Dynamic problem for a thin-walled bar with a monosymmetric profile

The paper presents an analytical solution to the dynamic problem for a thin-walled elastic rod, the cross-section of which has one axis of symmetry. The solution is constructed for an arbitrary dynamic load and two types of boundary conditions: hinged support in constrained torsion and free warping of the end sections of the rod; rigid fastening with constrained torsion and absence of warping. The peculiarity of the mathematical model lies in the fact that the differential equations of motion contain a complete system of inertial terms. Spectral expansions obtained as a result of using the method of integral transformations are represented as an effective method for solving linear non-stationary problems in mechanics. The structural algorithm of the method of finite multicomponent integral transformations proposed by Yu.E. Senitsky is used.