Stochastic vibration of axially loaded monosymmetric Timoshenko thin-walled beam

An analytical method is presented to perform the flexure–torsion coupled stochastic response analysis of monosymmetric axially loaded Timoshenko thin-walled beam subjected to various kinds of concentrated and distributed stochastic excitations with stationary and ergodic properties. The effects of warping stiffness, axial force, shear deformation and rotary inertia are included in the present formulations. First, the damped general governing differential equations of motion of axially loaded Timoshenko thin-walled beam are developed and the free vibration analysis is performed. Once the natural frequencies and mode shapes are obtained, mode superposition method in conjunction with receptance method is used to compute the mean square displacement response of the axially loaded thin-walled beam. Finally, the method is illustrated by its application to two test examples to investigate the effects of warping stiffness, axial force, shear deformation and rotary inertia on the stochastic response of the thin-walled beams.