Построение эквивалентных моделей балочных структур

The usage of a finite-element mathematical model to obtain an equivalent electrical circuit for mechanical components is suggested. Using of RLC reduction algorithm to reduce a dimension of the circuits obtained is proposed. An example of getting equivalent electrical circuit for beam structure is considered. The approach in question is applied to obtaining equivalent circuits for MEMS components.Предлагается использование конечно-элементной математической модели для получения эквивалентной электрической схемы замещения механических компонентов. Для уменьшения размерности полученных схем предложено использование RLC сокращения. Рассмотрен пример получения эквивалентной электрической схемы балочной структуры. Данный подход распространен на получение эквивалентных схем для МЭМС компонентов

Зменшення неоднозначності алгоритму скорочення розмірності RLC-схем

Пропонується модифікація алгоритму скорочення RLC-схем на основі Y-∆ перетворення, в якій усунуто недоліки, пов’язані з неоднозначністю та часом скорочення. Наведено результати досліджень, які підтверджують ефективність запропонованої модифікації.Modification of the Y-∆ transformation based RCL-circuit reduction algorithm was proposed that eliminates disadvantages related to the reduction indeterminacy and time. Results of practical experiments that prove efficiency of the proposed modification were represented

Theoretical and practical aspects of linear and nonlinear model order reduction techniques

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 133-142).Model order reduction methods have proved to be an important technique for accelerating time-domain simulation in a variety of computer-aided design tools. In this study we present several new techniques for model reduction of the large-scale linear and nonlinear systems. First, we present a method for nonlinear system reduction based on a combination of the trajectory piecewise-linear (TPWL) method with truncated-balanced realizations (TBR). We analyze the stability characteristics of this combined method using perturbation theory. Second, we describe a linear reduction method that approximates TBR model reduction and takes advantage of sparsity of the system matrices or available accelerated solvers. This method is based on AISIAD (approximate implicit subspace iteration with alternate directions) and uses low-rank approximations of a system's gramians. This method is shown to be advantageous over the common approach of independently approximating the controllability and observability gramians, as such independent approximation methods can be inefficient when the gramians do not share a common dominant eigenspace. Third, we present a graph-based method for reduction of parameterized RC circuits. We prove that this method preserves stability and passivity of the models for nominal reduction. We present computational results for large collections of nominal and parameter-dependent circuits. Finally, we present a case study of model reduction applied to electroosmotic flow of a marker concentration pulse in a U-shaped microfluidic channel, where the marker flow in the channel is described by a three-dimensional convection-diffusion equation. First, we demonstrate the effectiveness of the modified AISIAD method in generating a low order models that correctly describe the dispersion of the marker in the linear case; that is, for the case of concentration-independent mobility and diffusion constants.(cont) Next, we describe several methods for nonlinear model reduction when the diffusion and mobility constants become concentration-dependent.by Dmitry Missiuro Vasilyev.Ph.D