Vibrations and Impedances of Rectangular Plates with Free Boundaries

Contenu

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 LÉVY-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.