Nonlinear vibration analysis of a beam subjected to a random axial force

In this paper, nonlinear vibration of an Euler–Bernoulli beam excited by a harmonic random axial force is studied. The equation of motion contains a term with time-varying coefficient which is solved by modified Lindstedt–Poincaré method. Then the effect of the random axial force on the response is investigated using the obtained approximate solution. Two cases are considered in random analysis, namely random amplitude and random phase of the axial force. For both cases, the ensemble average, mean square value and the autocorrelation function are obtained. The results have indicated that for each case the mean and the mean square value are a function of time which means that the lateral displacement of the beam is a nonstationary process. A numerical study is also conducted based on the iteration of numerical solution in order to verify the derived analytical formulae. It is shown that a good agreement is seen between the analytical and numerical solution statistical properties.