Nonlinear Vibration Problem of Launch Vehicle Carrying a Moving Time-Dependent Mass

Abstract

In the present study, an analytical solution for nonlinear vibration problem of launch vehicle as a flexible beam model carrying moving with constant velocity mass which is time function is proposed. The nonlinear third and fifth order terms of partial differential equation with variable in time coefficients correspond to high amplitude and mid-plane stretching beam and the right term of initial equation of the problem represents the concentrated time-dependent moving mass effect. A hybrid asymptotic approach applied for an approximate analytical solution problem at given boundary and initial conditions an given. The resulting (approximate) solution has a form of a sum where each term consists of the product of two functions according to perturbation (on parameter at nonlinear terms) and phase-integral-Galerkin technique (on singular parameter at higher derivative) methods. The results of comparison of an approximate analytical solution and direct numerical integration of initial equation have shown a good enough accuracy as for “small” as well for “large ” scalar parameters for asymptotic expansion of the desired function.