An Accurate and Efficient Method for Dynamic Analysis of Two-Dimensional Periodic Structures

2016 ◽  
Vol 08 (02) ◽  
pp. 1650013 ◽  
Author(s):  
Q. Gao ◽  
H. W. Zhang ◽  
W. X. Zhong ◽  
W. P. Howson ◽  
F. W. Williams
Keyword(s):  
Dynamic Response ◽  
Efficient Method ◽  
Algebraic Structure ◽  
Integration Method ◽  
Periodic Structures ◽  
Computational Effort ◽  
Two Dimensional ◽  
Great Efficiency ◽  
Energy Propagation ◽  
Precise Integration

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

scholarly journals Subdomain Precise Integration Method for Periodic Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
F. Wu ◽  
Q. Gao ◽  
W. X. Zhong
Keyword(s):  
Integration Method ◽  
Periodic Structures ◽  
Computational Accuracy ◽  
Precise Integration ◽  
Numerical Examples ◽  
Structural Cell ◽  
Precise Integration Method ◽  
Memory Size ◽  
Runge Kutta

A subdomain precise integration method is developed for the dynamical responses of periodic structures comprising many identical structural cells. The proposed method is based on the precise integration method, the subdomain scheme, and the repeatability of the periodic structures. In the proposed method, each structural cell is seen as a super element that is solved using the precise integration method, considering the repeatability of the structural cells. The computational efforts and the memory size of the proposed method are reduced, while high computational accuracy is achieved. Therefore, the proposed method is particularly suitable to solve the dynamical responses of periodic structures. Two numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method through comparison with the Newmark and Runge-Kutta methods.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Exact analysis of the bending of wide beams by a modified elastica approach

2011 ◽  
Vol 225 (11) ◽  
pp. 2759-2764 ◽  
Author(s):  
L F Campanile ◽  
R Jähne ◽  
A Hasse
Keyword(s):  
Finite Element ◽  
Substantial Reduction ◽  
Short Review ◽  
Computational Effort ◽  
Two Dimensional ◽  
Finite Element Calculations ◽  
Dimensional Finite Element ◽  
Wide Beams ◽  
Insight Into ◽  
Selection Of

Classical beam models do not account for partial restraint of anticlastic bending and are therefore inherently inaccurate. This article proposes a modification of the exact Bernoulli–Euler equation which allows for an exact prediction of the beam's deflection without the need of two-dimensional finite element calculations. This approach offers a substantial reduction in the computational effort, especially when coupled with a fast-solving schema like the circle-arc method. Besides the description of the new method and its validation, this article offers an insight into the somewhat disregarded topic of anticlastic bending by a short review of the published theories and a selection of representative numerical results.

Multigrid Numerical Solutions of Non-Isothermal Laminar Recirculating Flows

1999 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Maximilian S. Mesquita
Keyword(s):  
Numerical Solutions ◽  
Rectangular Domain ◽  
Optimal Number ◽  
Computational Effort ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Discretization Scheme ◽  
Multigrid Algorithm ◽  
Finite Volume Discretization ◽  
Velocity And Temperature Fields

Abstract The present work investigates the efficiency of the multigrid numerical method applied to solve two-dimensional laminar velocity and temperature fields inside a rectangular domain. Numerical analysis is based on the finite volume discretization scheme applied to structured orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different inlet Reynolds number (Rein) and number of grids. Up to four grids were used for both V- and W-cycles. Simultaneous and uncoupled temperature-velocity solution schemes were also applied. Advantages in using more than one grid is discussed. Results further indicate an increase in the computational effort for higher Rein and an optimal number of relaxation sweeps for both V- and W-cycles.

scholarly journals Two-dimensional photonic crystals increasing vertical light emission from Si nanocrystal-rich thin layers

2018 ◽  
Vol 9 ◽  
pp. 2287-2296
Author(s):  
Lukáš Ondič ◽  
Marian Varga ◽  
Ivan Pelant ◽  
Alexander Kromka ◽  
Karel Hruška ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Light Emission ◽  
Periodic Structures ◽  
Normal Direction ◽  
Thin Layers ◽  
Two Dimensional ◽  
Lattice Constants ◽  
Leaky Modes ◽  
Si Nanocrystals ◽  
Si Nanocrystal

We have fabricated two-dimensional photonic crystals (PhCs) on the surface of Si nanocrystal-rich SiO2 layers with the goal to maximize the photoluminescence extraction efficiency in the normal direction. The fabricated periodic structures consist of columns ordered into square and hexagonal pattern with lattice constants computed such that the red photoluminescence of Si nanocrystals (SiNCs) could couple to leaky modes of the PhCs and could be efficiently extracted to surrounding air. Samples having different lattice constants and heights of columns were investigated in order to find the configuration with the best performance. Spectral overlap of the leaky modes with the luminescence spectrum of SiNCs was verified experimentally by measuring photonic band diagrams of the leaky modes employing angle-resolved spectroscopy and also theoretically by computing the reflectance spectra. The extraction enhancement within different spatial angles was evaluated by means of micro-photoluminescence spectroscopy. More than 18-fold extraction enhancement was achieved for light propagating in the normal direction and up to 22% increase in overall intensity was obtained at the spatial collection angle of 14°.

Motion in frequency domain for harmonic balance simulation of electrical machines

2018 ◽  
Vol 37 (4) ◽  
pp. 1449-1460
Author(s):  
Markus Wick ◽  
Sebastian Grabmaier ◽  
Matthias Juettner ◽  
Wolfgang Rucker
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Efficient Method ◽  
Harmonic Balance ◽  
Eddy Currents ◽  
Computational Effort ◽  
Electrical Machines ◽  
Accurate Approximation ◽  
Content Type ◽  
Magnetic Devices

Purpose The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Design/methodology/approach The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Findings The three-phase symmetry reduces the simulated geometry to the sixth part of one pole. The motion transforms to a frequency offset in the angular Fourier series decomposition. The calculation overhead of the Fourier integrals is negligible. The air impedance approximation increases the accuracy and yields a convergence speed of three iterations per decade. Research limitations/implications Only linear materials and two-dimensional geometries are shown for clearness. Researchers are encouraged to adopt recent harmonic balance findings and to evaluate the performance and accuracy of both formulations for larger applications. Practical implications This method offers fast-frequency domain simulations in the optimization process of rotating machines and so an efficient way to treat time-dependent effects such as eddy-currents or voltage-driven coils. Originality/value This paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

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