There exist many frame structural systems having some attachments reducible to damped spring-mass systems, concentracted masses and spring supports. For free and forced vibration analyses of such a system an analytical method based on the receptance method is presented. A framed structure having attachments is considered as a combined system composed of various Timoshenko beam and bar elements and the attachments. So, the vibration characteristics of the system are calculated by synthesizing receptances and Support Displacement Transfer Ratio (SDTR) of beam and bar elements In spectral and/or closed forms, and receptances of the attachments. In forced vibration analysis, arbitrary excitation forces at a point on the structure and displacement excitations at boundaries are considered. Numerical investigations are carried out for verification of the presented method, and the results show good accuracy and very high computational efficiency.