Abstract
In this work a numerical model is developed for vibration analysis of low folded shells under dynamic actions. At first it is done to describe the used finite element discrete model based on Lagrange variational principles. To solve the eigen value problem of these structures a numerical algorithm is proposed using Householder's QR-iteration transformations. This method provides a tridiagonal matrix whose eigen values coincide with those of the initial matrix and significantly reduces the iteration number compared to the Lanczos method. Implementation of the method is carried out on seven folded shell mathematical models. Obtained results show that accuracy can be improved and computational time can be significantly reduced compared to the methods available in the technical literature for this class of problems.
Highlights
Several finite element models are proposed for structure modeling
In this work a shell finite element model is proposed in which Householder's QR transformations are used to solve the eigenvalue problem of folded shells
From this work we can retain the following: 1 - A numerical solving algorithm is proposed for the problem in free vibrations of low folded shells
Summary
Several finite element models are proposed for structure modeling. for thin structures we have elements such as shell, plate, etc. In this work a shell finite element model is proposed in which Householder's QR transformations are used to solve the eigenvalue problem of folded shells. Because this method allows to obtain a tri-diagonal matrix whose mas.ccsenet .org. Introduction : a bibliographic synthesis of proposed works for the numerical analysis of eigenvalue problems is carried out It outlines the advantages and inconvenients of one compared to the other and a new approach is proposed to improve accuracy and computational time compared to the methods available in the literature. Methodology: is carried out a finite element formulation of the problem in dynamics of low shells and a method of solving the eigenvalue problem by Householder's transformations is proposed. A list of bibliography is drawn up at the end of the document
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