In drilling and blasting, large-scale blasting, and single high-energy blasts, it is often necessary to protect engineering system and equipment from force pulses.In order to determine the dynamic reactions of structures extended along a single coordinate (high buildings, main pipelines, high-voltage llne supports, drilling equipment elements, etc.) to impact or blast loading, it is necessary to understand the nature of the propagation of nonstationary disturbances in an elastic cylindrical system (waveguide) with dispersion. The cause of dispersion is the presence of physical or geometrical nonunlformity in the system.In some cases the dispersion of waves is due to masses coupled in some way to the waveguide. These take parz in the vibration process, redistribute the energy of the wave, and change the shape of its front. Coupled masses, on average, have a shock-absorbent effect, though in certain cases the level of the disturbances at certain moments of time can be greater than those in the system without the masses ~i-3].Many authors dealing with nonstationary deformation of structural elements acted on by impulsive loads, as a rule, consider uniform models. In general, the analytical methods used by them cannot be extended to the investigation of differential equations with variable coefficients. Numerical methods also encounter difficulties --limitations on the machine storage, parasitic effects due to dlscretizatlon of space and time, especially in calculations on fronts and quasifronts, and difficulties in elucidating qualitative features in multiparameter problems.In this article we will investigate the waveguide properties of a cylindrical elastic system to which masses are coupled via inertla-free links. Wewill use a combined numerical--analytic method. On the assumption that the masses are distributed continuously or discretely periodically along the system, we determine the asymptotic behavior (t § ~ where t is the time) of disturbances over some (large) distance from the site of the action. Using the method of minimization of the numerical dispersion [4], we obtain numerical solutions over the whole time interval; we determine the range of applicability of the asymptotic estimates.i. Suppose that a stepwise load QH@(t) is applied to some section of the wavegulde, where Ho(t) is the Heaviside function. Along the waveguide, a damped medium with density m is continuously distributed. For definiteness, we will consider a rod with damped masses [i]. The motion of the system is represented by the equations Here Uo and u, are the displacements of sections of the rod and mass, H,(x) is Dirac's function, x is the axial coordinate, f = (K/m) */2 is the damping frequency, K is the stiffness o~ the coupling; the units of measurement are the velocity of sound in the rod, co = (E/p) */2, the length fco-*, and the Young's modulus.
