The elastic moduli were determined using an algorithm (Figure 2) that compared the experimentally determined natural frequencies
with those using the finite element method (FEM).
(25) in the constitutive relations of different nonlocal beam theories and solving the resulting eigenvalue problem, the natural frequencies
of nanobeams embedded in an elastic medium can be obtained.
Assuming !=60m, E=25GPa, I=6.75[m.sup.4] [m.sub.1] = 150 kNp/in, [[zeta].sub.n] =0.05, the 1st and 5th natural frequencies
of the structure are 1.45 and 36.24 Hz, respectively.
It is recommended to validate the modal behavior of the FE model by comparing the analytical natural frequencies
and mode shapes with those measured experimentally.
Table 1: The first five natural frequencies
of the cantilever beam considering the bending moment.
Then, by solving characteristic equation (24), the natural frequencies
and characteristic vectors can be obtained.
As can be observed, there are a couple of trends in the MWD parameters of the HMW portion with the natural frequencies
of the bubble for the different resins: it is observed that the higher the [M.sub.w] and [M.sub.z] for the HMWD portion, the lower the natural frequency, with the exception of HDPE-8, and consequently the lower the stability index.
2013) calculated natural frequencies
of three-layered functionally graded cylindrical shells with middle layer consisting of isotropic material resting on Winkler and Pasternak elastic foundations.
To calculate the sensitivity of the natural frequencies
of local defects were considered damage to homogeneous reduction of all the stiffness at point without changing in mass of the structure.
In order to build the model, a finite element mesh of the bridge is used; and through a series of computer simulations by setting different conditions of the bridge, large numbers of natural frequencies
A damage detection problem using changes in natural frequencies
and/or mode shapes is basically an inverse problem, where one objective function, defined in terms of discrepancies between the vibration data identified by modal testing and those computed from analytical model, is minimized or maximized.
Zhao and DeWolf  presented a sensitivity study comparing the use of natural frequencies
, mode shapes, and modal flexibilities for monitoring.