This paper presents closed form solutions for active control of dynamic instability of initially curved piezolaminated columns. Piezoelectric sensors and actuators are used in control. The electromechanical piezoelectric constitutive laws are adopted along with classical laminated plate theory. A solution for the stability of the column is derived using the geometric imperfection approach. A constant gain feedback control algorithm is derived using modified stiffness and increased Euler's critical buckling load during piezoelectric actuation. Control of a geometrically imperfect piezolaminated column subject to static, periodic and arbitrary loading in the axial direction is demonstrated in both frequency domain and time domain. A novel limiting actuation concept is developed based on the bending strains.
The present paper demonstrates the effect of axial forces on smart columns that have adhesively bonded piezoelectric skins on substrates. Exact solutions for the piezolaminated columns have been presented. The solutions have been validated through experimental studies. The objectives of the present work are (1) to show the effect of axial force on sensing and actuation mechanisms of piezoelectric materials and (2) to demonstrate the active control of column type structures using these materials. In the experimental work, polyvinylidene fluoride (PVDF) films have been used as smart skins on a plastic substrate. PVDF films are shaped corresponding to the first mode shape of the cantilever column to ensure proportional sensing and actuation.
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