Civil Engineering Reference
In-Depth Information
Fig. 15.9
Natural frequency
affected by bolt preload at
Joint II
Mode 1
Mode 2
12
32
11.5
31
11
30
1
1.5
2
2.5
1
1.5
2
2.5
Bolt Preload/Nm
Bolt Preload/Nm
Mode 3
Mode 4
59
115
58
114.5
57
114
1
1.5
2
2.5
1
1.5
2
2.5
Bolt Preload/Nm
Bolt Preload/Nm
Mode 5
Mode 6
164
224
162
222
160
220
1
1.5
2
2.5
1
1.5
2
2.5
Bolt Preload/Nm
Bolt Preload/Nm
15.3.4.3 Group C
For Group C shown in Table
15.1
, the value of bolt preload at Joint I and III keep constant in each modal test, that is, 1.0, 1.5,
2.0 and 2.5 Nm, respectively; while the bolts at Joint II have the changing preload from 1.0 to 2.5 Nm. The effects of the bolt
preload at Joint II on the modal parameters are studied. Figure
15.9
depicts the natural frequencies of the first six modes for
this beam-like structure affected by bolt preload at Joint II.
As shown in Fig.
15.9
, the vertical axis is the value of the natural frequencies, and the horizontal axis is the value of bolt
preload at Joint I and III, The four lines in each figure represent the natural frequencies of the structure under different bolt
preloads at Joint II, such as, 1.0, 1.5, 2.0 and 2.5 Nm. For the even modes shown in Fig.
15.9
, it is obvious that the increment
of the bolt preload at Joint II cannot increase the natural frequencies of these even modes, because Joint II locates on the
midpoint of the structure, which is the nodal point of even modes for symmetrical structures. It can be also found that the
increment of the bolt preload at Joint I and III can increase the natural frequencies of even modes. For the odd modes shown
in Fig.
15.9
, the larger bolt preload at Joint II increases these natural frequencies of the structure. However, the increment of
the bolt preload at Joint I and III cannot increase the natural frequencies of the mode 1 and mode 5, because the locations of
Joint I and III are close to the nodal points of mode 1 and mode 5.
Above results indicate that the bolt preload determines the stiffness of the bolted connection, which influences the modal
parameters of the structure. It also validates the conclusions obtained from the numerical analysis in Sect.
15.2
, i.e. the larger
stiffness leads to larger natural frequencies. Furthermore, any changes at the nodal points of specific mode shape have little
influence on the corresponding frequency. These conclusions can be extended to other structures and these characteristics
can be utilized to obtain desirable modal parameters of the engineering structures during their design process.
15.4 Finite Element Model of Bolted Connection
Modal testing has been widely used to estimate the modal parameters of the test structure, while the cost of modal testing is
much more than the numerical analysis, such as finite element analysis (FEA). Besides, it is impracticable to conduct the
modal testing for some engineering structures during their practical applications. Therefore, it is necessary to setup the finite
element model (FEM) of the bolted connection, and the finite element analysis will be helpful to better understand the
characteristics of the bolted connection.
