Minimax-Based Finite Element Analysis of Electromechanical Interaction in a Piezoelectric Cantilevered Beam Using MATLAB

Abstract

The dimensions and loading of piezoelectric cantilever beams influence their coupled mechanical and electrical responses. This paper investigates the effects of beam length, width, and applied tip force on static displacement and electrical potential using a hybrid finite element and moving average approach. A mathematical model describing the governing electromechanical equations was developed and solved using eight-node quadratic quadrilateral finite elements. A moving average filter was then applied to smooth the numerical results and reduce fluctuations associated with differences in scale. The model was evaluated, followed by a parametric study of beam geometry and loading. With 30,000 elements, the filtered model predicts an electrical potential of 1.1376 mV. The corresponding differences in displacement and electrical potential are approximately 3.6% and 1.3%, respectively. The parametric study considers beam lengths of 80 to140 mm, widths of 40 to 80 mm, and tip forces of 0.05 to 1.2 N. Under a tip force of 1.2 N, increasing the beam length from 80 to 140 mm at a fixed width of 40 mm increases the electrical potential from 10.19 to 45.69 mV. Increasing the width from 40 to 80 mm at a fixed length of 120 mm reduces the electrical potential from 29.85 to 5.06 mV. Both displacement and electrical potential increase approximately linearly with applied force. These findings characterise the sensitivity of the modelled cantilevers to geometry and loading under static conditions and may inform the preliminary design of piezoelectric energy harvesters intended for energy harvester device applications.