Forced response of a viscoelastically damped rod using the superposition of modal contribution functions

In this communication the axial vibration problem of a uniform elastic rod with a viscoelastic end damper is studied. The analysis is carried out in the frequency domain, the properties of the damper being characterised by a complex stiffness, and the viscoelastic damping being represented by an exponential model. First, an analytical solution for frequency response functions is obtained using a direct method. Next the computation of the system response is proposed, by means of the modal contribution functions (MCF) superposition method. This method allows evaluating the individual participation of the eigenmodes in the total response (even if the system is not self-adjoint and thus the classical modal superposition cannot be applied), providing important information for practical engineering applications that is lost otherwise. Finally, a numerical example is presented, in which the response provided by both, direct and MCF methods, is compared aimed at validating the latter.