Optimal placement of piezoelectric material on a cantilever beam for maximum piezoelectric damping and power harvesting efficiency

The loss factor of an electromechanical system characterizes the induced piezoelectric damping of the system for shunt damping applications, and it can also be used to represent the power harvesting efficiency of the system. This paper investigates the effect of piezoelectric patch placement on the loss factor, with the aim of finding an optimal location for the same amount of piezoelectric material. An analytical relationship between the loss factor and placement is presented and discussed for beam configurations. In addition, a structural model is developed based on wave propagation which accounts for the effects of the PZT patch on the system and is used to obtain the natural frequencies and mode shapes of the composite system. After that, numerical studies demonstrate the effects of placement on damping of various vibration modes, and the effects of patch size on optimal placement. For small piezoelectric patches, the optimal location is very close to the location of the overall maximum bending moment, where the mechanical strain energy density is maximized. Larger patches could be used to improve the damping or power harvesting efficiency of the system; however, the associated optimal placement might not be at the point of overall maximum bending moment. Moreover, as the patch size extends beyond a critical point, increasing the size can actually deteriorate the systems performance.