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.


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


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