TY - JOUR

T1 - A Method for Separating the Matrix Spectrum by a Straight Line and an Infinite Strip Flutter Problem

AU - Biberdorf, E. A.

AU - Rudometova, A. S.

AU - Li, Wang

AU - Jumbaev, A. D.

N1 - This work was accomplished within the state assignment of the Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008.

PY - 2024/8

Y1 - 2024/8

N2 - A novel method for separating the matrix spectrum by a straight line based on a fractional linear transformation is proposed. This method has a number of advantages over the approaches based on an exponential transformation; more precisely, the range of its application is wider and the number of iterations needed for its convergence is much lower. The proposed method is used to study flutter problems for an infinite strip under various edge fastening conditions, which, after suitable discretization of differential operators, are reduced to spectral problems for linear operators. The study of stability regions by the method of spectrum dichotomy by the imaginary axis makes it possible to construct neutral curves in the plane of parameters of the flutter problem.

AB - A novel method for separating the matrix spectrum by a straight line based on a fractional linear transformation is proposed. This method has a number of advantages over the approaches based on an exponential transformation; more precisely, the range of its application is wider and the number of iterations needed for its convergence is much lower. The proposed method is used to study flutter problems for an infinite strip under various edge fastening conditions, which, after suitable discretization of differential operators, are reduced to spectral problems for linear operators. The study of stability regions by the method of spectrum dichotomy by the imaginary axis makes it possible to construct neutral curves in the plane of parameters of the flutter problem.

KW - discretization of differential operator

KW - flutter

KW - neutral curve

KW - spectrum dichotomy

KW - stability domain

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85205368278&origin=inward&txGid=940eb6f36caf7d7b81b6db2e5623e9ce

UR - https://www.mendeley.com/catalogue/c670cec3-ac80-3f10-8d35-9f4d440418b8/

U2 - 10.1134/S0965542524700891

DO - 10.1134/S0965542524700891

M3 - Article

VL - 64

SP - 1704

EP - 1714

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 8

ER -