WEEK 11

PREFACE TO WORK

Although the contact distances and materials can be estimated the results may not accurate after 80% of the antenna distance. (WEEK 8 TESTING THE RESONANCE POINT) . Rest of the distance (20%) might not be very useful in the real world application. But with the aim of analyzing the effect Vibration modal analysis was done for the antenna probe.

PROGRESS

The probe was numerically modeled using planer Euler-Bernoulli (E-B) beam elements. Euler-Bernoulli beam element has two nodes per element and each node has two degrees of freedom (DOF) which is shown in the Figure 32. These degrees of freedom are arranged as [ ] where the are the translational DOFs and are the rotational DOFs. By referring the 2D (two dimensional) global coordinates system, the stiffness matrix of the E-B beam element is given by the matrix K and the consistent mass matrix of the E-B beam element is given by matrix M .

The antenna probe used here was modeled with two E-B elements as shown in Figure 33. Since the antenna probe is in the horizontal plane, element local coordinate and global coordinate systems coincide, the rotational transformation matrix become the identity matrix. If the local and global coordinate systems aren’t coincided, K and M should be multiplied with a rotational transformation matrix. Since the antenna probe model has two E-B elements, in order to get the structure stiffness matrix K₁ and the structure mass matrix M₁, the K and M matrices of both elements should be assembled. The undamped free vibration modes of the antenna probe were given from “(2)”.Two frequencies of the vibration modes were obtained by the equation . By substituting those two values to “(2)”, the vibration mode shapes of the structure can be obtained from the Eigen vector of the .

The most flexible mode was the dominant mode and its frequency was considered as the dominant frequency of the structure. Vibration modes at each and every contact points could be obtained by changing the values of and . By taking as the 0.25 , 0.5, 0.75, 0.8 and 0.9 the system has been solved numerically. Then the mode shapes were obtained using the Eigen vectors of and most flexible mode shape was analyzed.

RESULTS

The dominant vibration modes were obtained from the numerical solution of the mathematical model. The shape of the dominant vibration mode changed, when contact point moved from hinge point to the tip. Therefore a change in the dominant vibration mode should be there.

When considering Figure 34, three zones can be identified in the frequency variation. Initially, it has a very slight variation with a less gradient. But when moving towards the antenna tip, the gradient of the linear variation has increased. As the contact object is very close to the hinge point, the beam element between the hinge point and the contact point has a high stiffness and the rest of the beam element has a cantilever action (see Figure 35 (a)). But the cantilever action becomes stiffer when the contact point moves towards the antenna tip as in Figure 35 (c). Therefore the antenna element between the contact point and hinge point becomes more flexible and again a slight variation can be observed but different compared with the initial variation as shown in the Figure 34 Zone 3. When the contact distance is in between the above two cases, a transition of the modes can be observed as in Figure 35 (b).. The vibration mode is changed in the range of Zone 2 (see Figure 34). So at the 80% of the total antenna length the mode of vibration was totally changed. This change in mode of vibration was the main reason for the deviation from the linear variation obtained in the signal processing algorithm.

The complete modal analysis with frequency and time variation will be done in the future to estimate the full distance of the antenna probe.

REFERENCE