Stability of an articulated column with two collocated piezoelectric actuators

This paper examines the stability and natural frequencies of the transverse vibrations of a slender articulated column with a pair of collocated piezoactuators. Buckling of the column can occur as one of the supports is subjected to a prescribed displacement, shortening the length of the system. The phenomenon can be counteracted by the tensile force generated by the actuators. The residual tensile force for a column with both ends restrained against longitudinal displacements and an arbitrary number of collocated actuators is derived by a variational principle, and applied to the considered system. The influence of such a created stress, along with the location of the hinge and adjacent piezoactuators of different lengths, on the stated objectives are numerically investigated after solving the boundary value problem. Any change in the relation between the axial stiffnesses of the piezo-column system and the core column affects the induced tensile force and also influences the adequate bending stiffnesses and mass per unit length of the structure, which is reflected in the numerical results. The absolute and relative enhancements in the critical force are presented for different geometrical parameters of the column. It is shown that the determined vibration modes can be employed to explain and interpret the first and second critical loads. Additional results show how a second pair of piezoactuators changes the courses of the natural vibration curves and affects the buckling force of the system.