Designing plates for minimum internal resonances

Structural and Multidisciplinary Optimization

Volumn 30, Issue 4, 2005, Pages 297-307

  Pedersen, N L ^a  

^a AALBORG UNIVERSITY   (Denmark)

Author keywords

Eigenfrequencies; Internal resonance; Plates; Topology optimization; Two materials

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; OPTIMIZATION; PLATES (STRUCTURAL COMPONENTS); PROBLEM SOLVING; STRUCTURAL DESIGN; TOPOLOGY;

EIGENFREQUENCIES; INTERNAL RESONANCES; PLATES; TOPOLOGY OPTIMIZATION; TWO-MATERIALS;

RESONANCE;

EID: 24944543257     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-005-0529-x     Document Type: Article

References (18)

1. Anlas G, Elbeyli O (2002) Nonlinear vibrations of a simply supported rectangular metallic plate subjected to transverse harmonic excitation in the presence of a one-to-one internal resonance. Nonlinear Dyn 30(1): 1-28
2. Bathe KJ (1996) Finite element procedures, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ
3. Bendsøe MP, Sigmund O (2003) Topology optimization, theory, methods and applications. Springer, Berlin Heidelberg New York
4. Chang SI, Lee JM, Bajaj AK, Krousgrill C (1997) Subharmonic responses in harmonically excited rectangular plates with one-to-one internal resonance. Chaos Solitons Fractals 8(4):479-498
5. Hashin Z, Shtrikman S (1963) A variational approach to the theory of elastic behavior of multiphase materials. J Mech Phys Solids 11:127-140
6. Jensen JS, Pedersen NL (2005) On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases. J Sound Vib (in press)
7. Nayfeh AH (2000) Nonlinear interactions: analytical, computational, and experimental methods. Wiley, New York
8. Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York
9. Nayfeh AH, Nayfeh SA, Andersen TA, Balachandran B (1994) Transfer of energy from high-frequency to low-frequency modes. In: Thompson JMT, Bishop SR (eds) Nonlinearity and chaos in engineering dynamics. Wiley, New York
10. Olhoff N (1977) Maximizing higher order eigenfrequencies of beams with constraints on the design geometry. J Struct Mech 5(2): 107-134
11. Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidisc Optim 20(1):2-11
12. Pedersen NL, Nielsen AK (2003) Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses and buckling. Struct Multidisc Optim 25(5-6):436-445
13. Ribeiro P, Petyt M (2000) Non-linear free vibration of isotropic plates with internal resonance. Int J Nonlinear Mech 35(2):263-278
14. Seyranian AP, Lund E, Olhoff N (1994) Multiple eigenvalues in structural optimization problems. Struct Optim 8(4):207-227
15. Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68-75
16. Svanberg K (1987) The method of moving asymptotes: a new method for structural optimization. Int J Numer Methods Eng 24:359-373
17. Thomsen JJ (2003) Vibrations and stability. Springer, Berlin Heidelberg New York
18. Wittrick WH (1962) Rates of change of eigenvalues, with reference to buckling and vibration problems. J R Aeronaut Soc 66:590-591