No abstract

The problems of Timoshenko beams and plates lateral vibrations under the influence of unsteady loads are considered. Both beam and plate is supposed to be unlimited. In case of the plate the problem has been simply studied. The approach to the solution was based on dominant function method and principle of superposition. Integral models of solutions with cores as dominant functions were built which could be analytically found with the help of the Fourier and Laplace integral transforms. Two original analytical methods for Fourier and Laplace transforms were offered and realized. The examples of calculations were given.

Non-stationary inverse problems of deformed solid mechanics are among the most underexplored due to, inter alia, increasing dimension of non-stationary problems per unit as compared with stationary and static problems, as well as necessity to consider the initial conditions. In the context of the continuing progress of the aviation and aerospace industries, the question arises about technical condition monitoring of aircraft for the purposes of their safe operation. A large proportion of an aircraft structure consists of beam and rod elements exposed to various man-made and natural effects which cause defects inaccessible for visual inspection and required to be identified well in advance. It is well known that defects (such as cracks, cavities, rigid and elastic inclusions) are concentrators of stresses and largely cause processes, which lead to the destruction of elastic bodies. Therefore, the problem of identification of such defects and their parameters, i.e. the problem of identification, represents a great practical interest. Mathematically, the problem of identification represents a non-linear inverse problem. The development of methods of solving such problems is currently a live fundamental research issue.

Carbon-carbon composite materials (CCCM) are characterized by high heat resistance and thermostability for which they, in most of their physical and mechanical characteristics, can be attributed to the most promising materials. Approximately 81% of all carbon-carbon composite materials are used for the manufacture of brake rotors for aircraft, 18% – in space rocket technology, and only 1% – for all other areas of application. This study discusses calculations of the strength, rigidity, and stability of a frame made of carbon-carbon composite materials. It is known that the strength of CCCM based on high-strength carbon fibers is higher than the strength of a composite material based on high-modulus carbon fibers obtained at various processing temperatures. The stress-strain behaviour (SSB) of the material is carried out. Among the special properties of CCCM are low porosity, low coefficient of thermal expansion, maintaining a stable structure and properties, as well as product dimensions.