In industrial applications, such as pump and compressor systems, pipe vibrations can exceed an acceptable level. Periodically spaced masses added to the piping are an appropriate method of attenuation, and investigations to develop valid prediction models and measurement techniques has been initiated in the Danish Makunet network. The present investigation concern the effect of three masses attached periodically to a pipe of small diameter. The pipe is small enough that it can be treated as a beam. The masses are eccentric to the center of the beam, to achieve a large change in the moment of inertia by the added elements. The theoretical model is formulated as a system of boundary equations, which describe propagation of flexural, axial and torsion waves within each segment of a tube between periodic elements. An exact solution of this system is obtained and the power transfer is dramatically reduced in some frequency 'stop bands' regardless the excitation conditions. Transfer impedance measurements between the force input and the acceleration on selected positions are used to find the insertion loss due to the application of the periodic elements, showing good agreement with theory.