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• Hybrid Elements for Modelling Squeeze Film Effects Coupled with Structural Interactions in Vibratory MEMS Devices
• Abstract We present a hybrid finite element based methodology to solve the coupled fluid structure problem of squeeze film effects in vibratory MEMS devices, such as gyroscopes, RF switches, and 2D resonators. The aforementioned devices often have a thin plate like structure vibrating normally to a fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping. For accurate modelling of such devices the squeeze film effects must be incorporated. Extensive literature is available on…
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• Non Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation
• Abstract Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain fractional Fornberg-Whitham equation. Using the single parametric form of fuzzy numbers, original fuzzy fractional Fornberg-Whitham equation is converted first to an interval based fuzzy differential…
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• Solution of Two-dimensional Linear and Nonlinear Unsteady Schrödinger Equation using
• Abstract A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear…
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• Approximate Analytical Solution of Time-fractional order Cauchy-Reaction Diffusion equation
• Abstract The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM.
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• MLPG Refinement Techniques for 2D and 3D Diffusion Problems
• Abstract Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations. One of pure meshless methods main applications is for implementing Adaptive Discretization Techniques. In this paper, we describe our fresh node–wise refinement technique, based upon estimations of the “local” Total Variation of the approximating function. We numerically analyze the accuracy and efficiency of our MLPG–based refinement. Solutions to test Poisson problems are approximated, which undergo large variations inside small portions of the domain. We show that 2D problems can be accurately solved. The gain in accuracy with respect to uniform discretizations is shown to be…
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• On the Formulation of Three-Dimensional Inverse Catenary for Embedded Mooring Line Modeling
• Abstract Embedded anchors have been widely used in offshore operations, and they are known to be effective and economical solutions to anchoring problems. Aiming at contributing to the definition and understanding of the embedded mooring line behavior, this paper expands the formulation adopted at DNV Recommended Practices, for two-dimensional modeling of the interaction between the seabed and the anchor line, to three-dimensional analysis. The formulation here presented, within an elegant differential geometry approach, can now model even out of plane lines. A reference problem is then defined and solved using the obtained governing equations. Corresponding equations are implemented and solved numerically…
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