Electromechanical deflections of piezoelectric tubes with quartered electrodes

Abstract

The deflection of a piezoelectric tube, with the outer (or inner) metal coating sectioned into four quadrants, is analyzed. We show that by applying a voltage V on one of the quadrants, the electromechanical deflection is (√2d₃₁VL²/πDh), where d₃₁ is the piezoelectric coefficient, L is the length, D the diameter, and h the wall thickness of the tube. The deflections calculated with it agree well with the results of finite‐element calculations and direct experimental measurements. The formula can be used in the design and application of tube scanners in scanning tunneling microscopes and scanning force microscopes.