Nonlinear beam-mass structures under combined deterministic and randon excitation

The response of a beam-mass structure under deterministic and random excitation is investigated. The deterministic excitation is due to a rotating appendage located at the tip-mass of the structure. The random excitation is introduced at the base of the structure. The equation of motion is obtained using Hamilton's extended principle and Galerkin's discretization procedure.

The investigation of the system response is carried out in three parts based on three forms of excitation, namely: pure deterministic, pure random, and combined deterministic and random excitations. The response of the system to pure deterministic excitation is studied by observing the system's time history, power spectrum, phase plane, and Poincare maps. For pure random and combined cases. the Gaussian and non-Gaussian closure schemes, in conjunction with stochastic averaging, are used to solve for the mean-square response.

The influence of the system parameters (e.g, beam length, tip-mass, and appendage rotation speed) on the response characteristics is studied. For pure deterministic excitation, periodic, subharmonic, and quasi-periodic motions are observed. For combined excitation, the deterministic component of the excitation was observed to manifest itself, as an oscillation, in the steady-state mean-square response. It is cdso shown that, for the pure random and combined excitations, the non-Gaussian solution yields higher steady-state mean-square responses than those obtained from the Gaussian solution. Relevant experimental responses are also presented.