Motion equations were formulated respectively for a simply-supported beam and TMD

and they have been transformed into modal equations in terms of the generalized coordinates with the mode superposition method.Moreover

the state equation of the beam has been derived on the basis of modern control theory and state-space method

and its dynamic simulation has been implemented with the SIMULINK system.First

a simulation was carried out with the SIMULINK for the beam without TMD

its result was compared with the equivalent one obtained with the Newmark-β method

and their closeness had shown the correctness of the dynamic simulation with the SIMULINK method.Upon the validation of the SIMULINK method

the beam with TMD was simulated with the SIMULINK method to show how the parameters of TMD affect the beam vibration in terms of structural dynamics so that the parameters’ ratios can be optimized in this paper and can be referred to in future practice.