Degree Candidacy: Master of Science in Mechanical Engineering
Date: Tuesday, May 6, 2014
Time: 10:00 AM
Location: 215 EIB
Advisor: Dr. Lonnie Thompson
Committee Members: Dr. Mohammed Daqaq and Dr. Gang Li
Title: Finite element beam model for piezoelectric energy harvesting using high-order shear deformation theory
Piezoelectric energy harvesting devices convert mechanical energy to usable electrical energy, which can be used to power other electronic devices and sensors. Typical piezoelectric harvesters are unimorph cantilever composite beams, which have a single active piezoceramic layer and a passive substrate or a bimorph that has a passive substrate sandwiched between two piezoceramic layers. Power is captured across a coupled load resistor circuit in either a series or parallel connection. The mathematical modeling approaches for piezoelectric beam harvesters present in literature range from analytical distributed parameter modeling, to approximate distributed parameter, Rayleigh- Ritz global discretization or finite element local discretization.
For slender electromechanical beam devices, the Classical Beam Theory, which assumes that transverse shear strain is zero, predicts natural frequencies accurately for lower frequencies. First Order Beam Theory accounts for transverse shear deformation in beam bending, but assumes that the shear strain and stress is constant through the thickness and the shear stiffness must be adjusted with a shear correction factor as an approximation. The shear correction factor depends on the lamina material properties and so for composite beams, a model, which does not require the use of shear correction factor, is desirable.
In the present work, a beam finite element model based on a high-order parabolic shear deformation theory for multi-layered composite piezoelectric beam energy harvesting device is developed. The proposed mathematical model based on the Higher Order Shear Deformation Theory accounts not only for transverse shear strains, but also for a parabolic variation of the transverse shear strains through thickness. This satisfies the zero transverse shear stresses condition on the boundary planes and consequently, there is no need for a shear correction factor. A layerwise theory is used to model the electric potential in the thickness direction, with a fully coupled load resistor circuit in both series and parallel configurations. The beam element uses four mechanical degrees-of-freedom per node, axial displacement, transverse displacement, slope, and independent section rotation angle. Comparisons of the natural frequencies, steady-state power and voltage values from time-harmonic base excitation obtained from piezoelectric bimorph cantilever beams using the Euler-Bernoulli, Timoshenko and the higher order shear deformation theory are presented. Comparisons for the different shear deformation theories are presented for different length-to-depth aspect ratios. The results show increased accuracy for steady-state power solutions using the higher-order beam elements for moderately thick beams at higher frequencies.