Skip to main content
SpringerLink
Log in

Dynamic Substructures

  • Chapter
Dynamic Stiffness and Substructures

Abstract

Regardless of their simplicity, all structures have an infinite number of degrees of freedom (d.o.f.) when subjected to dynamic loading. One of the main objectives in selecting a mathematical model is to reduce the infinite d.o.f. system to a model with a limited number of d.o.f. which capture the significant physical behaviour of the system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. RED Bishop, DC Johnson 1960. The mechanics of vibration. Cambridge University Press

    MATH  Google Scholar 

  2. WT Thomson 1972. Theory of vibration with applications. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  3. GB Warburtion 1976. The dynamical behaviour of structure, 2nd edn. Pergamon, Oxford

    Google Scholar 

  4. YT Leung 1978. An accurate method of dynamic condensation in structural vibration analysis. Int J Num Meth Engng 12, 1705

    Article  MATH  Google Scholar 

  5. R Guyan 1975. Reduction of stiffness and mass matrices. AIAA J 3, 380

    Google Scholar 

  6. BM Irons 1965. Structural eigenvalue problem: elimination of unwanted variables. AIAA J 3, 961 - 962

    Google Scholar 

  7. T Bamford et al 1971. Dynamic analysis of large structural system. In: Proc ASME synthesis of vibrating systems, Washington, DC

    Google Scholar 

  8. RD Henshell, JH Ong 1975. Automatic masters for eigenvalue economization. Earthquake Engng Struct Dyn 3, 375–383

    Article  Google Scholar 

  9. AYT Leung 1979. An accurate method of dynamic substructuring with simplified computation. Int J Num Meth Engng 14, 1241–1256

    Article  MATH  Google Scholar 

  10. M Paz 1984. Dynamic condensation. Am Inst Aeronaut J 22, 724–726

    Google Scholar 

  11. A Simpson 1980. The Kron methodology and practical algorithm for eigenvalue, sensitivity and response analysis of large scale structural systems. Aeronaut J 84, 417–433

    Google Scholar 

  12. WC Hurty 1969. Dynamic analysis by dynamic partitioning, AIAA J 7, 1152–1154

    Article  Google Scholar 

  13. RR Craig, MCC Bampton 1968. Coupling of structures for dynamic analysis. AIAA J 6, 1313–1319

    Article  MATH  Google Scholar 

  14. DN Herting et al 1977. Development of an automated mullet-stage modal synthesis system for NASTRAN. In: 6th NASTRAN user’s colloquium, NASA CP 2018

    Google Scholar 

  15. RL Goldman 1969. Vibration analysis by dynamic partitioning. AIAA J 7, 1152–1154

    Article  MATH  Google Scholar 

  16. SN Hou 1969. Review of modal synthesis techniques and a new approach. Shock Vib Bull 40(4), 25–39

    Google Scholar 

  17. WA Benfield, RF Hruda 1971. Vibration analysis of structures by component mode substitution. AIAA J 9, 1255–1261

    Article  MATH  Google Scholar 

  18. TL Wilson 1977. A NASTRAN DMAP alter for the coupling of modal and physical coordinates substructures. In: 6th NASTRAN user’s colloquium, NASA CP 2018

    Google Scholar 

  19. EL Wilson, EP Bayo 1986. Use of 4 special Ritz vectors in dynamic substructure analysis. Am Soc Civ Engrs J Struct Engng 112, 1944–1954

    Google Scholar 

  20. X Lu, Y Chen, J Chen 1986. Dynamic substructures analysis using Lanczos vectors. In: First world congress in computational mechanics, Austin, Texas

    Google Scholar 

  21. GH Sotiropoulos 1984. Comment on the substructure synthesis methods. J Sound Vib 98, 150–153

    Article  Google Scholar 

  22. AYT Leung 1988. A simple dynamic substructure method. Earthquake Engng Struct Dyn 16, 827–837

    Article  Google Scholar 

  23. AYT Leung 1988. Damped dynamic substructures. Int J Num Meth Engng 26, 2355–2365

    Article  MATH  Google Scholar 

  24. TK Hasselman 1976. Modal coupling in lightly damped structures. AIAA J 14, 1627–1628

    Article  Google Scholar 

  25. TK Hasselman 1976. Damping synthesis from substructures test. AIAA J 14, 1409–1418

    Article  Google Scholar 

  26. AL Hale 1984. Substructure synthesis and its iterative improvement for large non-conservative vibrator systems. AIAA J 22, 265–272

    Article  MATH  Google Scholar 

  27. AL Hale, LA Bergman 1985. The dynamic synthesis of general non-conservative structures from separately identified substructure models. J Sound Vib 98,431–446

    Article  MATH  Google Scholar 

  28. AYT Leung 1990. Non-conservative dynamic substructures. Dyn Stab Syst 5,45–47

    Article  Google Scholar 

  29. RR Craig 1977. Methods of component mode synthesis. Shock Vib Dig 9, 3–10

    Article  Google Scholar 

  30. L Meirovitch, AL Hale 1981. On the substructure synthesis method. AIAA J 19,940–947

    Article  Google Scholar 

  31. TH Richards, AYT Leung 1977. An accurate method in structural vibrating analysis. J Sound Vib 55, 363–376

    Article  MATH  Google Scholar 

  32. WH Wittrick, FW Williams 1971. A general algorithm for computing natural frequencies of elastic structures. Q J Mech Appl Math 24, 263–284

    Article  MATH  MathSciNet  Google Scholar 

  33. G Peters, JH Wilkinson 1971. Ax = λBx and the general eigenvalue problems. SIAM J Num Anal 7, 479

    Article  MathSciNet  Google Scholar 

  34. KJ Bathe, EL Wilson 1972. Large eigenvalue problems in dynamic analysis. ASCE Proc. Paper 9433

    Google Scholar 

  35. T Hopper, FW Williams 1977. Mode finding in nonlinear eigenvalue calculations. J Struct Mech 5, 255–278

    Article  Google Scholar 

  36. AL Hale, L Meirovitch 1982. Procedure for improving substructures representation in dynamic synthesis. J Sound Vib 84, 269–287

    MATH  Google Scholar 

  37. WC Hurty 1960. Vibrations of structural systems by component mode synthesis. J Engng Mech Div ASCE 86 (EM4), 51–69

    Google Scholar 

  38. W Romberg 1955. Vereinfachte numerische integration. Der Kgl Norske Vid Selsk Forh 28, 30–36

    MATH  MathSciNet  Google Scholar 

  39. V. Kolousek 1973 Dynamics in engineering structures. Butterworth, London

    MATH  Google Scholar 

  40. AS Deif 1982. Advanced matrix theory for scientists and engineers. Abacus Press, London

    MATH  Google Scholar 

  41. AYT Leung 1979. Accelerated convergence of dynamic flexibility in series form. Engng Struct 1, 203–206

    Article  Google Scholar 

  42. AB Palazzolo, BP Wang, WD Pilkey 1982. A receptance formula for general second degrees square lambda matrices. Int J Num Meth Engng 18, 829–843

    Article  MATH  MathSciNet  Google Scholar 

  43. AYT Leung 1987. Inverse iteration for damped natural vibration. J Sound Vib 118,193–198

    Article  Google Scholar 

  44. T Wah, LR Calcote 1970. Structural analysis by finite difference calculus. Van Nostrand Reinhold, New York

    MATH  Google Scholar 

  45. JP Ellington, H McCallion 1959. The free vibrations of grillages. Am Soc Mech Engrs J Appl Mech 26, 603–607

    MATH  MathSciNet  Google Scholar 

  46. C Sundararajan, DV Reddy 1975. Finite strip-difference calculus technique for plate vibration problems. Int J Solids Struct 11,425–435

    Article  MATH  Google Scholar 

  47. PH Denke, GR Eide, J Pickard 1975. Matrix difference equations analysis of vibrating periodic structures. Am Inst Aeronaut Astronaut J 13,160–166

    Google Scholar 

  48. YK Lin, TJ McDaniel 1969. Dynamics of beam-type periodic structures. Am Soc Mech Engrs, J Engng Indust 91, 1133–1141

    Google Scholar 

  49. L Meirovitch, RC Engels 1977. Response of periodic structures by Z transform method. Am Inst Aeronaut Astronaut J 15,167–174

    MATH  MathSciNet  Google Scholar 

  50. RC Engels, L Meirovitch 1978. Response of periodic structures by modal analysis. J Sound Vib 56, 481–493

    Article  MATH  Google Scholar 

  51. DJ Mead 1973. A general theory of harmonic wave propagation in linear periodic systems with multiple coupling. J Sound Vib 27, 235–260

    Article  MATH  Google Scholar 

  52. JE Walz, RE Fulton, NJ Cyrus, RT Eppink 1970. Accuracy of finite element approximations to structural problems. NASA TN D-5728

    Google Scholar 

  53. A A Liepins 1978. Rod and beam finite element matrices and their accuracy. Am Inst Aeronaut Astronaut J 16, 531–534

    MATH  Google Scholar 

  54. RH MacNeal 1972. The NASTRAN theoretical manual. NASA SP-221 (01)

    Google Scholar 

  55. JS Przemieniecki 1968. Theory of matrix structural analysis. McGraw-Hill. New York

    MATH  Google Scholar 

  56. J Casti, R Kalaba 1973. Imbedding methods in applied mathematics. Addison-Wesley, Palo Alto, CA

    MATH  Google Scholar 

  57. A Simpson 1974. Scanning Kron’s determinant. Q J Mech Appl Math 27, 27–43

    Article  MATH  MathSciNet  Google Scholar 

  58. YT Leung 1980. Accelerated converging methods in structural response analysis. Presented at the conference on advanced structural dynamics, University of Southampton

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Structural Engineering, University of Hong Kong, Pokfulam Road, Hong Kong, China

    Andrew Y. T. Leung MSc, PhD, CEng, FRAeS

Authors
  1. Andrew Y. T. Leung MSc, PhD, CEng, FRAeS
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag London Limited

About this chapter

Cite this chapter

Leung, A.Y.T. (1993). Dynamic Substructures. In: Dynamic Stiffness and Substructures. Springer, London. https://doi.org/10.1007/978-1-4471-2026-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-2026-1_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2028-5

  • Online ISBN: 978-1-4471-2026-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation