Design and optimization of piezoelectric unimorph beams with distributed excitation

A method is presented to design an optimal unimorph beam that flexes and generates voltage in response to a distributed load acting over its length using an analytical model. The objective is to design a beam that resonates at a specified frequency at which there is a peak in the excitation. The associated open-circuit voltage sensitivity and gain bandwidth product are functions to be maximized. For specific boundary conditions and pairs of materials, the dimensional ratio of the thickness of the piezoelectric layer to the square of the length of the beam is chosen such that the beam resonates at the specified frequency. The two optimum values of the dimensionless ratio of the thicknesses of the elastic and piezoelectric layers associated with the maximum values of the two functions of interest are determined through a simple one-dimensional search. Figures of merit and numerical results are used to show the effect of boundary conditions and properties of materials on the functions of interest. All beams with the optimum ratio of thicknesses are equally good and the dimensions of a beam for a specific application are to be chosen by considering principles of design for manufacture and the external electronic circuit.