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The frequency-response curve is an important information for the structural design, but the conventional time-history method for obtaining the frequency-response curve of a multi-degree-of-freedom (MDOF) system is time-consuming. Thus, this paper presents an efficient technique to determine the forced vibration response amplitudes of a multi-span beam carrying arbitrary concentrated elements. To this end, the "steady" response amplitudes|   Y   (  x  )    |    s    of the above-mentioned MDOF system due to harmonic excitations (with the specified frequencies    w  e    ) are determined by using the numerical assembly method (NAM). Next, the corresponding "total" response amplitudes|   Y   (  x  )    |    t    of the same vibrating system are calculated by using a relationship between|   Y   (  x  )    |    t    and|   Y   (  x  )    |    s    obtained from the single-degree-of-freedom (SDOF) vibrating system. It is noted that, near resonance (i.e.,    w  e   /  w≈  1.0), the entire MDOF system (with natural frequency  w  ) will vibrate synchronously in a certain mode and can be modeled by a SDOF system. Finally, the conventional finite element method (FEM) incorporated with the Newmark's direct integration method is also used to determine the "total" response amplitudes|   Y   (  x  )    |    t    of the same forced vibrating system from the time histories of dynamic responses at each specified exciting frequency    w  e    . It has been found that the numerical results of the presented approach are in good agreement with those of FEM, this confirms the reliability of the presented theory. Because the CPU time required by the presented approach is less than 1% of that required by the conventional FEM, the presented approach should be an efficient technique for the title problem.

An Efficient Approach for Determining Forced Vibration Response Amplitudes of a MDOF System with Various Attachments