Dynamics of Rod Structures
The course includes the nonlinear dynamic theory of spatially curved and naturally twisted thermoviscoelastic rods. This theory take into account the rotational inertia and all the basic types of deformation: bending, twisting, stretching, and transverse shear. The theory of rods includes all the known versions of rod theory, but it has a wider range of applicability. In particular, it describes the experimentally discovered Pointing’s effect, which consists in shortening of a rod under twisting deformations. The main peculiarity of the theory is that it can be used to model the dynamics of thin objects with complex internal structure. In particular, it can model multi-layer rods and rods with internal cavities, as well as rods with complex microstructure. In the course the use of the following methods is demonstrated: the general methods of the continuum mechanics with rotational degrees of freedom, the differential geometry, the direct tensor calculus, the generalized theory of symmetry, the dimension theory, methods for constructing exact solutions of differential equations, asymptotic methods for solving differential equations, and in particular, differential equations with a small parameter at the highest derivative.