlinear partial differential equations, respectiv ely. These equations are then reduced to a set of coupled nonlinear di fferential equations in terms of time-dependent modal coefficients. Ap proximate solution of the axial vibration and its substitution in the equation governing the transverse vibration of the column results in a single-degree-of-freedom Hill's equation. This equation together with a method based on the Floquet theory are employed to investigate para metric stability of a simply supported concrete column. Results, obtai ned from Strutt diagrams, indicate the existence of instability region s corresponding to principal and secondary resonances, and potential f or failure under sinusoidal amplitude of magnitudes far below that of static buckling. Moreover, the vibration parametric stability signatur e of columns are found to be relatively invariant with respect to thei r material and geometric characteristics.