Summary
In the presented paper the nonlinear response of doubly curved layered panels subjected to time-varying lateral loads is studied. The considered panels are composed of three thick perfectly bonded isotropic layers, which are symmetrically arranged with respect to the middle surface. The structural model utilized to analyze the panels is based on a first-order layerwise theory, which includes transverse shear flexibility, initial geometric imperfections, and Berger-type geometric nonlinearities. The boundaries of panels with polygonal planform are modeled as simply (hard hinged) supported edges with the displacements normal to the edge face fully restrained.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Marguerre (1950) Knick- und Beulvorgänge K. Marguerre (Eds) Neuere Festigkeitsprobleme des Ingenieurs Springer Berlin 229–235
K. M. Liew C. W. Lim S. Kitipornchai (1997) ArticleTitleVibration of shallow shells: A review with bibliography AMR 50 431–444
M. S. Qatu (2002) ArticleTitleRecent research advances in the dynamic behavior of shells: 1989–2000, Part 1: Laminated composite shells AMR 55 325–349
Y. M. Fu C. Y. Chia (1989) ArticleTitleMulti-mode nonlinear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panels Int. J. Non-Linear Mech. 24 365–381
A. Bhimaraddi (1989) ArticleTitleNonlinear free vibration analysis of composite plates with initial imperfections and in-plane loading Int. J. Solids Struct. 25 33–43 Occurrence Handle0671.73050
R. K. Kapania C. Byun (1992) ArticleTitleVibrations of imperfect laminated panels under complex preloads Int. J. Non-Linear Mech. 27 51–62
R. Heuer F. Ziegler (1998) ArticleTitleNonlinear resonance phenomena of panel-type structures Comput. Struct. 67 65–70 Occurrence Handle10.1016/S0045-7949(97)00157-0
L. Librescu M. P. Nemeth J. H. Starnes SuffixJr W. Lin (2000) ArticleTitleNonlinear response of flat and curved panels subjected to thermomechanical loads J. Thermal Stresses 23 549–582
C. Adam (2003) ArticleTitleModerately large flexural vibrations of composite plates with thick layers Int. J. Solids Struct. 40 4153–4166 Occurrence Handle1041.74512 Occurrence Handle2004g:68081
H. M. Berger (1955) ArticleTitleA new approach to the analysis of large deflection of plates J. Appl. Mech. 22 465–472 Occurrence Handle0066.42006 Occurrence Handle17,429e
Y.-Y. Yu (1995) Vibrations of elastic plates Springer New York
F. Ziegler (1998) Mechanics of solids and fluids EditionNumber2 Springer New York
M.-J. Yan E. H. Dowell (1972) ArticleTitleGoverning equations for vibrating constrained-layer damping sandwich plates and beams J. Appl. Mech. 39 1041–1046
R. Heuer (1992) ArticleTitleStatic and dynamic analysis of transversely isotropic, moderately thick sandwich beams by analogy Acta Mech. 91 1–9 Occurrence Handle10.1007/BF01194029 Occurrence Handle0850.73176 Occurrence Handle1492778
C. Adam (2001) ArticleTitleDynamic analysis of isotropic composite plates using a layerwise theory Compos. Struct. 51 427–437 Occurrence Handle10.1016/S0263-8223(00)00158-6
T. Wah (1963) ArticleTitleLarge amplitude flexural vibration of rectangular plates Int. J. Mech. Sci. 5 425–438 Occurrence Handle10.1016/0020-7403(63)90026-2
H. Irschik (1986) ArticleTitleLarge thermoelastic deflections and stability of simply supported polygonal panels Acta Mech. 59 31–46 Occurrence Handle10.1007/BF01177058 Occurrence Handle0581.73053
C.-I. Wu J. R. Vinson (1969) ArticleTitleInfluences of large amplitudes, transverse shear deformation, and rotatory inertia on lateral vibrations of transversely isotropic plates J. Appl. Mech. 36 254–260
Hochrainer, M., Pichler, U., Irschik, H.: Membrananalogie für Eigenfrequenzen flacher Schalen (in German). ZAMM 79(S2), S409–S410 (1999).
H. Irschik (1985) ArticleTitleMembrane type eigenmotions of Mindlin plates Acta Mech. 55 1–20 Occurrence Handle10.1007/BF01267975 Occurrence Handle0554.73058 Occurrence Handle1492778
R. Heuer F. Ziegler (2004) ArticleTitleThermoelastic stability of layered shallow shells Int. J. Solids. Struct. 41 2111–2120
W. J. Cunningham (1958) Introduction to nonlinear analysis McGraw-Hill New York
M. Sathyamoorthy (1998) Nonlinear analysis of structures CRC Press Boca Raton
Magrab, E. B.: Vibrations of elastic structural members. Alphen aan den Rijn: Sijthoff and Noordhoff 1979.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Adam, C. Nonlinear flexural vibrations of layered panels with initial imperfections. Acta Mechanica 181, 91–104 (2006). https://doi.org/10.1007/s00707-005-0269-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-005-0269-4