Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method

Reck, Kasper; Thomsen, Erik Vilain; Hansen, O.F.

doi:10.1364/oe.19.001808

Cited by 4 publications

(2 citation statements)

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“…Ghotbi et al [29] solved ratio-dependent predator-prey system with constant effort harvesting using HPM. Reck et al [30] solved the Helmholtz equation in conformal mapped AR-ROW structures using HPM. Andrianov et al [31] used HPM to analyze the natural in-plane vibration of rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

Geometric Nonlinear Vibration Analysis for Pretensioned Rectangular Orthotropic Membrane

et al. 2018

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The geometric nonlinear vibrations of pretensioned orthotropic membrane with four edges fixed, which is commonly applied in building membrane structure, are studied. The nonlinear partial differential governing equations are derived by von Kármán's large deflection theory and D'Alembert's principle. Because of the strong nonlinearity of governing equations, the homotopy perturbation method (HPM) to solve them is applied. The approximate analytical solution of the vibration frequency and displacement function is obtained. In the computational example, the frequency, vibration mode and displacement as well as the time curve of each feature point are analyzed. It is proved that HPM is an effective, simple and high-precision method to solve the geometric nonlinear vibration problem of membrane structures. These results provide some valuable computational basis for the vibration control and dynamic design of building and other analogous membrane structures.

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Section: Introductionmentioning

confidence: 99%

Geometric Nonlinear Vibration Analysis for Pretensioned Rectangular Orthotropic Membrane

et al. 2018

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“…The infinite strip and the semi-infinite strips can be analytically mapped using simple trigonometric functions, whereas analytical mapping of the square to the half-plane involves elliptic functions. 11 In order to avoid the use of elliptic functions and to demonstrate a method that may be applied to an arbitrary shape, the square is numerically mapped.…”

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confidence: 99%

Fast micro Hall effect measurements on small pads

Østerberg

Petersen

Nielsen³

et al. 2011

Journal of Applied Physics

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Sheet resistance, carrier mobility, and sheet carrier density are important parameters in semiconductor production, and it is therefore important to be able to rapidly and accurately measure these parameters even on small samples or pads. The interpretation of four-point probe measurements on small pads is non-trivial. In this paper we discuss how conformal mapping can be used to evaluate theoretically expected measurement values on small pads. Theoretical values calculated from analytical mappings of simple geometries are compared to the values found from the numerical conformal mapping of a square onto the infinite half-plane, where well-established solutions are known. Hall effect measurements are performed to show, experimentally, that it is possible to measure Hall mobility in less than one minute on squares as small as 70 Â 70 lm 2 with a deviation of 66.5% on a 1r level from accurate reference measurements, when only small sheet resistance variations are present. For samples with a sheet resistance variation of more than 5%, a more time consuming method must be used. Here, the theoretically expected measurement values are computed based on the sheet resistance variation using a finite element method. This more accurate method has an experimental repeatability of 61.6% even on inhomogeneous samples.

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Perturbation approximation for higher modes in nearly regular two-dimensional cavities

Korneev

2016

Cogent Physics

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Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method

Cited by 4 publications

References 15 publications

Geometric Nonlinear Vibration Analysis for Pretensioned Rectangular Orthotropic Membrane

Geometric Nonlinear Vibration Analysis for Pretensioned Rectangular Orthotropic Membrane

Fast micro Hall effect measurements on small pads

Perturbation approximation for higher modes in nearly regular two-dimensional cavities

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