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Tham khảo tài liệu 'advances in piezoelectric transducers part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Distributed-Parameter Modeling of Energy Harvesting Structures with Discontinuities 69 Beam properties L length 100 mm b width 20 mm ts thickness of substructure 0.75 mm tv thickness of PZT layer 0.5 mm Ps density of substructure 8070 kg m3 Pv density of PZT 7800 kg m3 c11 s Young s modulus of substructure 102 GPa cE c11 Young s modulus of PZT 66 GPa e31 piezoelectric constant -12.54 C m2 S 33 permittivity 15.93 nF m Table 1. Geometry and material properties. Fig. 6. Variation in fundamental short-circuit natural frequency with respect to patch coverage and layer thickness ratio. 70 Advances in Piezoelectric Transducers Fig. 7. Variation in coupling coefficient ratio with respect to patch coverage and layer thickness ratio. To quantify the effects on the transduction capabilities of these two designs the dimensionless electromechanical coupling coefficient is employed. The device i.e. entire structure coupling coefficient for the rh mode is given by k2 2 c0 2 j a term that has been used to non-dimensionalize power in the literature e.g. Shu and Lien 2006 Liao and Sodano 2008 Wickenheiser and Garcia 2010c . It has been shown by Wickenheiser 2011 that this term can be written in the form k2 k i M. E I 50 for single segment beams with or without tip mass where k2 e21l c j is the piezoelectric material coupling coefficient KM is a dimensionless term that depends on the distribution of inertia between the beam and tip mass and KEI is a dimensionless term that depends on the effective stiffness of the beam. Although the simple decomposition of Eq. 50 is not proven for more general structures it can be shown that the ratio k2 k2 is constant for a specific geometry. In the present study the ratio k2 k2 is plotted isolating the effects of geometry on the electromechanical coupling of the device. In Fig. 7 the piezoelectric layers are extended out from the base to xdiv . As the coverage decreases to 0 k2 k2 0 as expected. As it increases there is a maximum before xdiv L .
