Advertisement

Modeling and Parameter Estimation for an Imperfectly Clamped Plate

  • H. T. Banks
  • R. C. Smith
  • Yun Wang
Part of the Progress in Systems and Control Theory book series (PSCT, volume 20)

Abstract

An important consideration in the modeling of structural and structural acoustic systems involves the determination of appropriate boundary conditions for the vibrating structure. In many applications, the clamped nature of the structure leads to the use of clamped or fixed boundary conditions, in which case, it is assumed that zero displacements and slopes are maintained at the boundaries. For example, this can be an appropriate assumption when using shell equations to model a fuselage, plate equations to model panels in a transformer or beam equations to model a helicopter blade. In the first case, the experimental shell structures are often supported by heavy clamps at the ends, thus leading to the use of fixed boundary conditions. In a similar manner, the bonding of panels to an underlying substructure or the attachment of the blades to a central hub lead to models which involve fixed boundary conditions.

Keywords

Circular Plate Analytic Semigroup Plate Equation Clamp Boundary Condition Fixed Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H.T. BANKS and K. ITO, “A Unified Framework for Approximation in Inverse Problems for Distributed Parameter Systems,” Control Theory and Advanced Technology v. 4, no. 1, 1988, pp. 73 – 90.MathSciNetGoogle Scholar
  2. [2]
    H.T. BANKS and K. ITO, “Approximation in LQR Problems for Infinite Dimensional Systems with Unbounded Input Operators,” submitted to Journal of Mathematical Systems, Estimation and ControlGoogle Scholar
  3. [3]
    H.T. BANKS, K. ITO and Y. WANG, “Well-Posedness for Damped Second Order Systems with Unbounded Input Operators,” Center for Research in Scientific Computation Technical Report, CRSC-TR93–10, North Carolina State University, to appear in Differential and Integral Equations, March 1995.Google Scholar
  4. [4]
    H.T. BANKS and D.A. REBNORD, “Analytic Semigroups: Applications to Inverse Problems for Flexible Structures,”Differential Equations with Applications, (ed. by J. Goldstein, et. al. ), Marcel Dekker, 1991, pp. 21–35.Google Scholar
  5. [5]
    H.T. BANKS and R.C. SMITH, “The Modeling and Approximation of a Structural Acoustics Problem in a Hard-Walled Cylindrical Domain,” Center for Research in Scientific Computation Technical Report, CRSC-TR94–22.Google Scholar
  6. [6]
    H.T. BANKS and R.C. SMITH, “Well-Posedness of a Model for Structural Acoustic Coupling in a Cavity Enclosed by a Thin Cylindrical Shell,” ICASE Report 93–10, to appear in Journal of Mathematical Analysis and Applications.Google Scholar
  7. [7]
    H.T. BANKS, R.C. SMITH and Y. WANG, “Modeling Aspects for Piezoceramic Patch Activation of Shells, Plates and Beams,” Center for Research in Scientific Computation Technical Report, CRSC-TR92–12, N. C. State Univ., to appear in Quarterly of Applied Mathematics.Google Scholar
  8. [8]
    H.T. BANKS, Y. WANG, D.J. INMAN and J.C. SLATER, “Approximation and Parameter Identification for Damped Second Order Systems with Unbounded Input Operators,” Center for Research in Scientific Computation Technical Report, CRSC-TR93–9, North Carolina State University, to appear in Control: Theory and Advanced Technology.Google Scholar
  9. [9]
    A. HARAUX, “Linear Semigroups in Banach Spaces,” in Semigroups, Theory and Applications, II (H. Brezis, et al., eds.), Pitman Res. Notes in Math, Vol 152, Longman, London, 1986, pp. 93 – 135.Google Scholar
  10. [10]
    E.H. MANSFIELD, The Bending and Stretching of Plates, Volume 6 in the International Series of Monographs on Aeronautics and Astronautics, The MacMillan Company, New York, 1964.Google Scholar
  11. [11]
    J. ROBINSON, Acoustics Division, NASA Langley Research Center, personal communications.Google Scholar
  12. [12]
    R.C. SMITH, “A Galerkin Method for Linear PDE Systems in Circular Geometries with Structural Acoustic Applications,” ICASE Report No. 94–40, submitted to SIAM Journal on Scientific Computing.Google Scholar
  13. [13]
    W. SOEDEL, Vibrations of Shells and Plates, Second Edition, Marcel Dekker, Inc., New York, 1993.MATHGoogle Scholar
  14. [14]
    S. TIMOSHENKO, Theory of Plates and Shells, McGraw-Hill, NY, 1940.MATHGoogle Scholar

Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  • H. T. Banks
    • 1
  • R. C. Smith
    • 2
  • Yun Wang
    • 3
  1. 1.Center for Research in Scientific ComputationNorth Carolina State UniversityRaleighUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA
  3. 3.Mathematical Products DivisionArmstrong LaboratoryBrooks AFBUSA

Personalised recommendations