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Shock and Vibration
Volume 2019, Article ID 2364515, 22 pages
https://doi.org/10.1155/2019/2364515
Research Article

Dynamic Analysis of Rectangular Plate Stiffened by Any Number of Beams with Different Lengths and Orientations

1Naval Research Academy, Beijing 100161, China
2State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China
3Beijing Aerospace Technology Institute, China Aerospace Science & Industry Corp, Beijing 100074, China

Correspondence should be addressed to Dong Shao; moc.kooltuo@natasoahsgnod

Received 4 June 2019; Revised 19 August 2019; Accepted 17 October 2019; Published 7 November 2019

Academic Editor: Angelo Marcelo Tusset

Copyright © 2019 Yuan Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Mukherjee and M. Mukhopadhyay, “Finite element free vibration of eccentrically stiffened plates,” Computers & Structures, vol. 30, no. 6, pp. 1303–1317, 1988. View at Publisher · View at Google Scholar · View at Scopus
  2. T. P. Holopainen, “Finite element free vibration analysis of eccentrically stiffened plates,” Computers & Structures, vol. 56, no. 6, pp. 993–1007, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. K. M. Liew, Y. Xiang, S. Kitipornchai, and J. L. Meek, “Formulation of Mindlin-Engesser model for stiffened plate vibration,” Computer Methods in Applied Mechanics and Engineering, vol. 120, no. 3-4, pp. 339–353, 1995. View at Publisher · View at Google Scholar · View at Scopus
  4. H. P. Lee and T. Y. Ng, “Effects of torsional and bending restraints of intermediate stiffeners on the free vibration of rectangular plates,” Mechanics of Structures and Machines, vol. 23, no. 3, pp. 309–320, 1995. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Barrette, A. Berry, and O. Beslin, “Vibration of stiffened plates using hierarchical trigonometric functions,” Journal of Sound and Vibration, vol. 235, no. 5, pp. 727–747, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Zeng and C. W. Bert, “A differential quadrature analysis of vibration for rectangular stiffened plates,” Journal of Sound and Vibration, vol. 241, no. 2, pp. 247–252, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. A. K. L. Srivastava, P. K. Datta, and A. H. Sheikh, “Buckling and vibration of stiffened plates subjected to partial edge loading,” International Journal of Mechanical Sciences, vol. 45, no. 1, pp. 73–93, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. L. X. Peng, K. M. Liew, and S. Kitipornchai, “Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method,” Journal of Sound and Vibration, vol. 289, no. 3, pp. 421–449, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Dozio and M. Ricciardi, “Free vibration analysis of ribbed plates by a combined analytical-numerical method,” Journal of Sound and Vibration, vol. 319, no. 1-2, pp. 681–697, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Xu, J. Du, and W. L. Li, “Vibrations of rectangular plates reinforced by any number of beams of arbitrary lengths and placement angles,” Journal of Sound and Vibration, vol. 329, no. 18, pp. 3759–3779, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Bhar, S. S. Phoenix, and S. K. Satsangi, “Finite element analysis of laminated composite stiffened plates using FSDT and HSDT: a comparative perspective,” Composite Structures, vol. 92, no. 2, pp. 312–321, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. T. Nguyen-Thoi, T. Bui-Xuan, P. Phung-Van, H. Nguyen-Xuan, and P. Ngo-Thanh, “Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements,” Computers & Structures, vol. 125, no. 9, pp. 100–113, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. N. Nguyen-Minh, T. Nguyen-Thoi, T. Bui-Xuan, and T. Vo-Duy, “Static and free vibration analyses of stiffened folded plates using a cell-based smoothed discrete shear gap method (CS-FEM-DSG3),” Applied Mathematics and Computation, vol. 266, pp. 212–234, 2015. View at Publisher · View at Google Scholar · View at Scopus
  14. K. Bhaskar and A. Pydah, “An elasticity approach for simply-supported isotropic and orthotropic stiffened plates,” International Journal of Mechanical Sciences, vol. 89, pp. 21–30, 2014. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Pydah and K. Bhaskar, “Accurate discrete modelling of stiffened isotropic and orthotropic rectangular plates,” Thin-Walled Structures, vol. 97, pp. 266–278, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. D. S. Cho, N. Vladimir, and T. M. Choi, “Numerical procedure for the vibration analysis of arbitrarily constrained stiffened panels with openings,” International Journal of Naval Architecture and Ocean Engineering, vol. 6, no. 4, pp. 763–774, 2014. View at Publisher · View at Google Scholar · View at Scopus
  17. D. S. Cho, B. H. Kim, J.-H. Kim, T. M. Choi, and N. Vladimir, “Free vibration analysis of stiffened panels with lumped mass and stiffness attachments,” Ocean Engineering, vol. 124, pp. 84–93, 2016. View at Publisher · View at Google Scholar · View at Scopus
  18. D. S. Cho, J.-H. Kim, T. M. Choi, B. H. Kim, and N. Vladimir, “Free and forced vibration analysis of arbitrarily supported rectangular plate systems with attachments and openings,” Engineering Structures, vol. 171, pp. 1036–1046, 2018. View at Publisher · View at Google Scholar · View at Scopus
  19. X. C. Qin, C. Y. Dong, F. Wang, and X. Y. Qu, “Static and dynamic analyses of isogeometric curvilinearly stiffened plates,” Applied Mathematical Modelling, vol. 45, pp. 336–364, 2017. View at Publisher · View at Google Scholar · View at Scopus
  20. X. Yin, W. Wu, H. Li, and K. Zhong, “Vibration transmission within beam-stiffened plate structures using dynamic stiffness method,” Procedia Engineering, vol. 199, pp. 411–416, 2017. View at Publisher · View at Google Scholar · View at Scopus
  21. E. Damnjanović, M. Nefovska-Danilović, M. Petronijević, and M. Marjanović, “Application of the dynamic stiffness method in the vibration analysis of stiffened composite plates,” Procedia Engineering, vol. 199, pp. 224–229, 2017. View at Publisher · View at Google Scholar · View at Scopus
  22. I. E. Harik and G. L. Salamoun, “The analytical strip method of solution for stiffened rectangular plates,” Computers & Structures, vol. 29, no. 2, pp. 283–291, 1988. View at Publisher · View at Google Scholar · View at Scopus
  23. L. A. Louca, Y. G. Pan, and J. E. Harding, “Response of stiffened and unstiffened plates subjected to blast loading,” Engineering Structures, vol. 20, no. 12, pp. 1079–1086, 1998. View at Publisher · View at Google Scholar · View at Scopus
  24. A. H. Sheikh and M. Mukhopadhyay, “Linear and nonlinear transient vibration analysis of stiffened plate structures,” Finite Elements in Analysis and Design, vol. 38, no. 6, pp. 477–502, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. A. K. L. Srivastava, P. K. Datta, and A. H. Sheikh, “Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading,” Journal of Sound and Vibration, vol. 262, no. 5, pp. 1171–1189, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. X. D. Xu, H. P. Lee, Y. Y. Wang, and C. Lu, “The energy flow analysis in stiffened plates of marine structures,” Thin-Walled Structures, vol. 42, no. 7, pp. 979–994, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. X. D. Xu, H. P. Lee, and C. Lu, “Power flow paths in stiffened plates,” Journal of Sound and Vibration, vol. 282, no. 3–5, pp. 1264–1272, 2005. View at Publisher · View at Google Scholar · View at Scopus
  28. A. Borković, N. Mrđa, and S. Kovačević, “Dynamical analysis of stiffened plates using the compound strip method,” Engineering Structures, vol. 50, no. 3, pp. 56–67, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. D. S. Cho, B. H. Kim, J.-H. Kim, N. Vladimir, and T. M. Choi, “Forced vibration analysis of arbitrarily constrained rectangular plates and stiffened panels using the assumed mode method,” Thin-Walled Structures, vol. 90, pp. 182–190, 2015. View at Publisher · View at Google Scholar · View at Scopus
  30. R. L. Tian and P. Jie, “A closed form solution for the dynamic response of finite ribbed plates,” The Journal of the Acoustical Society of America, vol. 119, no. 2, pp. 917–925, 2006. View at Publisher · View at Google Scholar · View at Scopus
  31. R. L. Tian, “An analytical and experimental study of the vibration response of a clamped ribbed plate,” Journal of Sound and Vibration, vol. 331, no. 4, pp. 902–913, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. T. R. Lin and K. Zhang, “An analytical study of the free and forced vibration response of a ribbed plate with free boundary conditions,” Journal of Sound and Vibration, vol. 422, pp. 15–33, 2018. View at Publisher · View at Google Scholar · View at Scopus
  33. D.-S. Cho, T.-M. Choi, J.-H. Kim, and N. Vladimir, “Dominant components of vibrational energy flow in stiffened panels analysed by the structural intensity technique,” International Journal of Naval Architecture and Ocean Engineering, vol. 10, no. 5, pp. 583–595, 2018. View at Publisher · View at Google Scholar · View at Scopus
  34. G. Jia, X. Zhang, C. Wang, Y. He, and X. Chen, “Predicting dynamic response of stiffened-plate composite structures in a wide-frequency domain based on composite B-spline wavelet elements method (CBWEM),” International Journal of Mechanical Sciences, vol. 144, pp. 708–722, 2018. View at Publisher · View at Google Scholar · View at Scopus
  35. C. Liu, J. Zhang, and F. Li, “Power transmission and suppression characteristics of stiffened Mindlin plate under different boundary constraints,” Archive of Applied Mechanics, vol. 89, no. 9, pp. 1705–1721, 2019. View at Publisher · View at Google Scholar · View at Scopus
  36. D. Shi, H. Zhang, Q. Wang, and S. Zha, “Free and forced vibration of the moderately thick laminated composite rectangular plate on various elastic winkler and pasternak foundations,” Shock and Vibration, vol. 2017, Article ID 7820130, 23 pages, 2017. View at Publisher · View at Google Scholar · View at Scopus
  37. Y. Chen, G. Jin, M. Zhu, Z. Liu, J. Du, and W. L. Li, “Vibration behaviors of a box-type structure built up by plates and energy transmission through the structure,” Journal of Sound and Vibration, vol. 331, no. 4, pp. 849–867, 2012. View at Publisher · View at Google Scholar · View at Scopus
  38. Y. Chen, G. Jin, J. Du, and Z. Liu, “Power transmission analysis of coupled rectangular plates with elastically restrained coupling edge including in-plane vibration,” in Proceedings of the 20th International Congress on Acoustics (ICA), Sydney, Australia, August 2010.
  39. S. Jiang, W. L. Li, T. Yang, and J. Du, “Free vibration analysis of doubly curved shallow shells reinforced by any number of beams with arbitrary lengths,” Journal of Vibration and Control, vol. 22, no. 2, pp. 570–584, 2016. View at Publisher · View at Google Scholar · View at Scopus
  40. W. L. Li, “Free vibrations of beams with general boundary conditions,” Journal of Sound and Vibration, vol. 237, no. 4, pp. 709–725, 2000. View at Publisher · View at Google Scholar · View at Scopus
  41. S. Zhu, G. Jin, Y. Wang, and X. Ye, “A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations,” Acta Mechanica, vol. 227, no. 5, pp. 1493–1514, 2016. View at Publisher · View at Google Scholar · View at Scopus
  42. X. Shi, D. Shi, W. L. Li, and Q. Wang, “A unified method for free vibration analysis of circular, annular and sector plates with arbitrary boundary conditions,” Journal of Vibration and Control, vol. 22, no. 2, pp. 442–456, 2014. View at Publisher · View at Google Scholar · View at Scopus
  43. J. Du, W. L. Li, G. Jin, T. Yang, and Z. Liu, “An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges,” Journal of Sound and Vibration, vol. 306, no. 3–5, pp. 908–927, 2007. View at Publisher · View at Google Scholar · View at Scopus
  44. D. Shi, S. Zha, H. Zhang, and Q. Wang, “Free vibration analysis of the unified functionally graded shallow shell with general boundary conditions,” Shock and Vibration, vol. 2017, Article ID 7025190, 19 pages, 2017. View at Publisher · View at Google Scholar · View at Scopus
  45. D.-S. Cho, T.-M. Choi, J.-H. Kim, and N. Vladimir, “Structural intensity analysis of stepped thickness rectangular plates utilizing the finite element method,” Thin-Walled Structures, vol. 109, pp. 1–12, 2016. View at Publisher · View at Google Scholar · View at Scopus
  46. M. A. Neto, A. Amaro, L. Roseiro, J. Cirne, and R. Leal, Engineering Computation of Structures: The Finite Element Method, Springer, Berlin, Germany, 2015.