To the study of the dynamics of layered structures with plane inclusions

Abstract

We consider the problem of vibration for a layered package with defects such as hard inclusions on interlayer interfaces. Using the factorization approach, we obtain recurrence relations for the construction of functional-matrix equation systems for problems of elastic vibrations of a multilayer structure with a finite number of planar defects. When studying the resonance properties of the structures under consideration, the obtained representations of matrix kernel symbols of the integral equation systems allow us to implement numerical algorithms and construct the root and polar sets of their elements and determinants for a wide range of problems. The approach presented in this work makes it possible to efficiently study vibrational regimes for multilayer structures taking into account non-ideal interlayer contact. The developed scheme can also be applied to the case of an arbitrary number and alternation of parallel cracks and inclusions. Theoretical results can find applications in engineering practice when studying the strength properties of designed materials, when assessing the operational characteristics of composite structural elements, etc.