Nabeel T. Alshabatat and Koorosh Naghshineh


  1. [1] R. Grandhi, Structural optimization with frequencyconstraints – A review, AIAA Journal, 31(1), 1993, 2296–2303.
  2. [2] M.P. Bendsøe and N. Olhoff, A method of design againstvibration resonance of beams and shafts, Optimal ControlApplications and Methods, 6, 1985, 191–200.
  3. [3] S.P. Timoshenko, D.H. Young, and W. Weaver, Vibrationproblems in engineering (New York: John Wiley, 1974).
  4. [4] L. Meirovitch, Analytical method in vibrations (London:MacMillan, 1967).
  5. [5] D. Szelag and Z. Mroz, Optimal design of vibrating beams withunspecified support reactions, Computer Methods in AppliedMechanics and Engineering, 19 (3), 1979, 333–349.
  6. [6] P.W. Wang and C.C. Cheng, Natural frequency tuning usingstructural patches, Journal of Vibration and Acoustics, 127(1),2005, 28–35.
  7. [7] D. Zhou and T. Ji, Dynamic characteristics of a beam anddistributed spring–mass system, International Journal of SolidsStructures, 43, 2006, 5555–5569.
  8. [8] M.C. Ece, M. Aydogdu, and V. Taskin, Vibration of a variablecross-section beam, Mechanics Research Communications, 34,2007, 78–84.
  9. [9] J.W. Jaworski and E.H. Dowell, Free vibration of a cantileverbeam with multiple steps: Comparison of several theoreticalmethods with experiment, Journal of Sound Vibration, 312,2008, 713–725.143D
  10. [10] B.L. Karihaloo and F.I. Niordson, Optimum design of vibratingcantilevers, Journal of Optimization Theory and Applications,11(6), 1973, 638–654.
  11. [11] V.K. Gupta and P.N. Murthy, Optimal design of uniform non-homogeneous vibrating beams, Journal of Sound Vibration,59(4), 1978, 521–531.
  12. [12] N. Olhoff and R. Parbery, Designing vibrating beams and ro-tating shafts for maximum difference between adjacent naturalfrequencies, International Journal of Solids Structures, 20(1),1984, 63–75.
  13. [13] D. Wang, M.I. Friswell, and Y. Lei, Maximizing the naturalfrequency of a beam with an intermediate elastic support,Journal of Sound Vibration, 291, 2006, 1229–1238.
  14. [14] W.N. Cheng, C.C. Cheng, and G.H. Koopmann, Dynamicbeam modification using dimples, Journal of Vibration andAcoustics, 130(4), 2008.
  15. [15] J.H. Holland, Adaptation in natural and artificial system, (AnnArbor: The University of Michigan Press, 1975).
  16. [16] M. Gen and R. Cheng, Genetic algorithms and engineeringoptimization (New York: Wiley-Interscience, 2000).

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