General relations for waves in one-dimensional elastic systems

Wave resistance to the movement of objects along the rocket track guides

“…(which guarantees the absence of any other sources, including at infinity). Here 0 = � ⁄ -the speed of wave propagation in a string without taking into account the basement, * -the lowest frequency of oscillation of a string, due to the presence of an elastic basement, 0 = � 0 ⁄ , ω 0 = � 0 ⁄ -partial frequencies of oscillations of the object, determined without taking into account the influence of the string, = , ⁄ string density, Ω -forcing frequency, 0 = 01 ⁄ , 0 = 02 ⁄ , 01 , 02 -the amplitudes of the forcing forces applied to the lower and upper masses, respectively, -phase shift, ℎ ⁄ -energy transfer rate [4], ℎ -energy density, -energy flux density. The square brackets denote the difference between the limiting values, the quantities in them, to the right and left of the contact point.…”

“…Substituting (5) into (4), and averaging over the oscillation frequency of the object, we obtain the expression for the constant component of the wave resistance force…”