MODAL INTERACTIONS OF A RANDOMLY EXCITED HINGED–CLAMPED BEAM

An investigation into the response statistics of a hinged–clamped beam under broadband random excitation is made. By using Galerkinʹs method the governing equation is reduced to a system of non-autonomous non-linear ordinary differential equations. The Fokker– Planck equation is applied to generate a general first order differential equation in the dynamic moments of response co-ordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The analytical results for two- and three-mode interactions are also compared with results obtained by Monte Carlo simulation.