Variations in steepness of the probability density function of beam random vibration (Q1568350)

The authors consider nonlinear random vibrations of a clamped-clamped beam. The large deflections of the beam are simulated taking into account the axial stretching forces. The governing partial differential equation is derived using the Euler-Bernoulli theory and neglecting rotary inertia and shear deformation when curvature in bending is small. By applying Galerkin method, ignoring in-plane effects, and expanding the flexural deflection in eigenfunction series, the authors reduce the corresponding initial-boundary value problem to a set of nonlinear ordinary differential equations. The differential equations are solved by Runge-Kutta method. As an application, the authors study different random vibrations by applying a random non-Gaussian concentrated force at the middle point of the beam.