Senjanović, Ivo and Tomić, Marko and Vladimir, Nikola and Hadžić, Neven (2015) An approximate analytical procedure for natural vibration analysis of free rectangular plates. = An approximate analytical procedure for natural vibration analysis of free rectangular plates. Thin-walled structures, 95. pp. 101-114. ISSN 0263-8231. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q1 (2015). Točan broj autora: 3.
Full text not available from this repository.Abstract
Natural vibrations of free rectangular plates are usually analysed by numerical methods since it is not possible to obtain the closed form analytical solution. In this paper a simple analytical procedure for estimation of natural frequencies of free thin rectangular plates, based on the Rayleigh's quotient, is presented. First, natural modes are assumed in the usual form as products of beam natural modes in longitudinal and transverse direction, satisfying the grillage boundary conditions. Based on a detailed FEM analysis some additional natural modes are recognized, which are defined as sum and difference of the cross products of beam modes. Their frequency spectra are very close and identical in some special cases manifesting in such a way double frequency phenomenon. These three 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 application of the Rayleigh's quotient for estimation of higher natural frequencies. Application of the developed procedure is illustrated in the case of a free thin square and rectangular plate. The obtained results are compared with those determined by FEM and also with more rigorous ones from the relevant literature based on the Rayleigh-Ritz method. The achieved accuracy is acceptable from the engineering point of view, and the procedure can be applied to improve the hydroelastic analysis of VLFS.
| Item Type: | Article (["eprint_fieldopt_article_type_article" not defined]) |
|---|---|
| Keywords (Croatian): | Rectangular plate, Natural vibration, Rayleigh's quotient, Mode shapes, Frequency spectrum |
| Subjects: | 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: | Yes |
| Quartiles: | Q1 (2015) |
| Citations SCOPUS: | 3 (02.11.2017.) |
| Date Deposited: | 23 May 2016 09:12 |
| Last Modified: | 20 Dec 2017 12:12 |
| URI: | http://repozitorij.fsb.hr/id/eprint/5885 |
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