Abstract
In this article we summarize the second of a series of applications of the methods of intermediate problems to the determination of lower bounds for the eigenfrequencies of free vibration of built-up elastic structures. This study gives upper and lower bounds for frequencies of a rectangular thin elastic plate with a reinforcing rib bonded elastically to it along a portion of the center line.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bazley, N. W. and D. W. Fox: Lower bounds to eigenvalues using operator decompositions of the form B*B. Arch. Rat. Mech. and Anal. 10 (1962), 352–360.
Bazley, N. W. and D. W. Fox: Methods for lower bounds to frequencies of continuous elastic systems. J. Appl. Math. and Phys. (ZAMP) 17 (1966), 1–37.
Bazley, N. W., D. W. Fox and J. T. Stadter: Upper and lower bounds for the frequencies of rectangular clamped plates. Zeit. Ang. Math, und Mech. 47 (1967), 191–198.
Bazley, N. W., D. W. Fox and J. T. Stadter: Upper and lower bounds for the frequencies of rectangular cantilever plates. Zeit. Ang. Math. und Mech. 147 (1967), 251–260.
Bazley, N. W., D. W. Fox and J. T. Stadter: Upper and lower bounds for the frequencies of rectangular free plates. J. Appl. Math. and Phys. (ZAMP) 18 (1967), 445–460.
Fox, D. W.: Lower bounds for eigenvalues of thin skew plates. Developments in Mechanics: Proc. Sixteenth Midwest. Mech. Conf. 10 (1979), 127–130.
Fox, D. W. and V. G. Sigillito: Bounds for eigenfrequencies of a plate with an elastically attached reinforcing rib. To be submitted.
Weinstein, A. and W. Stenger: Methods of Intermediate Problems for Eigenvalues. Academic Press, New York, 1972.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer Basel AG
About this chapter
Cite this chapter
Fox, D.W., Sigillito, V.G. (1981). Bounds for Eigenvalues of Reinforced Plates. In: Albrecht, J., Collatz, L. (eds) Numerische Behandlung von Differentialgleichungen Band 3. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 56. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5454-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-0348-5454-2_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5455-9
Online ISBN: 978-3-0348-5454-2
eBook Packages: Springer Book Archive