This article discusses a projection method for nonlinear eigenvalue problems. The subspace of approximants is constructed by a Jacobi–Davidson type approach, and the arising eigenproblems of small dimension are solved by safeguarded iteration. The method is applied to a rational eigenvalue problem governing the vibrations of tube bundle immersed in an inviscid compressible fluid.

DC microgrids (MGs) are complex systems connecting a number of renewable energy sources to different types loads based on distributed networks. However, the strong reliance communication networks makes MGs vulnerable intentional cyber-attacks. In this paper, attack detection scheme is presented for MG system by proposing an observer. The proposed detector able detect attacks with only local kno...

We calculate the Clarke and Michel-Penot subdifferentials of the function which maps a symmetric matrix to its mth largest eigenvalue. We show these two subdifferentials coincide, and are identical for all choices of index m corresponding to equal eigenvalues. Our approach is via the generalized directional derivatives of the eigenvalue function, thereby completing earlier studies on the classi...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Abstract: In many practical systems, limit cycles can be predicted with suitable precision by frequency domain methods using describing functions. Within such an approach, limit cycles can be predicted using the “eigenvalue method” [7]. This contribution presents a novel and advantageous implementation of this method, using singular value instead of eigenvalue calculations, and enhancing comput...

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximat...

In this study, vibration of initially imperfect cracked thick plate has been investigated using the differential quadrature method. The crack modeled as an open crack using a no-mass linear spring. The governing equations of vibration of a cracked plate are derived using the Mindlin theory and considering the effect of initial imperfection in Von-Karman equations. Differential equations are dis...