Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures
type: Item
instance of: scholarly article
title: Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures
zbMATH Open document ID: 0614.73073
DOI: 10.1007/BF00282131
author: C. Eller
author: Yavuz Başar
author: Wilfried B. Krätzig
published in: Computational Mechanics
publication date: 1987-01-01T00:00:00Z
review text: A purely numerical method for the treatment of instability problems of parametric resonance is presented. The proposed way of solution, which is applicable to all types of structures, is based on the finite element discretization of an incremental variational principle. After the derivation of the theoretical background linear and quadratic eigenvalue problems for the critical excitation-frequencies of undamped and damped systems are presented and numerical procedures for the computation of the instability charts are established. Finally the efficiency of the developed algorithms is demonstrated by means of several shell responses.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 3995201
zbMATH Keywords: incremental principle of virtual work
zbMATH Keywords: Mathieu differential equation
zbMATH Keywords: Floquet's theory
zbMATH Keywords: matrix form
zbMATH Keywords: submatrix technique
zbMATH Keywords: instability problems
zbMATH Keywords: parametric resonance
zbMATH Keywords: incremental variational principle
zbMATH Keywords: linear and quadratic eigenvalue problems
zbMATH Keywords: critical excitation-frequencies
zbMATH Keywords: undamped
zbMATH Keywords: damped systems
MaRDI profile type: Publication
cites work: Q3703370
cites work: Q5329775
cites work: Q4151189
cites work: Stability of a spinning body containing elastic parts via Liapunov'sdirect method
cites work: Q5534050
cites work: Instability of parametric dynamic systems with non-uniform damping
cites work: Der eingespannte, achsial pulsierend belastete Stab als Stabilit�tsproblem
cites work: Q5553187
full work available at URL: https://doi.org/10.1007/bf00282131
OpenAlex ID: W2079698541
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description: scientific article; zbMATH DE number 3995201