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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 65 (1989), S. 35-40 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An analysis of the in-plane acceleration sensitivity of grooved ST- and SST-cut-quartz surface-wave resonators rigidly supported along the edges is performed. The biasing deformation fields are obtained using a new variational approximation procedure which is very accurate, computationally efficient, and convenient to use. The calculated extensional biasing states are employed in an existing perturbation equation along with the proper continuous representation of the acoustic surface-wave mode shape for arrays of reflecting grooves to calculate the in-plane acceleration sensitivity for both cuts. The calculations reveal that the ST cut is slightly less sensitive than the SST cut and that both are a few parts in 1011 per g.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 64 (1988), S. 4334-4341 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An analysis of the normal acceleration sensitivity of grooved ST-cut quartz surface wave resonators supported along the edges is performed. Both the simply supported and rigidly supported cases are treated. The variational principle with all natural conditions for anisotropic flexure, which is required for the new approximation procedure used in the calculation of the flexural biasing state for the case of rigid supports, is presented. The flexural biasing states are employed in an existing perturbation equation along with the proper continuous representation of the acoustic surface wave mode shape for arrays of reflecting grooves to calculate the normal acceleration sensitivity. It is shown that by appropriate selection of the planar aspect ratio of an ST-cut quartz substrate the normal acceleration sensitivity can be made to vanish.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 72 (1992), S. 1244-1254 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent work has shown that both the normal and resultant in-plane acceleration sensitivities of contoured quartz resonators vanish for a perfectly symmetric resonator and support system. It has also been shown that any loss of symmetry in the combined resonator plus support configuration results in a significant degradation in the acceleration sensitivity. Since it is essentially impossible to construct a perfectly symmetric resonator plus support configuration in practice, a stiffened structure is considered. The structure consists of the active biconvex quartz resonator attached to identical top and bottom quartz cover plates by means of small sidewalls around the periphery. The mounting clips are attached to the top and bottom cover plates without touching the active plate. An analysis of the normal acceleration sensitivity of this configuration is performed. Results are presented for a mispositioning of either a clip or the mode shape for a range of thickness of cover plates relative to the active plate.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 72 (1992), S. 971-975 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A mathematical model for a semiconductor heterojunction diode at equilibrium based on kinetic theory of inhomogeneous systems is presented. A generalized Boltzmann equation for variable effective mass is obtained from Marshak and van Vliet's extended Wannier–Slater Hamiltonian [Solid-State Electron. 21, 417 (1978)]. An Ehrenfest correspondence procedure has shown that only forces due to variation in band-edge energy and electric potential energy arise; the supposed force arising from the spatial gradient of effective mass does not exist. The diode model consists of three separate regions: two regions of homogeneous material composition and a finite interface region of inhomogeneous composition. Boltzmann's equation is solved in each region as a function of arbitrary electric potential. Physically reasonable boundary and continuity conditions are also established. Closed-form analytical solution of our model equations does not appear to be possible because of the coupling with Poisson's equation. To demonstrate the implications of our model without resorting to a numerical investigation, we make some reasonable simplifying assumptions to derive a new built-in potential formula. The formula suggests that an error exists in the currently accepted formula. The error is particularly large when carrier effective density-of-states ratios across the diode are appreciably greater than unity.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 83 (1998), S. 6126-6139 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Rotationally invariant electroelastic equations are extended to account for slow hysteretic effects in polarized ferroelectric ceramic plates by employing an internal variable in a thermodynamic state function. All material irreversibility is taken to be a consequence of the ferroelectric polarization-electric-field irreversibility. Since we are concerned with the slowest possible hysteresis, we ignore the evolution equation and take the known irreversible thickness polarization-electric-field saturation curve as the starting curve. After the general nonlinear three-dimensional equations are obtained, they are reduced to linear strain and then plane stress because all experimental data available to us are from strain measurements on a thin wide beam forced by voltages applied to very thin polarized ferroelectric ceramic actuators on the surfaces. The new irreversible material coefficients are obtained from data on one major hysteresis loop along with the coefficients in the saturation polarization-electric-field relation. These now known coefficients are then used to calculate other hysteresis loops, which are shown to agree quite well with measurement. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 76 (1994), S. 7201-7208 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The equation for transversely varying thickness modes in doubly rotated quartz resonators is applied in the analysis of trapped energy resonators with beveled cylindrical edges. The coefficients appearing in the planar differential operator are written as a sum of a mean or isotropic part plus a deviation. Asymptotic eigensolutions for the nearby isotropic case are obtained for the cylindrical beveled resonator. The resonant frequencies for the actual anisotropic case are obtained from an equation for the perturbation in eigenfrequency from the isotropic solution. A lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. Calculated results are presented for a few beveled AT- and SC-cut quartz resonators and the influence of the radius of curvature of the contour is exhibited. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 3389-3393 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Existing rotationally invariant electroelastic equations are reduced to the case of large electric fields and small strain. These latter equations are specialized to the case of thin plates with completely electroded major surfaces, and it is shown that in this case the charge equation of electrostatics is satisfied trivially to lowest order. It is further shown that for the thin stress-free polarized ferroelectric ceramic plate subject to large electric fields, the resulting equations readily account for experimental data in existence in the literature
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 74 (1993), S. 7067-7077 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: It has been shown that the resultant acceleration sensitivity of contoured quartz resonators vanishes for perfect symmetry of the resonator with respect to the support system. It has further been shown that any loss of symmetry in the combined resonator plus support configuration results in a linear increase in the acceleration sensitivity. Since it is impossible to construct a perfectly symmetric resonator plus support configuration in practice, a stiffened structure is investigated. The structure consists of the active biconvex quartz resonator attached to identical top and bottom quartz cover plates by means of small sidewalls around the periphery. The mounting clips are attached to the top and bottom cover plates without touching the active plate. An analysis of the linear increase in the in-plane acceleration sensitivity of the stiffened configuration is performed. Results are presented which show the influence on the in-plane and resultant acceleration sensitivities of differences in the properties of the clips and a mispositioning of either a clip or the mode shape for a range of thickness of the cover plates relative to the active plate.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 71 (1992), S. 4684-4692 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: It has recently been shown that the in-plane acceleration sensitivity of contoured quartz resonators vanishes for a perfectly symmetric combined resonator plus support system. This indicates that a biconvex resonator will have lower resultant in-plane acceleration sensitivity than a plano-convex one because of its inherent additional symmetry. Since a plano-convex resonator is easier to fabricate, an analysis of the degradation in the in-plane acceleration sensitivity that arises from the contour being on one side only is performed. The calculations show that the in-plane sensitivity of the plano-convex resonator increases with decreasing radius of curvature and that the magnitude ranges over a few parts in 1012 per g.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 69 (1991), S. 2862-2870 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: It is shown that the normal acceleration sensitivity of contoured quartz resonators with rectangular supports vanishes when the centers of the mode shape and support rectangle coincide. This result is a consequence of symmetry and applies to many other shapes. Since it is essentially impossible to realize this situation in practice, an analysis of the influence of an offset of the centers on the normal acceleration sensitivity is performed. The biasing deformation is determined by means of a variational approximation procedure using the variational principle with all natural conditions for anisotropic static flexure. The very important accompanying strains varying quadratically across the thickness are determined recursively, as in earlier work. The resulting flexural biasing states are employed in an existing perturbation equation along with the equivalent trapped-energy-mode shapes of the contoured resonators to calculate the normal acceleration sensitivities. It is shown that for small offsets the acceleration sensitivity increases linearly with offset, and orientations for which this effect is minimized are found.
    Type of Medium: Electronic Resource
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