b) Modal frequency
, using the matrix iterative method, which according to Rao (2009) determines various natural frequencies of vibration, starting from the lowest one, associating to each frequency the results of total displacement/deformation.
The vibration mode of unstable modal frequency
at 12,752.6 Hz is extracted from the results of complex modal analysis, as shown in Figure 13.
Table 5 shows the modal frequency
of the first two orders of the unit.
A damping ratio of 3% was chosen because of its strong agreement with the experimental results of the modal frequency
of the cables.
where E, [eta], [rho], I, and H are the elastic modulus, loss factor, density, length, and thickness of the beam, respectively, and [f.sub.n] and [DELTA][f.sub.n] denote the nth modal frequency
and half-power bandwidth, respectively and [C.sub.n] is a coefficient for mode n.
Miyamoto  studied the performance of unbonded pre-stressed concrete beams, provided the formula of beam modal frequency
in the case of a given pre-stress value and used the results of experiments and tests for correction.
Accordingly, the first significant modal frequency
is that of mode 7, in a set of 74 modes whose frequencies range from nearly 60 Hz up to approximately 1.2 kHz, as indicated in Table 1.
[w.sub.dk] and [w.sub.k] are undamped modal frequency
and damping modal frequencies of k order.
Previous researches have mainly optimized aircraft structures from the perspectives of both static and dynamic constraints such as stress, displacement, modal frequency
, and flutter constraints; see, for example, the previous publications by Sikes et al.
Yen, "A story damage index of seismically-excited buildings based on modal frequency
and mode shape," Engineering Structures, vol.