An analytical solution to free rectangular plate natural vibrations by beam modes – ordinary and missing plate modes

Senjanović, Ivo and Tomić, Marko and Vladimir, Nikola and Hadžić, Neven (2016) An analytical solution to free rectangular plate natural vibrations by beam modes – ordinary and missing plate modes. = An analytical solution to free rectangular plate natural vibrations by beam modes – ordinary and missing plate modes. Transactions of FAMENA, 40 (3). pp. 1-18. ISSN 1333-1124. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q4 (2016). Točan broj autora: 4.

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Abstract

Relatively simple analytical procedures for the estimation of natural frequencies of free thin rectangular plates, based on the Rayleigh quotient and the Rayleigh-Ritz method, are presented. First, natural modes are assumed in the usual form as products of beam natural modes in the longitudinal and transverse directions, satisfying the grillage boundary conditions. Based on a detailed FEM analysis, the missing of some natural modes, defined as a sum and a difference of the cross products of beam modes, is noted. The frequencies of these modes are very similar and identical in some special cases, manifesting in such a way a double frequency phenomenon. These families of natural mode shapes form a complete natural frequency spectrum of a free rectangular plate as a novelty. The reliable approximation of natural modes enables the application of the Rayleigh quotient for the estimation of higher natural frequencies. The application of the developed procedure is illustrated by the case of a free thin square plate. The obtained results are compared with those determined by FEM and also with rigorous ones from the relevant literature based on the Rayleigh-Ritz method. The achieved accuracy is acceptable from the engineering point of view. Furthermore, the same problem is solved by the Rayleigh-Ritz method using approximate natural modes as mathematical ones. Direct and iterative procedures are presented. A small number of mathematical modes and iteration steps are sufficient to achieve reliable results.

Item Type: Article (["eprint_fieldopt_article_type_article" not defined])
Keywords (Croatian): rectangular plate; natural vibration; Rayleigh quotient; Rayleigh-Ritz method; mode shapes; frequency spectrum
Subjects: TECHNICAL SCIENCE > Shipbuilding
TECHNICAL SCIENCE > Civil engineering
TECHNICAL SCIENCE > Mechanical Engineering
Divisions: 600 Department of Naval Engineering and Marine Technology > 620 Chair of Marine Structures Design
600 Department of Naval Engineering and Marine Technology > 650 Chair of Marine Machinery and System Design
Indexed in Web of Science: Yes
Indexed in Current Contents: No
Citations JCR: 0 (24.10.2017.)
Quartiles: Q4 (2016)
Date Deposited: 17 Mar 2017 13:51
Last Modified: 01 Feb 2018 08:30
URI: http://repozitorij.fsb.hr/id/eprint/7579

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