Abstract
In the previous chapter the principles of the finite element displacement method as applied to vibration problems were presented. This discussion is now extended to an examination of the factors which influence the choice of a displacement function for an element, with the particular cases of in-plane and transverse vibration of plates being considered. Different displacement functions are used to derive a number of elements, and the results which these different elements give when applied to sample problems compared. Finally, it is shown how in-plane plate elements, transverse plate elements and beam elements can be combined together to analyse a composite beam and plate structure.
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References
Love, A.E.H., The Mathematical Theory of Elasticity, 4th Edition, Dover Publications, New York, 1944.
Dawe, D.J., A finite element approach to plate vibration problems, Journal of Mechanical Engineering Science, Vol. 7, No.1, 28–32, 1965.
Bogner, F.K., R.L. Fox and L.A. Schmit, The generation of inter-element compatible stiffness and mass matrices by the use of interpolation formulae, Proceedings of the Conference on Matrix Methods in Structural Mechanics, AFFDL-TR-66–80, 397–444, Wright-Paterson Air Force Base, Ohio, 1965.
Henshell, R.D., D. Walters and G.B. Warburton, A new family of curvilinear plate bending elements for vibration and stability, Journal of Sound & Vibration, 1972, Vol.20, 381–397.
Deak, A.L. and T.H.H. Pian, Application of the smooth surface interpolation to the finite element analysis, AIAA Journal, Vol.5, No.1, 187–189, 1967.
Timoshenko, S.P. Vibration Problems in Engineering, 3rd Edition, Van Nostrand, Princeton, 1955.
Warburton, G.B. The vibration of rectangular plates, Proceedings of the Institution of Mechanical Engineers, Vol.168, 371–384, 1954.
Thomas, D.L., J.M. Wilson and R.R. Wilson, Timoshenko beam finite elements, Journal of Sound and Vibration, Vol.31, No.3, 315–330, 1973.
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© 1985 Springer-Verlag Berlin, Heidelberg
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Wilson, R.R. (1985). Two Dimensional and Plate Bending Applications. In: Vibrations of Engineering Structures. Lecture Notes in Engineering, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82390-9_8
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DOI: https://doi.org/10.1007/978-3-642-82390-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13959-1
Online ISBN: 978-3-642-82390-9
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