The feature of the special topics is that the design diagram of the structure differs from the corresponding design diagram used in the classical course of structural mechanics. Introduction of additional assumptions that do not contradict the assumptions of the classical theory of structures leads to a new mathematical model of the structure, and allows to not only clarify the results obtained in the framework of the classical theory, but also discover new effects and properties of the structure. The following topics are considered in this chapter: Timoshenko-Ehrenfest theory takes into account the rotary inertia and the shear deformation and allows investigating the vibration of short beams for which the classical assumption (the rods are long and thin) is not fulfilled. The theory of flexural vibration of compressed beam allows refining the idealized Bernoulli-Euler model. Galef’s formula, which establishes a simplest relationship between the frequency of transverse vibration of a beam, static compressive force, and critical buckling force, is presented. The theory of traveling load takes into account velocity of moving load, and inertial properties of the beam and the load. The feature of this problem is the loss of stability of the structure in case of critical velocity of a load. The parametric vibration of the rod occurs in case of its loading by the axial harmonic force. The feature of this problem: the initial linear dynamical structure (the uniform rod) turns out to have time-varying stiffness. As the result, on the plane of the “system–load” parameters, alternating zones of stable and unstable vibration appear. Vibration protection methods. Decreasing the level of mechanical vibration is one of the most important problems of modern engineering. The set of methods and means of reducing vibrations are reviewed. The theory of a dynamic absorber is considered in detail.
