Combination Resonance Instability of Curved Panels with Cutout Subjected to Nonuniform Loading with Damping
Publication: Journal of Engineering Mechanics
Volume 134, Issue 7
Abstract
The dynamic instability of doubly curved panels with a centrally located circular cutout, subjected to nonuniform compressive in-plane harmonic edge loading is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to single (mode) resonances in parametrically excited doubly curved panels with a central circular cutout. The method of multiple scales is used to obtain analytical expressions for the single (mode) and combination resonance instability regions. It is shown that other cases of the combination resonance can be of major importance and yield a significantly enlarged instability region in comparison to the principal instability region. The effects of nonuniform edge loading, centrally located circular cutout, damping, the static, and dynamic load factors on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as single (mode) resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which doubly curved panels cannot become dynamically unstable. A central circular cutout has the destabilizing effect on the dynamic stability behavior of doubly curved panels subjected to nonuniform edge loading. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.
Get full access to this article
View all available purchase options and get full access to this article.
References
Argento, A. (1993). “Dynamic stability of a composite circular cylindrical shell subjected to combined axial and torsional loading.” J. Compos. Mater., 29, 2000–2005.
Bailey, R., and Wood, J. (1996). “Stability characteristics of composite panels with various cutout geometries.” Compos. Struct., 35, 21–31.
Bolotin, V. V. (1964). The dynamic stability of elastic systems, Holden-Day, San Francisco.
Bolotin, V. V., Grishko, A. A., and Panov, M. Y. (2002). “Effect of damping on the post-critical behavior of autonomous nonconservative systems.” Int. J. Non-Linear Mech., 37, 1163–1179.
Brogan, F., Forseberg, K., and Smith, S. (1969). “Dynamic behavior of cylinder with a cutout.” AIAA J., 7, 903–911.
Cederbaum, G. (1991). “Dynamic instability of shear-deformable laminated plates.” AIAA J., 29, 2000–2005.
Cederbaum, G. (1992). “Dynamic instability of anti-symmetric laminated plates.” J. Sound Vib., 154, 271–279.
Chakravorty, D., Sinha, P. K., and Bandyopadhyay, J. N. (1998). “Application of FEM on free and forced vibration of laminated shells.” J. Eng. Mech., 124(1), 1–8.
Choo, Y. S., and Kim, J. H. (2000). “Dynamic stability of rectangular plates subjected to pulsating follower forces.” AIAA J., 38, 353–361.
Deolasi, P. J., and Datta, P. K. (1995). “Effects of damping on the parametric instability behaviour of plates under localized edge loading (compression or tension).” Struct. Eng. Mech., 3, 229–244.
Deolasi, P. J., and Datta, P. K. (1997). “Simple and combination resonances of rectangular plates subjected to nonuniform edge loading with damping.” Eng. Struct., 19, 1011–1017.
Evan-Iwanowski, R. M. (1965). “On parametric response of structures.” Appl. Mech. Rev., 18, 699–702.
Hsu, C. S. (1963). “On the parametric excitation of dynamic system having multiple degrees of freedom.” J. Appl. Mech., 30, 367–372.
Hutt, J. M., and Salam, A. E. (1971). “Dynamic stability of plates by finite-elements.” J. Engrg. Mech. Div., 97(3), 879–899.
Iwatsubo, T., Sugiyama, Y., and Ogino, S. (1974). “Simple and combination resonances of columns under periodic axial loads.” J. Sound Vib., 33, 211–221.
Kar, R. C., and Sujata, T. (1991). “Dynamic stability of a tapered symmetric sandwich beam.” Comput. Struct., 40, 1441–1449.
Kim, J. H., and Choo, Y. S. (1998). “Dynamic stability of a free-free Timoshenko beam subjected to a pulsating follower force.” J. Sound Vib., 216, 623–636.
Kumar, A., and Shrivastava, R. P. (2005). “Free vibration of square laminates with delamination around central cutout using HSDT.” Compos. Struct., 70, 317–333.
Larsson, P. (1989). “On buckling of orthotropic compressed plates with circular hole.” Compos. Struct., 13, 103–121.
Lee, H. P., and Lim, S. P. (1992). “Free vibration of isotropic and orthotropic square plates with square cutouts subjected to in-plane forces.” Compos. Struct., 43, 431–437.
Lee, W. K., and Kim, C. H. (1995). “Combination resonances of a circular plate with three-mode interaction.” J. Appl. Mech., 62, 1015–1022.
Lee, Y. J., Lin, H. J., and Lin, C. C. (1989). “A study of buckling behavior of an orthotropic square plate with central circular hole.” Compos. Struct., 13, 173–188.
Liew, K. M., and Lim, C. W. (1994). “Vibration of perforated doubly curved shallow shells with rounded corners.” Int. J. Solids Struct., 31, 1519–1536.
Matsunaga, H. (1999). “Vibration and stability of thick simply supported shallow shells subjected to in-plane stresses.” J. Sound Vib., 225, 41–60.
Mond, M., and Cederbaum, G. (1992). “Analysis of parametrically excited laminated shells.” Int. J. Mech. Sci., 34, 241–250.
Moorthy, J., Reddy, J. N., and Plaut, R. H. (1990). “Parametric instability of laminated composite plates with transverse shear deformation.” Int. J. Solids Struct., 26, 801–811.
Mundkur, G., Bhat, R. B., and Neriya, S. (1994). “Vibration of plates with cutouts using boundary characteristics orthogonal polynomial functions in the Rayleigh-Ritz method.” J. Sound Vib., 176, 136–144.
Nayfeh, A. H. (1973). Perturbation methods, Wiley, New York.
Nayfeh, A. H., and Mook, D. T. (1979). Nonlinear oscillations, Wiley, New York.
Nemeth, M. P. (1988). “Buckling behavior of compression loaded symmetrically laminated angle-ply plates with holes.” AIAA J., 26, 1495–1522.
Ostiguy, G. L., Samson, L. P., and Nguyen, H. (1993). “On the occurrence of simultaneous resonances in parametrically-excited rectangular plates.” J. Vibr. Acoust., 115, 344–352.
Prabhakara, D. L., and Datta, P. K. (1997). “Vibration, buckling and parametric instability behavior of plates with centrally located cutouts subjected to in-plane edge loading (tension or compression).” Thin-Walled Struct., 27, 287–310.
Reddy, J. N. (1982). “Large amplitude flexural vibration of layered composite plates with cutout.” J. Sound Vib., 83, 1–10.
Saha, K. N., Kar, R. C., and Datta, P. K. (1997). “Dynamic stability of a rectangular plate on non-homogeneous Winkler foundation.” Comput. Struct., 63, 1213–1222.
Sahu, S. K., and Datta, P. K. (2002). “Dynamic stability of curved panels with cutouts.” J. Sound Vib., 251, 683–696.
Sahu, S. K., and Datta, P. K. (2003). “Dynamic stability of laminated composite curved panels with cutouts.” J. Eng. Mech., 129(11), 1245–1253.
Sivakumar, K., Iyengar, N. G. R., and Deb, K. (1999). “Free vibration of laminated composite plates with cutout.” J. Sound Vib., 221, 443–470.
Sivasubramonian, B., Kulkarni, A. M., and Rao, G. V. (1997). “Free vibration of curved panels with cutouts.” J. Sound Vib., 200, 227–234.
Srivatsa, K. S., and Krishnamurthy, A. V. (1992). “Stability of laminated composite plates with cutouts.” Comput. Struct., 43, 273–279.
Szemplinska-Stupnicka, W. (1978). “The generalized harmonic balance method for determining the combination resonance in the parametric dynamic systems.” J. Sound Vib., 58, 347–361.
Takahashi, K. (1981). “An approach to investigate the instability of the multiple degree of freedom parametric dynamic systems.” J. Sound Vib., 78, 519–529.
Takahashi, K., and Konishi, Y. (1988). “Dynamic stability of a rectangular plate subjected to distributed in-plane dynamic force.” J. Sound Vib., 123, 115–127.
Toda, S., and Komatsu, K. (1977). “Vibrations of circular cylindrical shells with cutouts.” J. Sound Vib., 52, 497–510.
Udar, R. S., and Datta, P. K. (2005). “Parametric combination resonance characteristics of doubly curved panels subjected to non-uniform harmonic edge loading.” Int. J. Struct. Stab. Dyn., 5, 615–639.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 7 • July 2008
Pages: 555 - 566
Copyright
© 2008 ASCE.
History
Received: Sep 8, 2006
Accepted: Aug 17, 2007
Published online: Jul 1, 2008
Published in print: Jul 2008
Notes
Note. Associate Editor: Khaled W. Shahwan
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.