Coupled bending and torsional beam vibrations excited by a moving load

For a simply supported Bernoulli-Euler beam under moving load with constant velocity the bending and torsion vibrations are analysed. An analytical solution of decoupled partial differential equations is derived based on eigenmode expansion considering boundary initial conditions. pure analysis performed calculated. various longitudinal speeds results plotted. The coupled deformations computed using modal transformation. decoupling yields two separated ordinary in time which closed form solutions. solutions plotted discussed. A comparison numerical calculation finite element model shows good agreement.