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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.
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 boun
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, usua
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 e
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 wit
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. Her