Abstract: 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 ω
_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., &omega_e/ω≈ 1.0), the entire
MDOF system (with natural frequency ω) 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 ω _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.
Keywords: Frequency-response curve, steady response amplitude, total response amplitude, numerical assembly method, finite element method
