The paper addresses the power flow suppression in an elastic beam of the tubular cross section (a pipe) at relatively low excitation frequencies by deploying a small number of equally spaced inertial attachments. The methodology of boundary integral equations is used to obtain an exact solution of the problem in vibrations of this structure. The power flow analysis in a pipe with and without equally spaced eccentric inertial attachments is performed and the effect of suppression of the energy transmission is demonstrated theoretically. These results are put in the context of predictions from the classical Floquet theory for an infinitely long periodic structure. Parametric studies are performed to explore sensitivities of this effect to variations in the number of attachments. The theoretically predicted eigenfrequencies and insertion loss are compared with the dedicated experimental data.