Large amplitude vibration of heated corrugated circular plates with shallow sinusoidal corrugations

Applied Mathematical Modelling

Volumn 33, Issue 9, 2009, Pages 3523-3532

  Wang, Yong Gang ^a   Shi, Jing Ling ^a   Wang, Xin Zhi ^b  

^a CHINA AGRICULTURAL UNIVERSITY   (China)

^b LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Corrugated circular plate; Large amplitude vibration; Shooting method; Temperature change

Indexed keywords

CORRUGATED CIRCULAR PLATE; CORRUGATED PLATES; GOVERNING EQUATIONS; HAMILTON'S PRINCIPLES; KANTOROVICH METHODS; LARGE AMPLITUDE VIBRATION; NON LINEARITIES; NON-LINEAR FREE VIBRATIONS; NON-LINEAR VIBRATIONS; NONLINEAR BENDING; NONLINEAR FREQUENCIES; PARAMETRIC STUDIES; SHALLOW SHELLS; SHOOTING METHOD; SPATIAL VARIABLES; STATIC AMBIENT; TEMPERATURE CHANGE; TEMPERATURE DEPENDENTS; TIME VARIABLES; TWO-POINT BOUNDARY VALUE PROBLEMS;

CONTROL NONLINEARITIES; ORDINARY DIFFERENTIAL EQUATIONS; RELIABILITY ANALYSIS; THERMAL EFFECTS;

NONLINEAR EQUATIONS;

EID: 67349275657     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2008.11.016     Document Type: Article

References (52)

1. Haterboucha M., and Benamarb R. The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part I: iterative and explicit analytical solution for non-linear transverse vibrations. J. Sound Vib. 265 (2003) 123-154
2. Haterboucha M., and Benamarb R. The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part II: iterative and explicit analytical solution for non-linear coupled transverse and in-plane vibrations. J. Sound Vib. 277 (2004) 1-30
3. Huang C.L.D., and Huang S.T. Finite element analysis of non-linear vibration of a circular plate with a concentric rigid mass. J. Sound Vib. 131 (1989) 215-227
4. Huang C.L., and Aurora P.R. Non-linear oscillations of elastic orthotropic annular plates of variable thickness. J. Sound Vib. 62 (1979) 443-453
5. Dumir P.C., Kumarand C.R., and Gandhi M.L. Non-linear axisymmetric vibration of orthotropic thin circular plates on elastic foundations. J. Sound Vib. 103 (1985) 273-285
6. Dumir P.C., Nathand Y., and Gandhi M.L. Non-linear axisymmetric transient analysis of orthotropic thin annular plates with a rigid central mass. J. Sound Vib. 97 (1984) 387-397
7. Huang S. Non-linear vibration of a hinged orthotropic circular plate with a concentric rigid mass. J. Sound Vib. 214 (1988) 873-883
8. Rao S., Sheikh A., and Mukhopadhyay M. Large amplitude finite element flexural vibration of plates/stiffened plates. J. Acoust. Soc. Am. 93 6 (1993) 3250-3257
9. Dumir P.C. Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps. Acta Mech. 60 2 (1986) 121-132
10. Paliwal D.N., Kanagasabapathy H., and Gupta K.M. Vibrations of an orthotropic shallow spherical shell on a Kerr foundation. Int. J. Pres. Ves. Pip. 64 (1995) 17-24
11. Ribeiro P., and Petyt M. Nonlinear vibration of plates by the hierarchical finite element and continuation methods. Int. J. Mech. Sci. 41 (1999) 437-459
12. Ribeiro P., and Petyt M. Nonlinear free vibration of isotropic plates with internal resonance. Int. J. Nonlinear Mech. 35 (2000) 263-278
13. Ribeiro P., and Petyt M. Geometrical non-linear, steady-state, forced, periodic vibration of plates. Part I: Model and convergence studies. J. Sound Vib. 226 (1999) 955-983
14. Ribeiro P., and Petyt M. Geometrical non-linear, steady-state, forced, periodic vibration of plates. Part II: Stability study and analysis of multi-modal, multi-frequency response. J. Sound Vib. 226 (1999) 985-1010
15. Huang C.L.D., and Walker H.S. Non-linear vibration of hinged circular plate with a concentric rigid mass. J. Sound Vib. 126 (1988) 9-17
16. Li S.R., and Zhou Y.H. Shooting method for non-linear vibration and buckling of heated orthotropic plates. J. Sound Vib. 248 (2001) 379-386
17. Li S.R., and Zhou Y.H. Nonlinear vibration of heated orthotropic annular plates with immovably hinged edges. J. Therm. Stresses 26 (2003) 691-700
18. Li S.R., and Zhou Y.H. Nonlinear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass. J. Sound Vib. 251 (2002) 141-152
19. Allahverdizadeh A., Naei M.H., and Bahrami M.N. Nonlinear free and forced vibration analysis of thin circular functionally graded plates. J. Sound Vib. 310 (2008) 966-984
20. Chia C.Y. Nonlinear Analysis of Plates (1980), McGraw-Hill, New York
21. Sathyamoorthy M. Nonlinear vibration analysis of plates: a review and survey of current developments. Appl. Mech. Rev. 40 (1987) 1553-1561
22. Liew K.M., Lim C.W., and Kitipornchai S. Vibration of shallow shells: a review with bibliography. Appl. Mech. Rev. 50 (1997) 431-444
23. Panov D.Y. On large deflection of circular membrane with weak corrugations. Prikl. Mat. I Mekh. 5 2 (1941) 303-318 (in Russian)
24. Axelrad E.L. Large deflection of corrugated membrane as a non-shallow shell. Bull. Acad. Sci. USSR, Mekhanika Mashinostroenie 1 (1964) 46-53 (in Russian)
25. Hamada M., Seguchi Y., and Ito S. Numerical method for nonlinear axisymmetric bending of arbitrary shells of revolution and large deflection analyses of corrugated diaphragm and bellows. Bull. JSME 11 43 (1968) 24-33
26. Bihari I., and Elbert A. Deformation of circular corrugated plates and shells. Period. Polytech. Mech. Eng. 22 2 (1978) 123-143
27. Chen S.L. Elastic behavior of uniformly loaded circular corrugated plate with sine-shaped shallow waves in large deflection. Appl. Math. Mech. 1 2 (1980) 279-291
28. Liu R.H., and Yuan H. Nonlinear bending of corrugated annular plate with large boundary corrugation. Appl. Math. Mech. 2 3 (1997) 353-367
29. Liu R.H., and Yuan H. Nonlinear bending of corrugated diaphragm with large boundary corrugation under compound load. Appl. Math. Mech. 24 4 (2003) 414-420
30. Haringx J.A. Nonlinearity of corrugated diaphragms. Appl. Sci. Res. Ser. A 16 (1956) 45-52
31. Liu R.H., and Li D. On the nonlinear bending and vibration of corrugated circular plates. Int. J. Non-Linear Mech. 24 3 (1989) 165-176
32. Li D., and Liu R.H. Application of the modified iteration method to nonlinear vibration of corrugated circular plates. Appl. Math. Mech. 11 1 (1990) 13-22
33. Wang X.Z., Wang L.X., and Hu X.F. Nonlinear vibration of circular corrugated plates. Appl. Math. Mech. 8 3 (1987) 241-250
34. Zheng X.J. Exact solution of large deflection problem for corrugated circular plate under a central concentrated load. J. Lanzhou Univ. 30 3 (1994) 31-35 (in Chinese)
35. Liew K.M., Peng L.X., and Kitipornchai S. Nonlinear analysis of corrugated plates using a FSDT and a meshfree method. Comput. Meth. Appl. Mech. Eng. 196 (2007) 2358-2376
36. Peng L.X., Liew K.M., and Kitipornchai S. Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method. Int. J. Mech. Sci. 49 (2007) 364-378
37. Wang Y.G., Gao D., and Wang X.Z. On the nonlinear vibration of heated corrugated circular plates with shallow sinusoidal corrugations. Int. J. Mech. Sci. 50 (2008) 1082-1089
38. Wang Y.G., and Dai S.L. Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells. Appl. Math. Mech. 24 4 (2004) 430-439
39. Haterboucha M., and Benamarb R. Geometrically nonlinear free vibrations of simply supported isotropic thin circular plates. J. Sound Vib. 280 (2005) 903-924
40. Timoshenko S., and Woinowsky-Krieger S. Theory of Plates and Shells (1959), McGraw-Hill, New York
41. Wang Y.G., Dai S.L., and Wang X.Z. Nonlinear vibration of bimetallic circular thin plates under stationary thermal loads. In: Chien W.Z. (Ed). Proceedings of the Fourth International Congress on Nonlinear Mechanics (2002), Shanghai University Press, Shanghai 499-503
42. William H.P., Brain P.F., Sau A.T., et al. Numerical Recipes - The Art of Scientific Computing (1986), Cambridge University Press, New York
43. Wang Y.G., and Dai S.L. Nonlinear vibration of heated bimetallic thin circular plates. J. Tsinghua Univ. 43 2 (2003) 218-221 (in Chinese)
44. Gupta U.S., and Ansari A.H. Effect of elastic foundation on asymmetric vibration of polar orthotropic linearly tapered circular plates. J. Sound Vib. 254 3 (2002) 411-426
45. Rao J.S. Dynamics of Plates (1999), Narosa Publishing House, New Delhi
46. Stoykov S., and Ribeiro P. Periodic geometrically nonlinear free vibrations of circular plates. J. Sound Vib. 315 (2008) 536-555
47. Yamaki N. Influence of large amplitudes on flexural vibrations of elastic plates. Z. Angew. Math. Mech. 41 (1961) 501-510
48. Nowinski J.L. Non-linear transverse vibrations of circular elastic plates built-in at the boundary. In: Rosenberg R.M., et al. (Ed). Proceedings of the Fourth US National Congress on Applied Mechanics vol. 1 (1962), ASME, California 325-334
49. Kung G.C., and Pao Y.H. Non-linear flexural vibrations of a clamped circular plate. ASME J. Appl. Mech. 39 (1972) 1050-1054
50. Huang C.L.D., and Al-Khattat I.M. Finite amplitude vibrations of a circular plate. Int. J. Nonlinear Mech. 12 (1977) 297-306
51. Sathyamoorthy M. Transverse shear and rotatory inertia effects on non-linear vibrations of orthotropic circular plates. Comput. Struct. 14 (1981) 129-134
52. Wang Y.G., Song H.F., and Xu Z.S. Homotopy perturbation method for nonlinear vibrations of bimetallic shallow shells of revolution. J. Tsinghua Univ. 47 8 (2007) 1389-1392 (in Chinese)