Vibrations and impedances of rectangular plates with free boundaries

Bibliographic Information

Vibrations and impedances of rectangular plates with free boundaries

P. Hagedorn, K. Kelkel, J. Wallaschek

(Lecture notes in engineering, 23)

Springer-Verlag, 1986

  • : us
  • : gw

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Note

Bibliography: p. [147]-152

Description and Table of Contents

Table of Contents

1. Introduction.- 1.1 Substructure techniques in the dynamics of large flexible structures.- 1.2 Remarks on the mechanical impedance and on the dynamic stiffness of elastic systems.- 2. General considerations on the mechanical impedance and on the dynamic stiffness of plates.- 2.1 The classical plate theory.- 2.2 Plate impedances and the reduced multipoint impedance matrix.- 2.3 Singularities in Kirchhoff plates.- 2.4 Literature survey on plate vibrations.- 3. Dynamic stiffness of rectangular plates.- 3.1 Symmetric and antisymmetric vibrations.- 3.1.1 Double symmetric vibrations Wss.- 3.1.2 Symmetric-antisymmetric vibrations Wsa.- 3.1.3 Double antisymmetric vibrations Waa.- 3.2 The method of superposition.- 3.2.1 LEVY-type solutions.- 3.2.2 Determination of the beam functions.- 3.2.3 Superposition of building blocks.- 3.2.3.1 First approach: load developed along the x-axis.- 3.2.3.2 Second approach: load expanded in a double FOURIER series.- 3.3 Plate connected at center.- 3.3.1 Analytical solution.- 3.3.2 Numerical Tests.- 3.3.2.1 Comparison with known results for the free vibrations.- 3.3.2.2 Comparison with the rigid plate.- 3.3.2.3 Comparison with the beam.- 3.3.2.4 Irregularities of the distribution of zeroes and poles for the square plate connected at center.- 3.4 Plate connected at a point on a line of symmetry.- 3.4.1 Analytical solution.- 3.4.1.1 Double symmetric vibrations.- 3.4.1.2 Symmetric-antisymmetric vibrations.- 3.4.2 Numerical Tests.- 3.5 Plate connected at an arbitrary point.- 3.5.1 Analytical solution.- 3.5.1.1 Double symmetric vibrations.- 3.5.1.2 Symmetric-antisymmetric vibrations.- 3.5.1.3 Double antisymmetric vibrations.- 3.5.2 Numerical tests 121 3.5.2.1 Test for convergence.- 3.6 On the reduced multipoint stiffness and impedance matrices.- 3.7 Comparison with experiments.- 3.8 Conclusions.- 4. Final remarks.- 5. Literature.

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