Advertisement

Acta Mechanica Solida Sinica

, Volume 26, Issue 2, pp 129–139 | Cite as

Analysis and Experiment on Transient Dynamic Response in Finite Mindlin Plate

  • Fengming Li
  • Chunchuan Liu
  • Tingwei Liang
Article

Abstract

The transient wave propagation in the finite rectangular Mindlin plate is investigated by the analytical and experimental methods. The generalized ray method (GRM) which has been successfully applied to study the transient responses of beams, planar trusses, space frames and infinite layered media is extended to investigate the transient wave propagation and early short time transient response in finite Mindlin plate. Combining the wave solution, the shock source and the boundary conditions, the ray groups transmitted in the finite rectangular plate can be determined. Numerical simulations and experiments are performed and compared with each other. The results show that the transient wave propagation and early short time transient responses in the finite plate can be studied using the GRM. The early short time transient accelerations are very large for the finite plate subjected to the unit impulse, while the early short time transient displacements are very small. The early short time transient accelerations under the unit impulse are much larger than those under the unit step impulse. The thickness and material characteristics have remarkable effects on the early short time transient responses.

Key words

finite Mindlin plate transient wave propagation early short time transient response generalized ray method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Pavlou, D.G., An exact solution for transient wave propagation in an infinite layer under dynamic torsion. Mechanics Research Communications, 2010, 37: 372–376.CrossRefGoogle Scholar
  2. [2]
    Desceliers, C., Soize, C., Grimal, Q., Haiat, G. and Naili, S., A time-domain method to solve transient elastic wave propagation in a multilayer medium with a hybrid spectral-finite element space approximation. Wave Motion, 2008, 45: 383–399.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Alshaikh, I.A., Turhan, D. and Mengi, Y., Propagation of transient out-of-plane shear waves in viscoelastic layered media. International Journal of Mechanical Sciences, 2001, 43: 2911–2928.CrossRefGoogle Scholar
  4. [4]
    Guddati, M.N., Tassoulas, J.L., Space-time finite elements for the analysis of transient wave propagation in unbounded layered media. International Journal of Solids and Structures, 1999, 36: 4699–4723.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Lu, M.Y., Wang, J.G., Ergin, A.A. and Michielssen, E., Fast evaluation of two-dimensional transient wave fields. Journal of Computational Physics, 2000, 158: 161–185.CrossRefGoogle Scholar
  6. [6]
    Park, S.H. and Tassoulas, J.L., A discontinuous Galerkin method for transient analysis of wave propagation in unbounded domains. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 3983–4011.CrossRefGoogle Scholar
  7. [7]
    Liu, T.Y. and Li, Q.B., Transient elastic wave propagation in an infinite Timoshenko beam on viscoelastic foundation. International Journal of Solids and Structures, 2003, 40: 3211–3228.CrossRefGoogle Scholar
  8. [8]
    El-Raheb, M., Transient waves in an inhomogeneous hollow infinite cylinder. International Journal of Solids and Structures, 2005, 42: 5365–5376.CrossRefGoogle Scholar
  9. [9]
    Han, X., Liu, G.R., Xi, Z.C. and Lam, K.Y., Transient waves in a functionally grade cylinder. International Journal of Solids and Structures, 2001, 38: 3021–3037.CrossRefGoogle Scholar
  10. [10]
    Lam, K.Y., Zhang, J.Z., Gong, S.W. and Chan, E.S., The transient response of a two-layered elastic cylindrical shell impinged by an underwater shock wave. Composites Part B, 1998, 29B: 673–685.CrossRefGoogle Scholar
  11. [11]
    Hu, G.Y., Fei, X. and Li, J., The transient responses of two-layered cylindrical shells attacked by underwater explosive shock waves. Composite Structures, 2010, 92: 1551–1560.CrossRefGoogle Scholar
  12. [12]
    Li, J. and Hua, H.X., Transient vibrations of laminated composite cylindrical shells exposed to underwater shock waves. Engineering Structures, 2009, 31: 738–748.CrossRefGoogle Scholar
  13. [13]
    Yang, S. and Yuan, F.G., Transient wave propagation of isotropic plates using a higher-order plate theory. International Journal of Solids and Structures, 2005, 42: 4115–4153.CrossRefGoogle Scholar
  14. [14]
    Toh, S.L., Gong, S.W. and Shim, V.P.W., Transient stresses generated by low velocity impact on orthotropic laminated cylindrical shells. Composite Structures, 1995, 31: 213–228.CrossRefGoogle Scholar
  15. [15]
    Lee, Y.S. and Lee, K.D., On The dynamic response of laminated circular cylindrical shells under impulse loads. Computers and Structures, 1997, 63(1): 149–157.CrossRefGoogle Scholar
  16. [16]
    Gong, S.W., Lam, K.Y. and Reddy, J.N., The elastic response of functionally graded cylindrical shells to low-velocity impact. International Journal of Impact Engineering, 1999, 22: 397–417.CrossRefGoogle Scholar
  17. [17]
    Michalel, E.R. and Paul, W., Transient fexural waves in a disk and square plate from off-center impact. The Journal of the Acoustical Society of America, 2001, 110(6): 2991–3002.CrossRefGoogle Scholar
  18. [18]
    Han, X., Xu, D. and Liu, G.R., Transient response in a functionally graded cylindrical shell to a point Load. Journal of Sound and Vibration, 2002, 251(5): 783–805.CrossRefGoogle Scholar
  19. [19]
    Wang, R.T. and Lin, Z.X., Vibration analysis of ring-stiffened cross-ply laminated cylindrical shells. Journal of Sound and Vibration, 2006, 295: 964–987.CrossRefGoogle Scholar
  20. [20]
    Jafari, A.A., Khalili, S.M.R. and Azarafza, R., Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads. Thin-Walled Structures, 2005, 43: 1763–1786.CrossRefGoogle Scholar
  21. [21]
    Khalili, S.M.R., Azarafza, R. and Davar, A., Transient dynamic response of initially stressed composite circular cylindrical shells under radial impulse load. Composite Structures, 2009, 89: 275–284.CrossRefGoogle Scholar
  22. [22]
    Gong, S.W. and Lam, K.Y., Transient response of stiffened composite plates subjected to low velocity impact. Composites Part B, 1999, 30: 473–484.CrossRefGoogle Scholar
  23. [23]
    Rao, J.S., Yu, Y.D. and Shiau, T.N., Transient response of rotating laminated plates with interfacial friction under accelerating conditions. Journal of Sound and Vibration, 1999, 228(1): 37–50.CrossRefGoogle Scholar
  24. [24]
    Kumar, Y.V.S. and Mukhopadhyay, M., Transient response analysis of laminated stiffened plates. Composite Structures, 2002, 58: 97–107.CrossRefGoogle Scholar
  25. [25]
    Nayak, A.K., Shenoi, R.A. and Moy, S.S.J., Transient response of composite sandwich plates. Composite Structures, 2004, 64: 249–267.CrossRefGoogle Scholar
  26. [26]
    Nayak, A.K., Shenoi, R.A. and Moy, S.S.J., Transient response of initially stressed composite sandwich plates. Finite Elements in Analysis and Design, 2006, 42: 821–836.CrossRefGoogle Scholar
  27. [27]
    Pao, Y.H., Chen, W.Q. and Su, X.Y., The reverberation-ray matrix and transfer matrix analyses of unidirectional wave motion. Wave Motion, 2007, 44: 419–438.MathSciNetCrossRefGoogle Scholar
  28. [28]
    Pao, Y.H. and Gajewski, R.R., The generalized ray theory and transient response of layered elastic solids. In: Physical Acoustics. V. XIII, eds. by Mason, W.P. and Thurston, R.N., Academic Press, INC, New York: 1977.CrossRefGoogle Scholar
  29. [29]
    Su, X.Y. and Pao, Y.H., Normal mode, ray and hybrid analysis for transient waves in a finite beam. Journal of Sound and Vibration, 1992, 151(2): 351–368.CrossRefGoogle Scholar
  30. [30]
    Howard, S.M. and Pao, Y.H., Analysis and experiment on stress waves in planar trusses. Journal of Engineering Mechanics, 1998, 124(3): 884–891.CrossRefGoogle Scholar
  31. [31]
    Pao, Y.H., Keh, D.C. and Howard, S.M., Dynamics response and wave propagation in trusses and frames. AIAA Journal, 1999, 37(5): 594–603.CrossRefGoogle Scholar
  32. [32]
    Guo, Y.Q. and Chen, W.Q., Dynamic analysis of space structures with multiple tuned mass damper. Engineering Structures, 2007, 27(12): 3390–3403.CrossRefGoogle Scholar
  33. [33]
    Guo, Y.Q., Chen, W.Q. and Pao, Y.H., Dynamic analysis of space frame: the method of reverberation-ray matrix and orthogonality of normal modes. Journal of Sound and Vibration, 2008, 317(3–5): 716–738.CrossRefGoogle Scholar
  34. [34]
    Pao, Y.H., Su, X.Y. and Tian, J.Y., Reverberation method for propagation of sound in multilayered liquid. Journal of Sound and Vibration, 2000, 230(4): 743–760.CrossRefGoogle Scholar
  35. [35]
    Su, X.Y., Tian, J.Y. and Pao, Y.H., Application of the reverberation-ray matrix to the propagation of elastic waves in a layered solid. International Journal of Solids and Structures, 2002, 39: 5447–5463.CrossRefGoogle Scholar
  36. [36]
    Chen, J.F. and Pao, Y.H., Effects of causality and joint conditions on method of reverberation-ray matrix. AIAA Journal, 2003, 41(6): 1138–1142.CrossRefGoogle Scholar
  37. [37]
    Liu, C.C., Li, F.M., Liang, T.W. and Huang, W.H., Early short time transient response of finite L-shaped Mindlin plate. Wave Motion, 2011, 48: 371–391.MathSciNetCrossRefGoogle Scholar
  38. [38]
    Mindlin, R.D., Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics, 1951, 18: 31–38.zbMATHGoogle Scholar
  39. [39]
    Kane, T.R. and Mindlin, R.D., High frequency extensional vibrations of plates. Journal of Applied Mechanics, 1956, 23: 227–283.MathSciNetzbMATHGoogle Scholar
  40. [40]
    Mindlin, R.D. and Medick, M.A., Extensional vibrations of elastic plates. Journal of Applied Mechanics, 1959, 26: 561–569.MathSciNetGoogle Scholar
  41. [41]
    Liu, C.C., Li, F.M., Liang, T.W. and Huang, W.H., The wave and vibratory power transmission in finite L-shaped Mindlin plate. Acta Mechanica Sinica, DOI 10.1007/s10409-011-0477-1.Google Scholar
  42. [42]
    Miya, K., Vesaka, M. and Moon, F.C., Finite element analysis of vibration of toroidal field coils coupled with Laplace transform. Journal of Applied Mechanics, 1982, 49(3): 594–600.CrossRefGoogle Scholar
  43. [43]
    Kessissoglou, N.J., Ragnarsson, P. and Lofgren, A., An analytical and experimental comparison of optimal actuator and error sensor location for vibration attenuation. Journal of Sound and Vibration, 2003, 260: 671–691.MathSciNetCrossRefGoogle Scholar
  44. [44]
    Keir, J., Kessissoglou, N.J. and Norwood, C.J., Active control of connected plates using single and multiple actuators and error sensors. Journal of Sound and Vibration, 2005, 281: 73–97.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2013

Authors and Affiliations

  1. 1.College of Mechanical EngineeringBeijing University of TechnologyBeijingChina
  2. 2.School of AstronauticsHarbin Institute of TechnologyHarbinChina

Personalised recommendations