Modeling and Response Analysis of Piezoelectric Flag in Wind Flow

Within the past decade, research in the piezoelectric energy harvesting field has grown significantly concerning material selection, device configurations, and actuation methods. Oscillating cantilevered piezoelectric energy harvesters are one of the more common designs. The flag is modeled as a cantilevered Euler-Bernoulli beam with a low modulus of elasticity, and the representative equation for this is broadly accepted. The wind pressure is modeled by a method that is apparently well accepted in the aerospace field. Among other modeling assumptions, the partial differential equation is considered separable. Once separated, the spatial equation is adjusted using an auxiliary function in order to determine the mode shapes. With the mode shapes characterized, the time function is rendered, which can yield representations for either a damped or undamped system. Individually, these time functions are combined with the adjusted spatial function using the Galerkin method. Plotted results represent the periodic, two-dimensional system response over time.