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

Free vibration analysis of plates with openings represents an important issue in naval architecture and ocean engineering applications. Namely, they are often primary design members of complex structures and knowledge about their dynamic behavior becomes a prerogative for the proper structural design. This paper deals with application of assumed mode method to free vibration analysis of rectangular plates with multiple rectangular openings at arbitrary defined locations. Developed method can be applied to both thin and thick plates as well as to classical and non-classical edge constraints. In the assumed mode method natural frequencies and mode shapes of a corresponding plate 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 developed procedure actually represents an extension of a method for the natural vibration analysis of rectangular plates without openings, which has been recently presented in the relevant literature. The effect of an opening is taken into account in a simple and 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 single and multiple rectangular openings with various thicknesses and different combinations of boundary conditions. Also, the influence of the rectangular opening area on the plate dynamic response is analyzed. The comparisons of the results with those obtained using the finite element method (FEM) is also provided, and very good agreement is achieved. Finally, related conclusions are drawn and recommendations for future investigations are presented.

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Vibration analysis of thin circular plates with multiple openings by the assumed mode method

Proceedings of the Institution of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment ◽

10.1177/1475090215621578 ◽

2016 ◽

Vol 231 (1) ◽

pp. 70-85 ◽

Cited By ~ 1

Author(s):

Ivo Senjanović ◽

Neven Hadžić ◽

Nikola Vladimir

Keyword(s):

Vibration Analysis ◽

Rectangular Plates ◽

Circular Plates ◽

Engineering Structures ◽

Assumed Mode Method ◽

Annular Plates ◽

Mode Method ◽

Plate Area ◽

Assumed Mode ◽

Liquefied Gas

Circular plates with openings are used in many engineering structures, especially as swash bulkheads in cargo tanks of liquefied gas carriers. In this article, an approximate procedure is worked out for the vibration analysis of circular plates with different boundary conditions and a different number and size of openings with an arbitrary arrangement within the plate area. The assumed mode method, recently used in the vibration analysis of rectangular plates, is applied in this case. Following the basic idea, the effect of the openings is accounted for by subtracting the potential and kinetic energy of the cut-out plate parts corresponding to the total plate energies without openings. The procedure is illustrated with numerical examples related to the vibration analysis of annular plates and circular plates with openings. The results are evaluated through their comparison with an analytical and finite element method solution.

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