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 are generated.
A damage detection methodbased on
natural frequencies only needs two vibration sensors (or even one acceleration sensor) to obtain the modal frequencies.
