Parton VZ: Fracture mechanics of piezoelectric materials. Qin QH: Variational formulations for TFEM of piezoelectricity. kistler/ref/tech_theory_text.htm (2010). Kistler: The Piezoelectric Effect, Theory, Design and Usage. Higher Education Press & Springer, Beijing (2008). Qin QH, Yang QS: Macro-Micro Theory on Multifield Behaviour of Heterogeneous Materials. Qin QH: Green’s Function And Boundary Elements in Multifield Materials. Qin QH: Fracture Mechanics of Piezoelectric Materials. Rogacheva NN: The Theory of Piezoelectric Shells and Plates. Oxford Science Publications, New York (1990). Ikeda T: Fundamentals of Piezoelectricity. Gordon and Breach Science Publishers, New York (1988). Parton VZ, Kudryavtsev BA: Electromagnetoelasticity, Piezoelectrics and Electrically Conductive Solids. Tiersten HF: Linear Piezoelectric Plate Vibrations. Voigt W: General theory of the piezo and pyroelectric properties of crystals. Pa(1881).Ĭurie J, Curie P: Contractions et dilations productes par des tensions electriques dans les cristaux hemiedres a faces inclines. Lippmann HG: Sur le principe de la conversation de l’eletricite ou second principe de la theorie des phenomenes electriques. 4 de la Societe Mineralogique de France 3, 90(1880) and Comptes Rendus Acad. mat files attached at the bottom of this webpage.Curie J, Curie P: Development par compression de l’eletricite polaire dans les cristaux hemiedres a faces inclines. The data set numbers correspond to the names of the. Additionally, the 3-D printed mount stuck out from where it was held by the kinematic mount, and so this lever arm likely contributed to vibrations that affected the results as well. The mount for the bone was 3-D printed quite loosely, and so this was one source of noise. This is because there was a lot of noise in the experiment that we were unable to get rid of. In each case, the uncertainty on the value is higher than the actual value for the piezoelectric constant. The results for each trial are summarized in the table below. Thus, we began making measurements of the bone, and we were able to get five trials worth of good data with the bone oriented correctly. A previous group had found values in the range of 400 to 600 pm/V, so we felt confident about our setup. Additionally, the raw data sets for a test piezoelectric material, as well as all five trials of good collected bone data are attached.įor the test piezo, we got a value of -423 ± 4 pm/V for the piezoelectric constant. The analysis of the data was completed in Matlab, and the live script used for this is attached at the end of the page. These values were used with the first equation from the theory section to convert from the slope of the graph of V vs Δu to the piezoelectric constant. The bone samples were rectangular prisms with a thickness, X, of 0.25’’ and a square face with width, h, of 1’’. The mirror is shown attached to the right side of the bone, and the conductive tape was attached to the top and bottom sides of the bone sample, with leads from the scope and voltage source attached to this. The maroon cylindrical holder was 3D printed, and the bone was inserted into the notch in the mount. Solving for the displacement from this phase difference givesįigure 5: An image of the bone mount. The measurement arm remains circularly polarized, and an additional phase difference is added to both x and y- components by the bone displacement. The reference arm portion encounters the LP, which removes the phase shift introduced by the CP. The beam is then divided into the reference arm and the measurement arm by the NPBS. A λ=633 nm red laser is steered into a CP, which adds a 90°phase shift to the y -component of the beam’s electric field. An image of our interferometer as well as a schematic are shown below. We used quadrature interferometry to measure the displacement of the bone, ∆u. Mirror and measurement arm are relevant for the quadrature interferometer, explained in the experimental setup. The voltage is applied in the x direction, and the collagen fibers run in the z direction. Figure 2: This image shows the shear strain occurring in the bone, with the negative z side of the bone glued to the mount to fix this side in place.
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