Open AccessLINEAR AND NON‐LINEAR PROBLEMS OF PLATE DYNAMICS
Author(s) -
Petras Baradokas,
Edvard Michnevič,
Leonidas Syrus
Publication year - 2007
Publication title -
aviation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 13
eISSN - 1822-4180
pISSN - 1648-7788
DOI - 10.3846/16487788.2007.9635971
Subject(s) - polynomial , mathematics , amplitude , resonance (particle physics) , ritz method , dynamics (music) , mathematical analysis , power (physics) , physics , boundary value problem , thermodynamics , particle physics , acoustics , quantum mechanics
This paper presents a comparative analysis of linear and non‐linear problems of plate dynamics. By expressing the internal friction coefficient of the material by power polynomial γ= γ0 + γ1ϵ0 + γ2ϵ0 2+…, we assume γ= γ0 = const for a linear problem. When at least two polynomial terms are taken, a non‐linear problem is obtained. The calculations of resonance amplitudes of a rectangular plate yielded 3 per cent error: a linear problem yields a higher resonance amplitude. Using the Ritz method and the theory of complex numbers made the calculations. Similar methods of calculation can be used in solving the dynamic problems of thin‐walled vehicle structures.