Impact response of an unrestrained modified Timoshenko beam

In this paper, the modified motion equation of Timoshenkobeam is first introduced, which is then compared with that ofTimoshenko beam. The orthogonality conditions of the modifiedTimoshenko beam, where the rotary inertia caused by the shear deformation isconsidered, are derived. The impact response formulas of an unrestrainedmodified Timoshenko beam under the impact of a lumped mass are deduced, andthe corresponding numerical examples are analyzed. The evaluationresults are compared with the impact response of the classical unrestrainedTimoshenko beam with the same lumped mass. Finally, the effects ofthe beam stiffness and impact mass ratio on the response are discussed.