An advanced theory of moderately thick plate vibrations

Senjanović, Ivo; Vladimir, Nikola; Tomić, Marko

doi:10.1016/j.jsv.2012.11.022

Cited by 49 publications

(26 citation statements)

References 29 publications

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“…In the former, shear influence on deflection and rotary inertia are small and are therefore ignored. There are different analytical and numerical methods for plate vibration analysis, both associated with some advantages and drawbacks, as elaborated in details in [4,5]. Analytical methods are quite simple to use, but can be applied only to plates with certain combination of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method

Cho

Kim

Kim³

et al. 2015

Thin-Walled Structures

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Section: Introductionmentioning

confidence: 99%

Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method

Cho

Kim

Kim³

et al. 2015

Thin-Walled Structures

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“…, where m and n are the numbers of beam vibration nodes, then the plate mode shape function has to manifest m + n cross straight lines of zero displacement, Fig 3. Such a mesh can be noticed only in the modes 1, 8, and 17, and roughly in the modes 4,5,6,7,11,12,15,16,20,21, and 24 in Fig. 2.…”

Section: Generalmentioning

confidence: 88%

An Analytical Solution to Free Rectangular Plate Natural Vibrations by Beam Modes – Ordinary and Missing Plate Modes

et al. 2016

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SummaryRelatively 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.

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“…In this case the obtained results are compared with recently presented analytical solutions (Xing and Liu, 2009;Senjanović et al, 2013), as well as with numerical results obtained by finite element method (MSC, 2010). Generally, it is obvious from the shown results, Table 1, that the developed procedure provides very good results comparing to the analytical solution.…”

Section: Rectangular Plate Without Openingsmentioning

confidence: 93%

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

Cho¹,

Vladimir²,

Choi³

2013

International Journal of Naval Architecture and Ocean Engineeri

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Natural vibration analysis of plates with openings of different shape represents an important issue in naval architecture and ocean engineering applications. In this paper, a procedure for vibration analysis of plates with openings and arbitrary edge constraints is presented. It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. The presented solution represents an extension of a procedure for natural vibration analysis of rectangular plates without openings, which has been recently presented in the literature. The effect of an opening is taken into account in an intuitive way, i.e. by subtracting its energy from the total plate energy without opening. Illustrative numerical examples include dynamic analysis of rectangular plates with rectangular

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An advanced theory of moderately thick plate vibrations

Cited by 49 publications

References 29 publications

Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method

Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method

An Analytical Solution to Free Rectangular Plate Natural Vibrations by Beam Modes – Ordinary and Missing Plate Modes

Approximate natural vibration analysis of rectangular plates with openings using assumed mode method

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