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Derivation of linear beam equations using nonlinear continuum mechanics

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Abstract

Familiar linear elastic and viscoelastic beam equations (Euler-Bernoulli, Rayleigh, Kelvin-Voigt, Timoshenko, and Shear Diffusion) and boundary conditions are derived from a nonlinear theory of large motions rather than the usual variational techniques. Also included is a fairly detailed derivation of the nonlinear theory and a careful discussion of the hypotheses.

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References

  1. S. S. Antman, Theory of Rods,Handbuch der Physik, Vol. VIa, Springer-Verlag, Berlin 1972.

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  3. D. L. Russell,Spectral and asymptotic properties of linear elastic systems with internal energy dissipation (1988) to appear in the Proceedings of a Conference on Boundary Control & Stability, Clarmont-Ferrand, June 1988.

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Authors and Affiliations

  1. Dept of Mathematics and ICAM, Virginia Polytechnic Institute and State University, 24061-0123, Blacksburg, Virginia, USA

    Robert C. Rogers

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  1. Robert C. Rogers
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Additional information

This work has been partially supported by the Office of Naval Research under grant number N00014-88-K0417 and by the National Science Foundation under grant number DMS-8801412.

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Rogers, R.C. Derivation of linear beam equations using nonlinear continuum mechanics. Z. angew. Math. Phys. 44, 732–754 (1993). https://doi.org/10.1007/BF00948486

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  • DOI: https://doi.org/10.1007/BF00948486

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