Dynamic analysis of composite rods with variable cross-section

A general approach to the direct dynamic problem of calculation of the stress-strain state in composite rods is developed. These rods are elements of the system of plane arbitrary composite rods tested for a variety of materials and dynamic loading modes. The proposed computational model takes into account average shear deformations and visco-elastic medium interactions. Being the elements of rod systems such heterogeneous rods are characterized by high strength and rigidity ratios and, at the same time, by lower production cost in comparison with homogeneous rods. The equations of motion and physical relations include several functional characteristics, namely 4ch of rigidity, 4ch of viscosity, 3ch of mass, in order to represent correctly the dynamic deformation of heterogeneous elements in terms of one-dimensional model. Dynamic loads and displacement are products of separate functions of space and time. The time function is represented as a trigonometric Fourier series. Solution to the homogeneous problem is obtained using a matrizant for first-order equations. For different loading modes, partial solutions are found using an approximation of these loads and desired displacements as trigonometrical series. Generally, momentary explosive, blasting and harmonic loads are investigated. Special cases of the design scheme of rods along with simplification of basic relations are described, and the results obtained under the assumption that a number of terms in physical and motion equations are ignored are given. The example problem of metal-brick smoke-stack unsteady oscillations is solved. The smoke-stack was exposed to the dynamic wind load. It is shown that the unsteady dynamic motion parameters have a significant effect on the strength and rigidity of the structure, as well as on the functional dynamic factors.