ASYMPTOTIC SOLUTION OF THE FIRST 3D DYNAMIC ELASTICITY THEORY PROBLEM ON FORCED VIBRATIONS OF A THREE-LAYER PLATE WITH AN ASYMMETRIC STRUCTURE

摘要

The first 3D dynamic problem on forced vibrations of an orthotropic three-layer plate with an asymmetric structure is solved asymptotically. On faces of the package, conditions of the first boundary-value problem of elasticity theory, i.e., the values of corresponding components of the stress tensor, are set. It is assumed that they vary harmonically in time. An asymptotic solution of the internal (external) problem is found. Conditions for the origination of resonance are established. The cases where the solution of the internal problem becomes mathematically exact are indicated, and an illustrative example is given. The question about the conjugation of solutions of the inner and boundary-layer problems is discussed.