Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

rotation

Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum

The paper contains new results related to extension of the field theoretical approach and its formalism to non-linear coupled micropolar thermoelastic media. A mathematical model of micropolar (MP) type-II (GNII) thermoelastic (TE) continuum is considered. A formulation of the least thermoelastic action principle is discussed. Partial differential equations subsequent to the least action principle are derived. The translational symmetries of non-linear Lagrangians are adopted. Those include an additional symmetry: translations of the thermal displacement.

Oscillations of shallow shells at abrupt influence of thermal flow

On the basis of the closed integrals of the initial and boundary problems for incoherent thermoelastisity of shallow shells the quantitative analysis of influence of the geometrical parameters on the oscillations of constant rotation and cylindrical shells, which are conditioned by the thermal shock to outbound surface of shallow shell are carried out.