The deviation between the natural frequencies
obtained using FEM (simulated) and the experimental method was determined using Equation 2:
For Euler-Bernoulli beam theory, the natural frequencies
can be expressed as:
Figure 1 shows the simulated acceleration res-ponses of a moving sensor at a constant velocity of v=3 m/s when the structure is excited with a sinusoidal load with a frequency equal to the 1st and 5th natural frequencies
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.
In the computation of vibration, the natural frequencies
are highly depend on mass distribution, and following masses must be taken into account:
While it is difficult to obtain the natural frequencies
at the higher mode due to the sampling rate of smartphone camera, the frequency components including the natural frequency of the first mode were estimated accurately at the lower vibration mode.
The experimental natural frequencies
of different vibration modes are listed in Table 2 for comparison.
As can be observed, as the COP frequencies increase, the natural frequencies
increase as well.
Powerful mathematical tool MATLAB has been utilized to extract natural frequencies
and mode shapes of the cylindrical shell for certain material as well as physical parameters.
The natural frequencies
of the model were carried out using [HBI.
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 methodbased on natural frequencies
only needs two vibration sensors (or even one acceleration sensor) to obtain the modal frequencies.