The present work investigates dynamic response of a class of linear oscillators. The common characteristic of the systems analyzed is that they possess damping properties close to those resulting in classical normal modes. Regular perturbation expansions are utilized for analyzing the eigenproblem as well as the vibration response of such systems. The analysis is based on a proper splitting of the damping matrix. The advantage of this approach is that it sets the stage for application of standard modal analysis methodologies, reducing the main mathematical problem to that of finding the frequencies and mode shapes of the corresponding undamped model. The validity and effectiveness of the present analysis is illustrated and verified by a numerical example.
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