New High Efficiency and Strength Bending Strain Sensor Based on Piezoelectric Stacks

This article is devoted to a mathematical model of a new piezoelectric sensor used for measuring bending strains. The first simple model of a piezoelectric sensor of bending deformations (we will call it a classical sensor) was presented in our previous paper. The classical sensor is a one-dimensional three-layer structure, in which the two outer layers are made of piezoelectric ceramic with preliminary polarization across the thickness of the sensor, and one elastic middle layer is located between these piezoelectric layers. In the present modified model of the new sensor, piezoelectric stacks are used instead of simple piezoelectric elements. As shown in the paper, this kind of piezoelectric composite sensor with stacks allows us to significantly increase the value and stability of the measured electrical signal and increase the accuracy of strains measurement. Piezoelectric ceramic is a brittle material. The use of stacks significantly reduces brittleness by enclosing thin layers of piezoelectric ceramic in a metal matrix. Piezoelectric laminated stacks have a periodic structure, and we will use the mathematical homogenization method to correctly determine their effective moduli (physical constants). Increasing the reliability of the proposed sensors, as well as the accuracy and stability of their deformation measurements, is aimed at enhancement of the mechanical safety of building structures, increasing the efficiency of their monitoring. The most important characteristic of any sensor is its efficiency. Our first classical bending strain sensor has a simple structure and an efficiency approaching the value of the coupling coefficient k31 (k31 is a constant describing a known physical property of a piezoelectric material). Our classic piezoelectric flexural strain sensor has an efficiency of the order of the coupling coefficient k31. For piezoelectric materials with a strong piezoelectric effect, the k31 value is approximately 0.30–0.35. The efficiency of our classical sensor is hundreds of times greater than the efficiency of the most popular tangential (longitudinal) strain sensor, developed by Lord Kelvin. The efficiency of the flexural strain sensor using stacks is of the order of the coupling coefficient k33. For the sensor with piezoelectric stacks, the value of efficiency is approximately 0.60–0.70. Note that the efficiency of the improved sensor is twice as high as the efficiency of our classic flexural strain sensor.

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