Abstract:
Article represents the study of applied problems of mathematics, whose mathematical modeling leads
to boundary problems for equations in partial derivatives. Mathematical methods, applied to these
models, enable to obtain exact analytical results. Detailed result is represented for boundary
problem of oscillations of thin structures with boundary conditions in general terms. Application
of spectral decomposition for sufficiently smooth function, characterizing the membrane deviation
from equilibrium state, enables to define exact analytic representation of inflection function for
studied problem. To calculate multilayer plates, method of finite elements is applied.
