International Journal of Naval Architecture and Ocean Engineering

The Society of Naval Architects of Korea (대한조선학회)
권호 표지
DOI QR코드

DOI QR Code

A unified solution for vibration analysis of plates with general structural stress distributions

  • Yang, Nian (State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University) ;
  • Chen, Lu-Yun (State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University) ;
  • Yi, Hong (State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University) ;
  • Liu, Yong (Ship Scientific Research Center of China)
  • Received : 2016.03.06
  • Accepted : 2016.05.30
  • Published : 2016.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

Complex stress distributions often exist in ocean engineering structures. This stress influences structural vibrations. Finite Element Methods exhibit some shortcomings for solving non-uniform stress problems, such as an unclear physical interpretation, complicated operation, and large number of computations. Analytical methods research considers mainly uniform stress problems, and often, their methods cannot be applied in practical marine structures with non-uniform stress. In this paper, an analytical method is proposed to solve the vibration of plates with general stress distributions. Non-uniform stress is expressed as a special series, and the stress influence is inserted into a vibration equation that is solved through decoupling to obtain an analytical solution. This method has been verified using numerical examples and can be used in arbitrary stress distribution cases. This method requires fewer computations and it provides a clearer physical interpretation, so it has advantages in some qualitative research.

Keywords

References

  1. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A., Tounsi, A., 2015. Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories. Struct. Eng. Mech. 53 (6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  2. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Anwar Bég, O., 2014. An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Compos. Part B 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  3. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A., Tounsi, A., 2016. Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. J. Braz. Soc. Mech. Sci. Eng. 38, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  4. Bennoun, M., Houari, M.S.A., Tounsi, A., 2016. A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates. Mech. Adv. Mater. Struct. 23 (4), 423-431 https://doi.org/10.1080/15376494.2014.984088
  5. Bokaian, A., 2004. Thermal expansion of pipe-in-pipe systems. Mar. Struct. 17, 475-500. https://doi.org/10.1016/j.marstruc.2004.12.002
  6. Bouderba, B., Houari, M.S.A., Tounsi, A., 2013. Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations. Steel Compos. Struct. 14 (1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  7. Bourada, M., Kaci, A., Houari, M.S.A., Tounsi, A., 2015. A new simple shear and normal deformations theory for functionally graded beams. Steel Compos. Struct. 18 (2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  8. Brunelle, E.J., Robertson, S.R., 1976. Vibrations of an initially stressed thick plate. J. Sound Vib. 45 (3), 405-416. https://doi.org/10.1016/0022-460X(76)90395-3
  9. Cao, Z., 1989. Vibration Theory of Plates and Shells. Chinese Railway Press.
  10. Chen, L., Li, L., Zhang, Y., 2014. Characteristics analysis of structuralacoustic of cylindrical shell with prestress in local areas. J. Shanghai Jiao Tong Univ. 48 (8), 1084-1089.
  11. Cho, D.S., Kim, B.H., Kim, J.H., Vladimir, N., Choi, T.M., 2016. Frequency response of rectangular plates with free-edge openings and carlings subjected to point excitation force and enforced displacement at boundaries. Int. J. Nav. Archit. Ocean Eng. 8 (2), 117-126. https://doi.org/10.1016/j.ijnaoe.2015.06.001
  12. Dong, P.A., 2001. Structural stress definition and numerical implementation for fatigue analysis of welded joints. Int. J. Fatigue 23 (10), 865-876. https://doi.org/10.1016/S0142-1123(01)00055-X
  13. Doong, J.L., 1987. Vibration and stability of an initially stressed thick plate according to a high-order deformation theory. J. Sound Vib. 113 (3), 425-440. https://doi.org/10.1016/S0022-460X(87)80131-1
  14. Fuller, C.R., Fahy, F.J., 1982. Characteristics of wave propagation and energy distributions in cylindrical elastic shells filled with fluid. J. Sound Vib. 81 (4), 501-518. https://doi.org/10.1016/0022-460X(82)90293-0
  15. Gannon, L., Liu, Y., Pegg, N., et al., 2012. Effect of welding-induced residual stress and distortion on ship hull girder ultimate strength. Mar. Struct. 28 (1), 25-49. https://doi.org/10.1016/j.marstruc.2012.03.004
  16. Gao, Y., Su, Z., Jiao, Q., Tang, G., 2002. Influence on the natural frequency of component with residual stress. J. Mech. Strength 24 (2), 289-292.
  17. Gao, Y., Tang, G., Wan, W., 2014. The calculations of natural frequency of quadrate thin plate with welding residual stress. J. Vib. Shock 33 (9), 165-167.
  18. Hamidi, A., Houari, M.S.A., Mahmoud, S.R., Tounsi, A., 2015. A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates. Steel Compos. Struct. 18 (1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  19. He, Z., 2001. Structural Vibration and Radiation. Harbin Engineering University Press.
  20. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A., Adda Bedia, E.A., 2014. A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. ASCE J. Eng. Mech. 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  21. Khan, I., Zhang, S., 2011. Effects of welding-induced residual stress on ultimate strength of plates and stiffened panels. Ships Offshore Struct. 6 (4), 297-309. https://doi.org/10.1080/17445301003776209
  22. Lee, C.K., Chiew, S.P., et al., 2013. 3D residual stress modelling of welded high strength steel plate-to-plate joints. J. Constr. Steel Res. 84, 94-104. https://doi.org/10.1016/j.jcsr.2013.02.007
  23. Li, L., Wan, Z., Pan, G., Wang, Z., 2010. Review on welding residual stresses of submarine structures. Ship Sci. Technol. 32 (10), 130-134.
  24. Liu, Z., 2009. Characteristics of Power Flow and Sound Radiation in Cylindrical Shell-fluid System Considering Hydrostatic Pressure. PhD Dissertation. Huazhong University of Science & Technology, Wuhan, China.
  25. Liu, Z., Li, T., Zhu, X., et al., 2010. The effect of hydrostatic pressure fields on the dispersion characteristics of fluid-shell coupled system. J. Mar. Sci. Appl. 9 (2), 129-136. https://doi.org/10.1007/s11804-010-9010-3
  26. Liu, Z., Li, T., Zhu, X., et al., 2011. The effect of hydrostatic pressure on input power flow in submerged ring-stiffened cylindrical shells. J. Ship Mech. 15 (3), 301-312.
  27. Mahi, A., Adda Bedia, E.A., Tounsi, A., 2015. A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Appl. Math. Model. 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  28. Meziane, Ait Amar, et al., 2014. An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. J. Sandw. Struct. Mater. 16 (3), 293-318. https://doi.org/10.1177/1099636214526852
  29. Niemi, E., 1995. Stress Determination for Fatigue Analysis of Welded Component. Woodhead Publishing.
  30. Paik, J.K., Sohn, J.M., 2012. Effects of welding residual stresses on high tensile steel plate ultimate strength: nonlinear finite element method investigations. J. Offshore Mech. Arct. Eng. 134 (2), 021401. https://doi.org/10.1115/1.4004510
  31. Radaj, D., 2012. Heat Effects of Welding: Temperature Field, Residual Stress. Distortion. Springer Science & Business Media.
  32. Senjanovic, I., Vladimir, N., Cho, D.S., 2015. A new finite element formulation for vibration analysis of thick plates. Int. J. Nav. Archit. Ocean Eng. 7 (2), 324-345. https://doi.org/10.1515/ijnaoe-2015-0023
  33. Senjanovic, I., Vladimir, N., Tomic, M., 2016. On new first-order shear deformation plate theories. Mech. Res. Commun. 73, 31-38. https://doi.org/10.1016/j.mechrescom.2016.02.005
  34. Tounsi, A., Houari, M.S.A., Benyoucef, S., Adda Bedia, E.A., 2013. A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates. Aerosp. Sci. Technol. 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  35. Yahnioglu, N., 2007. On the stress distribution in a prestretched simply supported strip containing two neighboring circular holes under forced vibration. Int. Appl. Mech. 43 (10), 1179-1183. https://doi.org/10.1007/s10778-007-0119-2
  36. Zhang, X.M., 2002. Frequency analysis of submerged cylindrical shells with the wave propagation approach. Int. J. Mech. Sci. 44 (7), 1259-1273. https://doi.org/10.1016/S0020-7403(02)00059-0
  37. Zhang, Y., Gorman, D., Reese, J., 2001a. A finite element method for modelling the vibration of initially tensioned thin-walled orthotropic cylindrical tubes conveying fluid. J. Sound Vib. 245 (1), 93-112. https://doi.org/10.1006/jsvi.2000.3554
  38. Zhang, X.M., Liu, G.R., Lam, K.Y., 2001b. Coupled vibration analysis of fluid-filled cylindrical shells using the wave propagation approach. Appl. Acoust. 62 (3), 229-243. https://doi.org/10.1016/S0003-682X(00)00045-1
  39. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A., Anwar Bég, O., 2014. Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory. Aerosp. Sci. Technol. 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

Cited by

  1. Vibration characteristic analysis of a circular thin plate with complex pre-stress distribution vol.20, pp.8, 2018, https://doi.org/10.21595/jve.2018.19244
  2. Active Vibration Distribution through Restricted Topology and Single Node Control vol.2020, pp.None, 2020, https://doi.org/10.1155/2020/8823527
  3. Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution vol.39, pp.4, 2016, https://doi.org/10.1177/1461348419852456
  4. Effect of shape mode and crack length on stress distribution in fiber metal laminates vol.1034, pp.1, 2016, https://doi.org/10.1088/1757-899x/1034/1/012022