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Minimum-mass design of sandwich structures with frequency and section constraints

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Abstract

An optimal design procedure for sandwich structures subject to frequency and section constraints is developed from direct comparison theorems for different designs. These theorems are derived from the Rayleigh quotient for the structure. Applications to the axial motion of a bar and to the vibration of a portal frame are given.

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References

  1. Prager, W.,Optimality Criteria in Structural Design, AGARD Report No. 589-71, 1971.

  2. Prager, W., andTaylor, J. E.,Problems of Optimal Structural Design, Journal of Applied Mechanics, Vol. 35, No. 1, 1968.

  3. Turner, M. J.,Design of Minimum-Mass Structures with Specified Natural Frequencies, AIAA Journal, Vol. 5, No. 3, 1967.

  4. Taylor, J. E.,Minimum Mass Bar for Axial Vibration at Specified Natural Frequency, AIAA Journal, Vol. 5, No. 10, 1967.

  5. Taylor, J. E.,Optimum Design of a Vibrating Bar with Specified Minimum Cross Section, AIAA Journal, Vol. 6, No. 7, 1968.

  6. Sippel, D. L., andWarner, W. H.,Minimum-Mass Design of Multielement Structures under a Frequency Constraint, AIAA Journal, Vol. 11, No. 4, 1973.

  7. Brach, R. M.,On the Extremal Fundamental Frequencies of Vibrating Beams, International Journal of Solids and Structures, Vol. 4, No. 7, 1968.

  8. McCart, B. R., Haug, E. J., andStreeter, T. D.,Optimal Design of Structures with Constraints on Natural Frequency, AIAA Journal, Vol. 8, No. 6, 1970.

  9. Cardou, A.,Minimum Mass Structural Design with a Frequency Requirement, University of Minnesota, Ph.D. Thesis, 1972.

  10. Niordson, F. I.,On the Optimum Design of a Vibrating Beam, Quarterly of Applied Mathematics, Vol. 23, No. 1, 1965.

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Authors and Affiliations

  1. Départment de Génie Mécanique, Université Laval, Québec, Canada

    A. Cardou (Assistant Professor)

  2. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota

    W. H. Warner (Professor)

Authors
  1. A. Cardou
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  2. W. H. Warner
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Additional information

Communicated by W. Prager

This paper is based in part upon a thesis submitted by the first author to the University of Minnesota in partial fulfillment of the requirements for the Ph.D. degree.

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Cardou, A., Warner, W.H. Minimum-mass design of sandwich structures with frequency and section constraints. J Optim Theory Appl 14, 633–647 (1974). https://doi.org/10.1007/BF00932965

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  • DOI: https://doi.org/10.1007/BF00932965

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