Size-dependent modeling and performance enhancement of functionally graded piezoelectric energy harvesters

Functionally graded materials (FGMs) are a unique type of composite in which the material properties vary in one or more directions from one material to another. FGMs are usually composed of a metal and a ceramic. One special type of FGM is known as functionally graded piezoelectric materials (FGPM) which can be utilized for energy-harvesting applications. The FGPM of interest in this work is composed of Platinum and PZT. FGMs of these types are especially suited for energy-harvesting applications because the designer can control their material properties, such as the stiffness and natural frequencies of the energy-harvesting system through changes in the FGM composition and material distribution. The variation of the material properties throughout the thickness of the energy harvester causes a shift in the neutral axis of the system. The resulting shift of the neutral axis must be accounted for to obtain effective energy harvester properties and hence the accurate design of the energy-harvesting system. In this work, the effects of small-scale phenomena on the natural frequencies and power density of macro- to nano-scale functionally graded energy harvesters with beam lengths ranging from 62.5 mm to 6.25 μm are investigated and discussed. The modified couple stress theory is employed to account for micro-rotations within the material. Surface elasticity theory is considered to account for the residual stresses on the surface of the energy harvester. Both small-scale effects depend on the material parameters that vary throughout the thickness of the FGM. It is demonstrated that size-dependent effects have a significant influence on the design and performance of effective micro-/nano-energy harvesters. Couple stress and surface elasticity both cause significant increases in the effective stiffness of energy harvesting systems. Therefore, neglecting these effects may lead to underestimation of the harvester’s natural frequencies resulting in ineffective designs.