Simplified procedure for the free vibration analysis of rectangular plate structures with holes and stiffeners

• Autorzy: Cho D. S. , Vladimir N. , Choi T. M.
• Języki publikacji: EN

Abstrakty

EN

Thin and thick plates, plates with holes, stiffened panels and stiffened panels with holes are primary structural members in almost all fields of engineering: civil, mechanical, aerospace, naval, ocean etc. In this paper, a simple and efficient procedure for the free vibration analysis of such elements is presented. It is based on the assumed mode method and can handle different plate thickness, various shapes and sizes of holes, different framing sizes and types as well as different combinations of boundary conditions. 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. Mindlin theory is applied for a plate and Timoshenko beam theory for stiffeners. The applicability of the method in the design procedure is illustrated with several numerical examples obtained by the in-house developed code VAPS. Very good agreement with standard commercial finite element software is achieved.

Słowa kluczowe

EN

energy approach; plate with hole; stiffened panel; thick plate; VAPS software; free vibration analysis

• Wydawca: Gdańsk University of Technology, Faculty of Ocean Engineering & Ship Technology
• Czasopismo: Polish Maritime Research
• Rocznik: 2015
• Tom: nr 2
• Strony: 71--78
• Opis fizyczny: Bibliogr. 26 poz., rys., tab.

Twórcy

autor

Cho D. S.

• Pusan National University 63 beon-gil Busandaehak-ro Geumjeong-gu, Busan, 609-735, Korea

autor

Vladimir N.

• University of Zagreb Faculty of Mechanical Engineering and Naval Architecture Ivana Lucica 5, 10000 Zagreb, Croatia

autor

Choi T. M.

• Createch Co. Ltd., Rm. 206, 11 Engineering Bldg. San 30, Jangjeon 2-dong, Gumjeong-gu, Busan, 609-735, Korea

Bibliografia

• 1. Reissner E.: The effect of transverse shear deformation on the bending of elastic plate. Transactions of ASME Journal of Applied Mechanics, 12, (1945), pp. 69-77
• 2. Mindlin R. D.: Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics, 18, 1(1951), pp. 31-38
• 3. Liew K. M., Xiang Y., Kitipornchai S.: Research on thick plate vibration: a literature survey. Journal of Sound and Vibration, 180, (1995), pp. 163-176
• 4. Senjanović I., Vladimir N., Tomić M.: An advanced theory of moderately thick plate vibrations. Journal of Sound and Vibration, 332, (2013), pp. 1868-1880
• 5. Senjanović I., Tomić M., Vladimir N.: Cho D. S.: Analytical solution for free vibrations of a moderately thick rectangular plate. Mathematical Problems in Engineering, 2013, (2013), Article ID 207460
• 6. Liew K. M., Xiang Y., Kitipornchai S.: Transverse vibration of thick plates – I. Comprehensive sets of boundary conditions. Computers and Structures, 49, (1993), pp. 1-29
• 7. Dawe D. J., Roufaeil O. L.: Rayleigh-Ritz vibration analysis of Mindlin plates. Journal of Sound and Vibration, 69, 3(1980), pp. 345-359
• 8. Kim K.H., Kim B.H., Choi T.M., Cho D.S.: Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method. International Journal of Naval Architecture and Ocean Engineering, 4, (2012), pp. 267-280
• 9. Chung J.H., Chung T.Y., Kim K.C.: Vibration analysis of orthotropic Mindlin plates with edges elastically restrained against rotation. Journal of Sound and Vibration, 163, (1993), pp. 151-163
• 10. Auricchio F., Taylor R.L.: A triangular thick plate finite element with an exact thin limit. Finite Elements in Analysis and Design, 19, (1995), pp. 57-68
• 11. Lovadina C.: Analysis of a mixed finite element method for the Reissner-Mindlin plate problems. Computer Methods in Applied Mechanics and Engineering, 163, (1998), pp. 71-85
• 12. Hughes T.J.R., Tezduyar T.: Finite elements based upon Mindlin plate theory with particular reference to the four-node isoparametric element. Journal of Applied Mechanics, 48, (1981), pp. 587-596
• 13. Bletzinger K., Bischoff M., Ramm E.: A unified approach for shear-locking free triangular and rectangular shell finite elements. Computers and Structures, 75, (2000), pp. 321-334
• 14. Nguyen-Xuan H., Liu G. R., Thai-Hong C.: Nguyen-Thoi T. An edge-based smoothed finite element method (ESFEM) with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates. Computer Methods in Applied Mechanics and Engineering, 199, (2010), pp. 471-489
• 15. Senjanović I., Vladimir N., Hadžić N. Modified Mindlin plate theory and shear locking-free finite element formulation. Mechanics Research Communications, 55, (2014), pp. 95-104
• 16. Cho D.S., Vladimir N., Choi T.M.: Approximate natural vibration analysis of rectangular plates with openings using assumed mode method. International Journal of Naval Architecture and Ocean Engineering, 5, 3(2013), pp. 478-491
• 17. Paramasivam P.: Free vibration of square plates with openings. Journal of Sound of Vibration, 30, (1973), pp. 173-178
• 18. Kwak M.K., Han S.: Free vibration analysis of rectangular plate with a hole by means of independent coordinate coupling method. Journal of Sound of Vibration, 306, (2007), pp. 12-30
• 19. Grossi R.O., del V. Arenas B., Laura P.A.A.: Free vibration of rectangular plates with circular openings. Ocean Engineering, 24, 1(1997), pp. 19-24
• 20. Monahan L.J., Nemergut P.J., Maddux G.E.: Natural frequencies and mode shapes of plates with interior cutouts. The Shock and Vibration Bulletin, 41, (1970), pp. 37-49
• 21. Cho D.S., Vladimir N., Choi T.M.: Natural vibration analysis of stiffened panels with arbitrary edge constraints using the assumed mode method. Proceedings of the IMechE, Part M: Journal of Engineering for the Maritime Environment, (2014), DOI: 10.1177/1475090214521179, published online
• 22. Samanta A., Mukhopadhyay M.: Free vibration analysis of stiffened shells by the finite element technique. European Journal of Mechanics, A Solids, 23, (2004), pp. 159-179
• 23. Sivasubramonian B., Kulkarni A. M., Rao G.V.; Krishnan A.: Free vibration of curved panels with cutouts. Journal of Sound and Vibration, 200, (1997), pp. 227-234
• 24. Sivasubramonian B., Rao G.V., Krishnan A.: Free vibration of longitudinally stiffened curved panels with cutout. Journal of Sound and Vibration, 226, 1(1999), pp. 41-55
• 25. Srivastava A.K.L.: Vibration of stiffened plates with cutout subjected to partial edge loading. Journal of the Institution of Engineers (India) Series A, 93, 2(2012), pp. 129-135
• 26. MSC. MD Nastran 2010 Dynamic analysis user’s guide. MSC Software, 2010