Skip to main content
SpringerLink
Log in

Free vibration analysis of a thin rectangular plate with multiple circular and rectangular cut-outs

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The present work is to investigate the variation in the natural frequency of a rectangular plate with the change in position of cut outs of different sizes along its diagonal and major axis line by considering different aspect ratios of plates. In this regard the free vibration analysis of an isotropic rectangular plate of various aspect ratios with different sizes of multiple circular and rectangular cut-outs is carried out by using an Independent coordinate coupling method (ICCM) under simply supported boundary condition. The ICCM utilizes independent coordinates separately for plate domain and hole domain, in which the reduced mass and stiffness matrices can be derived, by matching the deflection conditions for each hole imposed on the expressions. The resulting equation is useful for the calculation of the Eigen values. The position, size, and number of cutouts have been varied in all the possible ways to investigate their effects on the natural frequency of the rectangular plate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Paramasivam, Free vibration of square plates with square opening, Journal of Sound and Vibration, 30 (1973) 173–178.

    Article  Google Scholar 

  2. R. F. Hegarty and T. Ariman, Elasto-dynamic analysis of rectangular plates with circular holes, International Journal of Solids and Structures, 11 (1975) 895–906.

    Article  MATH  Google Scholar 

  3. F. E. Eastep and F. G. Hemmig, Estimation of fundamental frequency of non-circular plates with free, circular cutouts, Journal of Sound and Vibration, 56 (2) (1978) 155–165.

    Article  MATH  Google Scholar 

  4. K. Nagaya, Transverse vibration of a rectangular plate with an eccentric circular inner boundary, International Journal of Solids and Structures, 16 (1980) 1007–1016.

    Article  MATH  Google Scholar 

  5. G. Aksu and R. Ali, Determination of dynamic characteristics of rectangular plates with cut-outs using a finite difference formulation, Journal of Sound and Vibration, 44 (1976) 147–158.

    Article  MATH  Google Scholar 

  6. A. Rajamani and R. Prabhakaran, Dynamic response of composite plates with cut-outs. Part I: Simply-supported plates, Journal of Sound and Vibration, 54 (1977) 549–564.

    Article  MATH  Google Scholar 

  7. A. Rajamani and R. Prabhakaran, Dynamic response of composite plates with cut-outs. Part II: Clamped-clamped plates, Journal of Sound and Vibration, 54 (1977) 565–576.

    Article  MATH  Google Scholar 

  8. R. Ali and S. J. Atwal, Prediction of natural frequencies of vibration of rectangular plates with rectangular cutouts, Computers and Structures, 12 (1980) 819–823.

    Article  MATH  Google Scholar 

  9. H. S. Lee and K. C. Kim, Transverse vibration of rectangular plates having an inner cutout in water, Journal of the Society of Naval Architects of Korea, 21 (1) (1984) 21–34.

    Google Scholar 

  10. R. B. Bhat, Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method, Journal of Sound and Vibration, 102 (1985) 493–499.

    Article  Google Scholar 

  11. R. B. Bhat, Plate deflections using orthogonal polynomials, American Society of Civil Engineers, Journal of the Engineering Mechanics Division, 111 (1985) 1301–1309.

    Article  Google Scholar 

  12. R. B. Bhat, Numerical experiments on determination of natural frequencies of transverse vibrations of rectangular plates of non-uniform thickness, Journal of Sound and Vibration, 138 (1990) 205–219.

    Article  Google Scholar 

  13. K. Y. Lam, K. C. Hung and S. T. Chow, Vibration analysis of plates with cut-outs by the modified Rayleigh-Ritz method, Applied Acoustics, 28 (1989) 49–60.

    Article  Google Scholar 

  14. K. Y. Lam and K. C. Hung, Vibration study on plates with stiffened openings using orthogonal polynomials and partitioning method, Computers and Structures, 37 (1990) 295–301.

    Article  Google Scholar 

  15. K. C. Kim, S. Y. Han and J. H. Jung, Transverse vibration of stiffened rectangular plates having an inner cutout, Journal of the Society of Naval Architects of Korea, 24 (3) (1987) 35–42.

    Google Scholar 

  16. R. O. Grossi, Blanca del V. Arenas and P. A. A Laura, Free vibration of rectangular plates with circular openings, Ocean Engg, 24 (1) (1997) 19–24.

    Article  Google Scholar 

  17. P. A. A. Laura, E. Romanelli and R. E. Rossi, Transverse vibrations of simply-supported rectangular plates with rectangular cutouts, Journal of Sound and Vibration, 202 (2) (1997) 275–283.

    Article  Google Scholar 

  18. T. Sakiyama and M. Huang, Free vibration of orthotropic square plates with a square hole, Journal of Sound and Vibration, 259 (1) (2003) 63–80.

    Article  Google Scholar 

  19. D. R. Avalos and P. A. A. Laura, Transverse vibrations of simply-supported rectangular plates with two rectangular cutouts, Journal of Sound and Vibration, 267 (2003) 967–977.

    Article  Google Scholar 

  20. K. M. Liew, S. Kitipornchai, A. Y. Tleung and C. W. Lim, Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method, International Journal of Mechanical Sciences, 45 (2003) 941–959.

    Article  MATH  Google Scholar 

  21. K. Torabi and A. R. Azadi, Vibration analysis for Rectangular plate having a circular central hole with point support by Rayleigh-Ritz method, Journal of Solid Mechanics, 6 (1) (2014) 28–42.

    Google Scholar 

  22. A. W. Leissa, The free vibration of rectangular plates, Journal of Sound and Vibration, 31 (3) (1973) 257–293.

    Article  MATH  Google Scholar 

  23. F. Tornabene, N. Fantuzzi, M. Bacciocchi, A. M. A. Neve and A. J. M. Ferreira, MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells, Composites Part B: Engineering, 99 (1) (2016) 30–47.

    Article  Google Scholar 

  24. N. Fantuzzi and F. Tornabene, Strong formulation isogeometric analysis (SFIGA) for laminated composite arbitrarily shaped plates, Composites Part B: Engineering, 96 (1) (2016) 173–203.

    Article  Google Scholar 

  25. N. Fantuzzia and F. Tornabene, Four-parameter functionally graded cracked plates of arbitrary shape: A GDQFEM solution for free vibrations, Mechanics of Advanced Materials and Structures, 23 (1) (2016) 89–107.

    Article  Google Scholar 

  26. X. Liu, Spectral dynamic stiffness formulation for in plane modal analysis of composite plate assemblies and prismatic solids with arbitrary classical/non-classical boundary conditions, Composite Structures, 158 (2016) 262–280.

    Article  Google Scholar 

  27. X. Liu and J. R. Banerjee, Free vibration analysis for plates with arbitrary boundary conditions using a novel spectraldynamic stiffness method, Computers and Structures, 164 (2016) 108–126.

    Article  Google Scholar 

  28. X. Liu and J. R. Banerjee, An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies - Part I: Theory, Composite Structures, 132 (2015) 1274–1287.

    Article  Google Scholar 

  29. I. Shufrin and M. Eisenberger, Semi-analytical modeling of cutouts in rectangular plates with variable thickness -Free vibration analysis, Applied Mathematical Modelling, 40 (2016) 6983–7000.

    Article  MathSciNet  Google Scholar 

  30. M. Eisenberger and A. Deutsch, Static analysis for exact vibration analysis of clamped plates, International Journal of Structural Stability and Dynamics, 15 (8) (2015) 1540030 (13 pages).

    Article  MathSciNet  MATH  Google Scholar 

  31. I. Shufrin, O. Rabinovitch and M. Eisenberger, Elastic nonlinear stability analysis of thin rectangular plates through a semi-analytical approach, International Journal of Solids and Structures, 46 (2009) 2075–2092.

    Article  MATH  Google Scholar 

  32. S. M. Mirkhalaf, Transverse vibration of clamped and simply supported circular plates with an eccentric circular perforation and attached concentrated mass, Journal of Solid Mechanics, 1 (1) (2009) 37–44.

    Google Scholar 

  33. M. M. Najafizadeh and S. M. M. Valashani, Vibration analysis of circular plates with an eccentric circular perforation with a free edge and attached concentrated mass at any arbitrary position, Australian Journal of Basic and Applied Sciences, 5 (12) (2011) 3052–3058.

    Google Scholar 

  34. M. Anjibabu, R. N. Mohan and V. V. Subbarao, Free vibration analysis of an elliptical plate with cut-outs, Journal of Vibroengineering, 19 (4) (2016) 13.

    Google Scholar 

  35. K. Itao and S. H. Crandall, Natural modes and natural frequencies of uniform, circular, free-edge plates, Journal of Applied Mechanics, Transactions of the ASME, 46 (1979) 448–453.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University College of Engineering Kakinada, Jawaharlal Nehru Technological University Kakinada, Kakinada, India

    Anjibabu Merneedi, Mohan RaoNalluri & V. V. Subba Rao

Authors
  1. Anjibabu Merneedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohan RaoNalluri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. V. Subba Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anjibabu Merneedi.

Additional information

Recommended by Associate Editor Eung-Soo Shin

Anjibabu Merneedi is a Regular Research Scholar in the Mechanical Engineering Department at University College of engineering Kakinada, Kakinada, India. He completed his post-graduation in the Machine Design stream and currently he is working in the area of free vibrations analysis of structures.

Mohan Rao Nalluri received his Ph.D. in the area of Robot kinematics from University College of engineering Kakinada, Kakinada, India, in 2008. Now he works as a Professor in Mechanical Engineering Department at University college of Engineering Kakinada, JNTUK. His current research includes free vibration analysis of structure, Robot kinematics and Mechanisms and composites.

Venkata SubbaRao Vissakodeti received his Ph.D. in the area of Composites from IIT kharagpur, India, in 2004. Now he works as a Professor in Mechanical Engineering Department at University college of Engineering Kakinada, JNTUK. His current research includes Finite Element Methods, and composites.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Merneedi, A., RaoNalluri, M. & Rao, V.V.S. Free vibration analysis of a thin rectangular plate with multiple circular and rectangular cut-outs. J Mech Sci Technol 31, 5185–5202 (2017). https://doi.org/10.1007/s12206-017-1012-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-017-1012-5

Keywords

Search

Navigation