Analytical solutions for bending of piezoelectric micro-beam sensors under surface stress effects

Piezoelectric sensors have been extensively utilized for the specific identification of biomolecules and the detection of chemical toxins. The optimization of piezoelectric micro-beam sensor design is crucial for applications in medical and environmental protection. This study analytically addresses the bending of piezoelectric micro-beams under surface stress by reformulating it as a plane stress problem within the framework of elasticity. A polynomial solution for stress and electric displacement is derived using the semi-inverse method for both cantilever and simply supported micro-beams. The numerical results concerning the components of stress, deflection, and electric potential are thoroughly discussed. Additionally, the influence of material parameters on the stresses, deflection, and electric potential of the piezoelectric micro-beams is examined in case of three kinds of common piezoelectric materials, thereby validating the plane-section assumption of material mechanics. The study provides theoretical guidance for the design and optimization of piezoelectric micro-beam sensors.