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Register a new userAn Analysis of Nonlinear Thickness-shear Vibrations of Quartz Crystal Plates by Two-Dimensional Finite Element Method
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A nonlinear analysis of high-frequency thickness-shear vibrations of AT-cut quartz crystal plates is presented with the two-dimensional finite element method. We expanded both kinematic and constitutive nonlinear Mindlin plate equations and then truncated them to the first-order equations as an approximation, which is used later for the formulation of nonlinear finite element analysis with all zeroth- and first-order displacements and electric potentials. The matrix equation of motion is established with the first-order harmonic approximation and the generalized nonlinear eigensystem is solved by a direct iterative procedure. A backbone curve and corresponding mode shapes are obtained and analyzed. The nonlinear finite element program is developed based on earlier linear edition and can be utilized to predict nonlinear characteristics of miniaturized quartz crystal resonators in the design process.
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In this article, global stabilization results for the two dimensional (2D) viscous Burgers equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law. Then, applying $C^0$-conforming finite element method in spatial direction, optimal error estimates in $L^infty(L^2)$ and in $L^infty(H^1)$- norms for the state variable and convergence result for the boundary feedback control law are derived. All the results preserve exponential stabilization property. Finally, several numerical experiments are conducted to confirm our theoretical findings.
We present a detailed analysis of the bounds on the integration step in Discrete Element Method (DEM) for simulating collisions and shearing of granular assemblies. We show that, in the numerical scheme, the upper limit for the integration step, usually taken from the average time $t_c$ of one contact, is in fact not sufficiently small to guarantee numerical convergence of the system during relaxation. In particular, we study in detail how the kinetic energy decays during the relaxation stage and compute the correct upper limits for the integration step, which are significantly smaller than the ones commonly used. In addition, we introduce an alternative approach, based on simple relations to compute the frictional forces, that converges even for integration steps above the upper limit.
We present experimental results and numerical Finite Element analysis to describe surface swelling due to the creation of buried graphite-like inclusions in diamond substrates subjected to MeV ion implantation. Numerical predictions are compared to experimental data for MeV proton and helium implantations, performed with scanning ion microbeams. Swelling values are measured with white light interferometric profilometry in both cases. Simulations are based on a model which accounts for the through-the-thickness variation of mechanical parameters in the material, as a function of ion type, fluence and energy. Surface deformation profiles and internal stress distributions are analyzed and numerical results are seen to adequately fit experimental data. Results allow us to draw conclusions on structural damage mechanisms in diamond for different MeV ion implantations.
Single-crystal diamond plates with surfaces oriented in a (111) crystal plane are required for high-performance solid-state device platforms ranging from power electronics to quantum information processing architectures. However, producing plates with this orientation has proven challenging. In this paper, we demonstrate a method for reliably and precisely fabricating (111)-faced plates from commercially available, chemical-vapor-deposition-grown, type-IIa single-crystal diamond substrates with (100) faces. Our method uses a nanosecond-pulsed visible laser to nucleate and propagate a mechanical cleave in a chosen (111) crystal plane, resulting in faces as large as 3.0 mm$times$0.3 mm with atomically flat surfaces, negligible miscut angles, and near zero kerf loss. We discuss the underlying physical mechanisms of the process along with potential improvements that will enable the production of millimeter-scale (111)-faced single-crystal diamond plates for a variety of emerging devices and applications.
To obtain crystalline thin films of alpha-Quartz represents a challenge due to the tendency for the material towards spherulitic growth. Thus, understanding the mechanisms that give rise to spherulitic growth can help regulate the growth process. Here the spherulitic type of 2D crystal growth in thin amorphous Quartz films was analyzed by electron back-scatter diffraction (EBSD). EBSD was used to measure the size, orientation, and rotation of crystallographic grains in polycrystalline SiO2 and GeO2 thin films with high spatial resolution. Individual spherulitic Quartz crystal colonies contain primary and secondary single crystal fibers, which grow radially from the colony center towards its edge, and fill a near circular crystalline area completely. During their growth, individual fibers form so-called rotational crystals, when some lattice planes are continuously bent. The directions of the lattice rotation axes in the fibers were determined by an enhanced analysis of EBSD data. A possible mechanism, including the generation of the particular type of dislocation(s), is suggested.
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