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A justification of the method of junction of asymptotic expansions applied to a vibrating plate problem. Estimate of the impedance matrix. (Une justification de la méthode de raccordement des développements asymptotiques appliquée à un problème de plaque en flexion. Estimation de la matrice d’impédance.) (French) Zbl 0877.35125

The authors consider the problem of a thin plate, area \(\Omega\), with a small inclusion, area \(\varepsilon\Omega\), with a given motion. An approximate solution for the problem is given using inner and outer expansions, and the impedance matrix, relating a rigid motion of the inclusion to the force system acting on the plate is obtained in terms of \(\text{log }\varepsilon\). The treatment is highly theoretical involving a variety of abstract spaces, and there is no indication of how the ideas developed in the paper may be applied to any actual problem.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
74K20 Plates
65J10 Numerical solutions to equations with linear operators
74H45 Vibrations in dynamical problems in solid mechanics
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