0
TECHNICAL PAPERS

One-to-One Internal Resonance of Symmetric Crossply Laminated Shallow Shells

[+] Author and Article Information
A. Abe

Department of Mechanical Engineering, Fukui University, Fukui 910-8507, Japan

Y. Kobayashi, G. Yamada

Division of Mechanical Science, Hokkaido University, Sapporo 060-8628, Japan

J. Appl. Mech 68(4), 640-649 (Aug 22, 2000) (10 pages) doi:10.1115/1.1356416 History: Received December 22, 1999; Revised August 22, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chia, C. Y., 1980, Nonlinear Analysis of Plates, McGraw-Hill, New York.
Chia,  C. Y., 1988, “Geometrically Nonlinear Behavior of Composite Plates: A Review,” ASME Appl. Mech. Rev., 41, pp. 439–451.
Sathyamoorthy,  M., 1987, “Nonlinear Vibration Analysis of Plates: A Review and Survey of Current Developments,” ASME Appl. Mech. Rev., 40, pp. 1553–1561.
Fu,  Y. M., and Chia,  C. Y., 1989, “Multi-Mode Non-Linear Vibration and Post-buckling of Anti-Symmetric Imperfect Angle-Ply Cylindrical Thick Panels,” Int. J. Non-Linear Mech., 24, pp. 365–381.
Fu,  Y. M., and Chia,  C. Y., 1993, “Non-Linear Vibration and Postbuckling of Generally Laminated Circular Cylindrical Thick Shells With Non-Uniform Boundary Conditions,” Int. J. Non-Linear Mech., 28, pp. 313–327.
Raouf,  R. A., and Palazotto,  A. N., 1994, “On the Non-Linear Free Vibrations of Curved Orthotropic Panels,” Int. J. Non-Linear Mech., 29, pp. 507–514.
Xu,  C. S., Xia,  Z. Q., and Chia,  C. Y., 1996, “Non-Linear Theory and Vibration Analysis of Laminated Truncated, Thick, Conical Shells,” Int. J. Non-Linear Mech., 31, pp. 139–154.
Cheung,  Y. K., and Fu,  Y. M., 1995, “Nonlinear Static and Dynamic Analysis for Laminated, Annular, Spherical Caps of Moderate Thickness,” Nonlinear Dyn., 8, pp. 251–268.
Hadian,  J., Nayfeh,  A. H., and Nayfeh,  J. F., 1995, “Modal Interaction in the Response of Antisymmetric Cross-ply Laminated Rectangular Plates,” J. Vib. Control, 1, pp. 159–182.
Abe,  A., Kobayashi,  Y., and Yamada,  G., 1998, “Two-Mode Response of Simply Supported, Rectangular Laminated Plates,” Int. J. Non-Linear Mech., 33, pp. 675–690.
Abe,  A., Kobayashi,  Y., and Yamada,  G., 1998, “Internal Resonance of Rectangular Laminated Plates With Degenerate Modes,” JSME Int. J., Ser. C, 41, pp. 718–726.
Abe,  A., Kobayashi,  Y., and Yamada,  G., 1998, “Three-Mode Response of Simply Supported, Rectangular Laminated Plates,” JSME Int. J., Ser. C, 41, pp. 51–59.
Yasuda,  K., and Kushida,  G., 1984, “Nonlinear Forced Oscillations of a Shallow Spherical Shell,” Bull. JSME, 27, pp. 2233–2240.
Nayfeh,  A. H., and Raouf,  R. A., 1987, “Nonlinear Forced Response of Infinitely Long Circular Cylindrical Shells,” ASME J. Appl. Mech., 54, pp. 571–577.
Nayfeh,  A. H., Raouf,  R. A., and Nayfeh,  J. F., 1991, “Nonlinear Response of Infinitely Long Circular Cylindrical Shells to Subharmonic Radial Loads,” ASME J. Appl. Mech., 58, pp. 1033–1041.
Chin,  C., and Nayfeh,  A. H., 1996, “Bifurcation and Chaos in Externally Excited Circular Cylindrical Shells,” ASME J. Appl. Mech., 63, pp. 565–574.
Chia,  C. Y., 1987, “Nonlinear Vibration and Postbuckling of Unsymmetrically Laminated Imperfect Shallow Cylindrical Panels with Mixed Boundary Conditions Resting on Elastic Foundation,” Int. J. Eng. Sci., 25, pp. 427–441.
Yamaguchi,  T., and Nagai,  K., 1997, “Chaotic Vibrations of Cylindrical Shell-Panel With an In-Plane Elastic-Support at Boundary,” Nonlinear Dyn., 13, pp. 259–277.
Eslami,  H., and Kandil,  O. H., 1989, “Nonlinear Forced Vibration of Orthotropic Rectangular Plates using Method of Multiple Scales,” AIAA J., 27, pp. 961–967.
Sassi,  S., Thomas,  M., and Laville,  F., 1996, “Dynamic Response Obtained by Direct Numerical Integration for Pre-Deformed Rectangular Plates Subjected to In-Plane Loading,” J. Sound Vib., 191, pp. 67–83.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, John Wiley and Sons, New York.
Tamura,  H., and Matsuzaki,  K., 1996, “Numerical Scheme and Program for the Solution and Stability Analysis of a Steady Periodic Vibration Problem,” JSME Int. J., Ser. C, 39, pp. 456–463.
Vinson, J. R., and Seerakowski, R. L., 1986, The Behavior of Structures Composed of Composite Materials, Martinus Nijhoff Publishers, Dordrecht.
Kobayashi,  Y., and Leissa,  A. W., 1995, “Large Amplitude Free Vibration of Thick Shallow Shells Supported by Shear Diaphragms,” Int. J. Non-Linear Mech., 30, pp. 57–66.
Wolf,  A., Swift,  J. B., Swinney,  H. L., and Vastano,  J. A., 1985, “Determining Lyapunov Exponents From a Time Series,” Physica D, 16, pp. 285–317.

Figures

Grahic Jump Location
Geometry of a laminated shallow shell and coordinate systems
Grahic Jump Location
Frequency-response curves for the shell with a/b=1,Rx/a=Ry/a=10 and h/a=0.01,(ω1=20.68,ω2=28.59,ω3=48.77,ω4=43.95 and F/ω22=0.015). (a) (1,1) mode, (b) (2,1) mode and (c) (3,1) mode.
Grahic Jump Location
Time histories at Ω/ω2=1.3 (upper branch) in Fig. 2. (a) (2,1) mode, (b) (1,1) and (3,1) modes, and (c) the amplitude of the shell at (x,y)=(a/4, b/2).
Grahic Jump Location
Frequency-response curves for the shell with a/b=0.704,Rx/a=Ry/a=10 and h/a=0.01 obtained by the two-mode analysis, (ω1=18.79,ω2=28.15,ω3=28.68, and F/ω22=0.01). (a) (2,1) mode and (b) (1,2) mode.
Grahic Jump Location
Frequency-response curves for the same shell as in Fig. 4 obtained by the three-mode analysis. (a) (1,1) mode, (b) (2,1) mode, and (c) (1,2) mode.
Grahic Jump Location
Lyapunov exponents in the region where stable periodic responses do not exist
Grahic Jump Location
Poincaré sections. (a) Ω/ω2=1.01200, (b) Ω/ω2=1.01250, (c) Ω/ω2=1.01263, and (d) Ω/ω2=1.01451.
Grahic Jump Location
Frequency-response curves for the shell with a/b=0.581,Rx/a=Ry/a=50, and h/a=0.01 obtained by the three-mode analysis, (ω1=7.075,ω2=16.69,ω3=16.90, and F/ω22=0.01). (a) (1,1) mode, (b) (2,1) mode, and (c) (1,2) mode.
Grahic Jump Location
Effect of damping ratio on frequency-response curves for the same shell as in Fig. 4 obtained by the three-mode analysis, (F/ω22=0.01, ○: Hopf bifurcation point, ▵: saddle-node bifurcation point and □: pitchfork bifurcation point). (a) (1,1) mode, (b) (2,1) mode, and (c) (1,2) mode.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In